{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-10-23T00:19:30.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-10-23T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":2323,"title":"Pandigital number n°3 (Inspired by Project Euler 32)","description":"After Problem 2319 and 2320.\r\n\r\nAn n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE. For example, the 5-digit number 15234, is 1 through 5 pandigital.\r\n\r\nThe product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital ([391867254]).\r\n\r\nFind the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through n pandigital (n is given in input).\r\n\r\nHINT1: Some products can be obtained in more than one way so be sure to only include it once in your sum.\r\n\r\nHINT2: All in good time...  \r\n\r\n","description_html":"\u003cp\u003eAfter Problem 2319 and 2320.\u003c/p\u003e\u003cp\u003eAn n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE. For example, the 5-digit number 15234, is 1 through 5 pandigital.\u003c/p\u003e\u003cp\u003eThe product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital ([391867254]).\u003c/p\u003e\u003cp\u003eFind the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through n pandigital (n is given in input).\u003c/p\u003e\u003cp\u003eHINT1: Some products can be obtained in more than one way so be sure to only include it once in your sum.\u003c/p\u003e\u003cp\u003eHINT2: All in good time...\u003c/p\u003e","function_template":"function y = pandigital_sum(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 3;\r\ny_correct = [];\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n%%\r\nx = 4;\r\ny_correct = 12;\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n%%\r\nx = 5;\r\ny_correct = 52;\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n%%\r\nx = 6;\r\ny_correct = 162;\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n%%\r\nx = 7;\r\ny_correct = []; % Strange no ?\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n\r\n%%\r\nx = 8;\r\ny_correct = 13458;\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n\r\n\r\n%% You obtain the Project Euler n°32 solution with n=9\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":5390,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":48,"test_suite_updated_at":"2019-10-23T23:21:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-05-15T10:08:43.000Z","updated_at":"2026-10-15T13:54:29.000Z","published_at":"2014-05-15T10:20:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAfter Problem 2319 and 2320.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE. For example, the 5-digit number 15234, is 1 through 5 pandigital.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital ([391867254]).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through n pandigital (n is given in input).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHINT1: Some products can be obtained in more than one way so be sure to only include it once in your sum.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHINT2: All in good time...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":46066,"title":"Evaluate the logarithmic integral","description":"The \u003chttps://en.wikipedia.org/wiki/Logarithmic_integral_function logarithmic integral\u003e li(x) plays a role in number theory because the related function Li(x) = li(x) - li(2) provides an estimate for the number of primes less than x. MATLAB's Symbolic Toolbox has the function \u003chttps://www.mathworks.com/help/symbolic/sym.logint.html |logint|\u003e, but it is not available in basic MATLAB or Cody. \r\n\r\nWrite a function to evaluate the logarithmic integral.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 123px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 61.5px; transform-origin: 407px 61.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.0667px 7.91667px; transform-origin: 12.0667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Logarithmic_integral_function\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003elogarithmic integral\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"li(x)\" style=\"width: 30.5px; height: 19px;\" width=\"30.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 184px 7.91667px; transform-origin: 184px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e plays a role in number theory because the related function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Li(x) = li(x) - li(2)\" style=\"width: 126px; height: 19px;\" width=\"126\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.0667px 7.91667px; transform-origin: 40.0667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e provides an estimate for the number of primes less than x. MATLAB's Symbolic Toolbox has the function\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/symbolic/sym.logint.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003elogint\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75px 7.91667px; transform-origin: 75px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, but it is not available in basic MATLAB or Cody.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 158.967px 7.91667px; transform-origin: 158.967px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to evaluate the logarithmic integral.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.1833px 7.91667px; transform-origin: 29.1833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSee also \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46081-set-soldner-s-constant\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 46081 \"Set Soldner's constant\"\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logarithmicIntegral(x)\r\n  y = f(x);\r\nend","test_suite":"%%\r\nx = 0;\r\ny_correct = 0;\r\nassert(abs(logarithmicIntegral(x)-y_correct)\u003c1e-8)\r\n\r\n%%\r\nx = 0.2;\r\ny_correct = -0.085126486728794;\r\nassert(abs(logarithmicIntegral(x)-y_correct)\u003c1e-8)\r\n\r\n%%\r\nx = 0.5;\r\ny_correct = -0.378671043061088;\r\nassert(abs(logarithmicIntegral(x)-y_correct)\u003c1e-8)\r\n\r\n%%\r\nx = 1;\r\ny = logarithmicIntegral(x);\r\nassert(isinf(y) \u0026\u0026 sign(y) == -1)\r\n\r\n%%\r\nx = 2;\r\ny_correct = 1.045163780117493;\r\nassert(abs(logarithmicIntegral(x)-y_correct)\u003c1e-8)\r\n\r\n%%\r\nx = 5;\r\ny_correct = 3.634588310032652;\r\nassert(abs(logarithmicIntegral(x)-y_correct)\u003c1e-8)\r\n\r\n%%\r\nx = 8;\r\ny_correct = 5.253718299558931;\r\nassert(abs(logarithmicIntegral(x)-y_correct)\u003c1e-8)\r\n\r\n%%\r\nx = 3+2i;\r\ny_correct = 2.558790740400258 + 1.594445119241119i;\r\ny = logarithmicIntegral(x);\r\nassert(abs(real(y)-real(y_correct))\u003c1e-8 \u0026\u0026 abs(imag(y)-imag(y_correct))\u003c1e-8)\r\n\r\n%%\r\nx = 3-0.2i;\r\ny_correct = 2.169086896211800 - 0.181703645882027i;\r\ny = logarithmicIntegral(x);\r\nassert(abs(real(y)-real(y_correct))\u003c1e-8 \u0026\u0026 abs(imag(y)-imag(y_correct))\u003c1e-8)\r\n\r\n%%\r\nx = -0.3-2i;\r\ny_correct = 0.999726888286245 - 3.238096925989443i;\r\ny = logarithmicIntegral(x);\r\nassert(abs(real(y)-real(y_correct))\u003c1e-8 \u0026\u0026 abs(imag(y)-imag(y_correct))\u003c1e-8)\r\n\r\n%%\r\nx = -5-3i;\r\ny_correct = 0.500720609942772 - 5.020802115037742i;\r\ny = logarithmicIntegral(x);\r\nassert(abs(real(y)-real(y_correct))\u003c1e-8 \u0026\u0026 abs(imag(y)-imag(y_correct))\u003c1e-8)\r\n\r\n%%\r\nx = 0.3i;\r\ny_correct = 0.074754684076440 + 3.053886180297906i;\r\ny = logarithmicIntegral(x);\r\nassert(abs(real(y)-real(y_correct))\u003c1e-8 \u0026\u0026 abs(imag(y)-imag(y_correct))\u003c1e-8)\r\n \r\n%%\r\nx = 0.4-2i;\r\ny_correct = 1.171012435933119 - 2.861745062394908i;\r\ny = logarithmicIntegral(x);\r\nassert(abs(real(y)-real(y_correct))\u003c1e-8 \u0026\u0026 abs(imag(y)-imag(y_correct))\u003c1e-8)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-07-28T15:11:20.000Z","updated_at":"2026-10-01T13:27:39.000Z","published_at":"2020-07-29T01:46:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Logarithmic_integral_function\\\"\u003e\u003cw:r\u003e\u003cw:t\u003elogarithmic integral\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"li(x)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{\\\\rm li}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e plays a role in number theory because the related function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Li(x) = li(x) - li(2)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{\\\\rm Li}(x) = {\\\\rm li}(x) - {\\\\rm li}(2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e provides an estimate for the number of primes less than x. MATLAB's Symbolic Toolbox has the function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/symbolic/sym.logint.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elogint\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, but it is not available in basic MATLAB or Cody.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to evaluate the logarithmic integral.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee also \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46081-set-soldner-s-constant\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 46081 \\\"Set Soldner's constant\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44374,"title":"Tautology","description":"Check if the given expression is always true. For example, the sentence\r\n\r\n  '~(A \u0026 B) == (~A | ~B)'\r\n\r\nis always true.\r\n\r\nCharacters in the input sequences may include *~ \u0026 | == ( )*, whitespace, 0 for false, 1 for true and letters for variables.","description_html":"\u003cp\u003eCheck if the given expression is always true. For example, the sentence\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e'~(A \u0026 B) == (~A | ~B)'\r\n\u003c/pre\u003e\u003cp\u003eis always true.\u003c/p\u003e\u003cp\u003eCharacters in the input sequences may include \u003cb\u003e~ \u0026 | == ( )\u003c/b\u003e, whitespace, 0 for false, 1 for true and letters for variables.\u003c/p\u003e","function_template":"function y = tautology(x)\r\n  y = true;\r\nend","test_suite":"%%\r\nx = '0';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '1';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|1';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '1\u0026A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A\u0026B';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|~A';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '0==0';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~0';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~(A \u0026 B) == (~A | ~B)';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~(Z \u0026 Y) == (~Y | ~Z)';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|X|V|W|Y|Z';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B|C|D|E|F|G|H|I|J|K|L|M|~A|O|P|Q|R|S|T|U|X|V|W|Y|Z';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nassert(isequal(tautology('(A|B)|C'),false));\r\n%%\r\nassert(isequal(tautology('(A|B)|(C == C)'),true));\r\n%%\r\nassert(isequal(tautology('(A == B)|(B == C)|(C == A)'),true));\r\n%%\r\nassert(isequal(tautology('~(~(~(~(~(~(0))))))'),false)); \r\n%%\r\nassert(isequal(tautology('~(~(~(~(~(~(~0))))))'),true));\r\n% provided by Alfonso:\r\nassert(isequal(tautology('((0\u00261)|~B)\u0026~B'),false)); \r\n%%\r\nassert(isequal(tautology('((0\u0026~B)\u0026~B)'),false)); \r\n%%\r\nassert(isequal(tautology('((0|A)\u0026~A)'),false)); \r\n%%\r\nassert(isequal(tautology('((0|A)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((0|~B)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((1\u00260)|B)'),false)); \r\n%%\r\nassert(isequal(tautology('((1\u00261)\u0026A)'),false)); \r\n%%\r\nassert(isequal(tautology('((1|0)|A)'),true)); \r\n%%\r\nassert(isequal(tautology('((1|A)|0)'),true)); \r\n%%\r\nassert(isequal(tautology('((1|~A)\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('((A\u00261)|~A)|A'),true)); \r\n%%\r\nassert(isequal(tautology('((A\u0026~A)\u0026~B)|~A'),false)); \r\n%%\r\nassert(isequal(tautology('((A\u0026~B)\u00261)|B'),false)); \r\n%%\r\nassert(isequal(tautology('((A|0)\u00261)\u0026~B'),false)); \r\n%%\r\nassert(isequal(tautology('((A|A)\u0026A)|~A'),true)); \r\n%%\r\nassert(isequal(tautology('((B|0)\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('((B|1)\u0026B)\u0026A'),false)); \r\n%%\r\nassert(isequal(tautology('((B|A)|~A)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)\u00260)\u0026B'),false)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)|0)'),false)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)|~A)|1'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|A)|~B)\u00261'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|B)|A)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|~A)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|~B)\u00260)'),false)); \r\n%%\r\nassert(isequal(tautology('((~B\u00260)\u0026A)'),false)); \r\n%%\r\nassert(isequal(tautology('(0\u00261)|1\u00261'),true)); \r\n%%\r\nassert(isequal(tautology('(0|~A\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('(1|A\u00260)'),true)); \r\n%%\r\nassert(isequal(tautology('(A\u0026A\u0026~B)'),false)); \r\n%%\r\nassert(isequal(tautology('(A\u0026~A|1)'),true)); \r\n%%\r\nassert(isequal(tautology('(A|1)|B'),true)); \r\n%%\r\nassert(isequal(tautology('(A|A)|A|1'),true)); \r\n%%\r\nassert(isequal(tautology('(B\u00261)|~B'),true)); \r\n%%\r\nassert(isequal(tautology('(B\u0026~B)\u0026~B\u00260'),false)); \r\n%%\r\nassert(isequal(tautology('(B|~B)|B'),true)); \r\n%%\r\nassert(isequal(tautology('(~A\u0026B\u00260)'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|0)|~B\u0026~A'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|1)|1'),true)); \r\n%%\r\nassert(isequal(tautology('(~A|B\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|B)|~B'),true)); \r\n%%\r\nassert(isequal(tautology('(~A|~A)|0'),false)); \r\n%%\r\nassert(isequal(tautology('(~B\u00260)\u00261|1'),true)); \r\n%%\r\nassert(isequal(tautology('1\u0026B|~B|0'),true)); \r\n%%\r\nassert(isequal(tautology('B\u00261\u0026A\u00261'),false)); \r\n%%\r\nassert(isequal(tautology('~A\u00260\u00261|1'),true)); \r\n%%\r\nassert(isequal(tautology('~B\u00260\u0026~A|B'),false)); \r\n%%\r\nassert(isequal(tautology('~B|1|1|~B'),true)); \r\n%%\r\nassert(isequal(tautology('~B|~B\u00261|1'),true));\r\n%%\r\nassert(isequal(tautology('A==~A'),false));\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":30,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":45,"test_suite_updated_at":"2017-10-31T07:45:16.000Z","rescore_all_solutions":true,"group_id":35,"created_at":"2017-10-10T23:20:08.000Z","updated_at":"2026-08-07T05:32:19.000Z","published_at":"2017-10-16T01:51:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCheck if the given expression is always true. For example, the sentence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA['~(A \u0026 B) == (~A | ~B)']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eis always true.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCharacters in the input sequences may include\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e~ \u0026amp; | == ( )\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, whitespace, 0 for false, 1 for true and letters for variables.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45451,"title":"Don't be Too Greedy!!","description":"Refer to the prev problem \u003chttps://www.mathworks.com/matlabcentral/cody/problems/45450-don-t-be-too-greedy\u003e\r\n\r\nFor this time, calculate the maximum number of marks he can achieve after finishing all his assignments.","description_html":"\u003cp\u003eRefer to the prev problem \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/45450-don-t-be-too-greedy\"\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/45450-don-t-be-too-greedy\u003c/a\u003e\u003c/p\u003e\u003cp\u003eFor this time, calculate the maximum number of marks he can achieve after finishing all his assignments.\u003c/p\u003e","function_template":"function y = greedy_3(p,t,mark)","test_suite":"%%\r\np=[ 10,  4,  1,  2,  5,  2];\r\nt=[  2,  4,  3,  8,  1, 10];\r\nassert(isequal(greedy_3(p,t,100),515))\r\n\r\n%%\r\n p=[4,2,1, 5, 3, 2, 6];\r\n t=[1,8,2, 3, 1, 4, 2];\r\nassert(isequal(greedy_3(p,t,10),-16))\r\n\r\n%%\r\np=[9,10,2,10,7,1,3,6,10,10,2,10];\r\nt=[48    25    41     8    22    46    40    48    33     2    43    47];\r\nassert(isequal(greedy_3(p,t,200),-4008))\r\n\r\n%%\r\np=[1,3,1,2,4];\r\nt=[1,4,10,2,5];\r\nassert(isequal(greedy_3(p,t,200),950))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-13T12:04:50.000Z","updated_at":"2026-08-28T01:44:40.000Z","published_at":"2020-04-13T12:04:50.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRefer to the prev problem\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45450-don-t-be-too-greedy\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/45450-don-t-be-too-greedy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this time, calculate the maximum number of marks he can achieve after finishing all his assignments.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":51783,"title":"Solve an ODE: equation B","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.25px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 106.625px; transform-origin: 407px 106.625px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.358px 7.91667px; transform-origin: 211.358px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to solve the following ordinary differential equation:  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 39px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.5px; text-align: left; transform-origin: 384px 19.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg 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alt=\"y\u0026quot; + (1/x) y' - (a^2 + p^2/x^2) y = 0\" style=\"width: 181.5px; height: 39px;\" width=\"181.5\" height=\"39\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.125px; text-align: left; transform-origin: 384px 21.125px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.3917px 7.91667px; transform-origin: 14.3917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewith \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y(x1) = y1\" style=\"width: 64.5px; height: 20px;\" width=\"64.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.0083px 7.91667px; transform-origin: 35.0083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and either \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y(x0) = y0\" style=\"width: 64.5px; height: 20px;\" width=\"64.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 7.91667px; transform-origin: 10.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y'(x0) = y'0\" style=\"width: 74px; height: 20px;\" width=\"74\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38.1167px 7.91667px; transform-origin: 38.1167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Along with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ey1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.275px 7.91667px; transform-origin: 25.275px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, one of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ey0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 7.91667px; transform-origin: 11.55px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eyp0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109.708px 7.91667px; transform-origin: 109.708px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be assigned numerical values, and the other will be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 7.91667px; transform-origin: 11.55px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eNaN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 128.742px 7.91667px; transform-origin: 128.742px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The function should return the values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.9px 7.91667px; transform-origin: 80.9px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at the specified values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 194.483px 7.91667px; transform-origin: 194.483px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOne of the applications for this equation is in groundwater. For \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a = 1\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p = 0\" style=\"width: 38px; height: 18px;\" width=\"38\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 136.567px 7.91667px; transform-origin: 136.567px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the equation arises in the flow of water to a well pumping in a leaky confined aquifer; the independent variable \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 141.975px 7.91667px; transform-origin: 141.975px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the normalized distance from the well, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.94167px 7.91667px; transform-origin: 8.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is related to the piezometric head, a combination of the elevation and pressure of the water. Specifying the derivative at a point amounts to specifying the flow to the well.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = solveODEB(x,coeff,Xbc,bc)\r\n%  y = values of the solution\r\n%  x = values of the independent variable where the solution is requested\r\n%  coeff = [a p], the two parameters in the ODE\r\n%  Xbc = values of x where the boundary conditions are specifified\r\n%  bc = [y0 yp0 y1] = boundary values (see description)\r\n\r\n  y = f(x,coeff,Xbc,bc);\r\nend","test_suite":"%%\r\ncoeff = [1 0];\r\nXbc = [1 4];\r\nbc = [1 NaN 0];\r\nx = linspace(1,4,7);\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [1 0.505461057363874 0.265959532078956 0.140787844664873 0.071276733472728 0.029333752731051 0];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\ncoeff = [3 1];\r\nXbc = [0.5 4.5];\r\nbc = [0 NaN 2];\r\nx = [cos(pi/4) cos(pi/6) sqrt(2) (1+sqrt(5))/2 sqrt(3) sqrt(5) exp(1) pi 4+psi(1)];\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [0.000035290165611 0.000065476121971 0.000315436935125 0.000552779648598 0.000757412623201 0.003086031722519 0.012031119481478 0.040129255417251 0.089700339919646];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\ncoeff = [1 1/2];\r\nXbc = [1 5];\r\nbc = [4 NaN -1];\r\nx = 1.2:0.75:4.95;\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [2.974028994378906 1.041176175714286 0.308462205553512 -0.076175488441917 -0.426089583908447 -0.952692417292867];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\ncoeff = [2 4];\r\nXbc = [1 Inf];\r\nbc = [3 NaN 0];\r\nx = 1:2:9;\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [3 0.005688558853080 0.000051725255081 0.000000653418086 0.000000009396692];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n%-------------------------------\r\n%%\r\ncoeff = [1 0];\r\nXbc = [1 4];\r\nbc = [NaN 1 0];\r\nx = linspace(1,4,7);\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [-0.696760997897786 -0.352185550727323 -0.185310228971762 -0.098095479140575 -0.049662847941353 -0.020438614824974 0];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n \r\n%%\r\ncoeff = [3 1];\r\nXbc = [0.5 4.5];\r\nbc = [NaN 0 2];\r\nx = [cos(pi/4) cos(pi/6) sqrt(2) (1+sqrt(5))/2 sqrt(3) sqrt(5) exp(1) pi 4+psi(1)];\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [0.000053997354167 0.000075728700374 0.000316920386259 0.000553525214653 0.000757922298088 0.003086129240342 0.012031140116004 0.040129260776539 0.089700342119009];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\ncoeff = [1 1/2];\r\nXbc = [1 5];\r\nbc = [NaN 4 -1];\r\nx = 1.2:0.75:4.95;\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [-2.047695617799804 -0.816404083826666 -0.431398160565887 -0.374418157507686 -0.532801281305956 -0.958228725044217];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\ncoeff = [1 0];\r\nXbc = [1 Inf];\r\nbc = [NaN 3 0];\r\nx = 1:2:9;\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [-2.098451806781317 -0.173147136186896 -0.018397012773047 -0.002117248575316 -0.000253600440751];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-05-16T01:10:22.000Z","updated_at":"2026-09-15T06:59:48.000Z","published_at":"2021-05-16T01:19:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to solve the following ordinary differential equation:  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\u0026quot; + (1/x) y' - (a^2 + p^2/x^2) y = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{d^2y}{dx^2} +\\\\frac{1}{x} \\\\frac{dy}{dx}-\\\\left(a^2+\\\\frac{p^2}{x^2}\\\\right)y = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewith \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y(x1) = y1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey(x_1) = y_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and either \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y(x0) = y0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey(x_0) = y_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y'(x0) = y'0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\\\\prime(x_0) = y\\\\prime_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Along with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, one of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eyp0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be assigned numerical values, and the other will be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNaN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The function should return the values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at the specified values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOne of the applications for this equation is in groundwater. For \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the equation arises in the flow of water to a well pumping in a leaky confined aquifer; the independent variable \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the normalized distance from the well, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is related to the piezometric head, a combination of the elevation and pressure of the water. Specifying the derivative at a point amounts to specifying the flow to the well.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61175,"title":"[Master Regular Expression] Goat Latin","description":"You are given a string sentence that consist of words separated by spaces. Each word consists of lowercase and uppercase letters only.\r\nWe would like to convert the sentence to \"Goat Latin\" (a made-up language similar to Pig Latin.) The rules of Goat Latin are as follows:\r\nIf a word begins with a vowel ('a', 'e', 'i', 'o', or 'u'), append \"ma\" to the end of the word.\r\nFor example, the word \"apple\" becomes \"applema\".\r\nIf a word begins with a consonant (i.e., not a vowel), remove the first letter and append it to the end, then add \"ma\".\r\nFor example, the word \"goat\" becomes \"oatgma\".\r\nAdd one letter 'a' to the end of each word per its word index in the sentence, starting with 1.\r\nFor example, the first word gets \"a\" added to the end, the second word gets \"aa\" added to the end, and so on.\r\nReturn the final sentence representing the conversion from sentence to Goat Latin.\r\n \r\nExample 1:\r\nInput: sentence = \"I speak Goat Latin\"\r\nOutput: \"Imaa peaksmaaa oatGmaaaa atinLmaaaaa\"\r\nExample 2:\r\nInput: sentence = \"The quick brown fox jumped over the lazy dog\"\r\nOutput: \"heTmaa uickqmaaa rownbmaaaa oxfmaaaaa umpedjmaaaaaa overmaaaaaaa hetmaaaaaaaa azylmaaaaaaaaa ogdmaaaaaaaaaa\"\r\n \r\nConstraints:\r\n1 \u003c= sentence.length \u003c= 150\r\nsentence consists of English letters and spaces.\r\nsentence has no leading or trailing spaces.\r\nAll the words in sentence are separated by a single space.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 809.375px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 404.688px; transform-origin: 408px 404.688px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given a string sentence that consist of words separated by spaces. Each word consists of lowercase and uppercase letters only.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe would like to convert the sentence to \"Goat Latin\" (a made-up language similar to Pig Latin.) The rules of Goat Latin are as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf a word begins with a vowel ('a', 'e', 'i', 'o', or 'u'), append \"ma\" to the end of the word.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the word \"apple\" becomes \"applema\".\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf a word begins with a consonant (i.e., not a vowel), remove the first letter and append it to the end, then add \"ma\".\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the word \"goat\" becomes \"oatgma\".\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAdd one letter 'a' to the end of each word per its word index in the sentence, starting with 1.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the first word gets \"a\" added to the end, the second word gets \"aa\" added to the end, and so on.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e the final sentence representing the conversion from sentence to Goat Latin\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 1:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sentence = \"I speak Goat Latin\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \"Imaa peaksmaaa oatGmaaaa atinLmaaaaa\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 2:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sentence = \"The quick brown fox jumped over the lazy dog\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \"heTmaa uickqmaaa rownbmaaaa oxfmaaaaa umpedjmaaaaaa overmaaaaaaa hetmaaaaaaaa azylmaaaaaaaaa ogdmaaaaaaaaaa\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConstraints:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1 \u0026lt;= sentence.length \u0026lt;= 150\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esentence consists of English letters and spaces.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esentence has no leading or trailing spaces.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAll the words in sentence are separated by a single space.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function result = solution(sentence)\r\n\r\nend","test_suite":"%%\r\nsentence = 'I speak Goat Latin';\r\ncorrect_answer = 'Imaa peaksmaaa oatGmaaaa atinLmaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'The quick brown fox jumped over the lazy dog';\r\ncorrect_answer = 'heTmaa uickqmaaa rownbmaaaa oxfmaaaaa umpedjmaaaaaa overmaaaaaaa hetmaaaaaaaa azylmaaaaaaaaa ogdmaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'YLI Tdy kh dXKaa yRlPm WCVHO jVA tkLqg KWvQP Vo x aF IJSb DJUn q';\r\ncorrect_answer = 'LIYmaa dyTmaaa hkmaaaa XKaadmaaaaa RlPmymaaaaaa CVHOWmaaaaaaa VAjmaaaaaaaa kLqgtmaaaaaaaaa WvQPKmaaaaaaaaaa oVmaaaaaaaaaaa xmaaaaaaaaaaaa aFmaaaaaaaaaaaaa IJSbmaaaaaaaaaaaaaa JUnDmaaaaaaaaaaaaaaa qmaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'win QKDZ zoI pFP OFxhk XHUl qbQw W Em tzur Nm Wolnm wQ kQZh mvqwr I';\r\ncorrect_answer = 'inwmaa KDZQmaaa oIzmaaaa FPpmaaaaa OFxhkmaaaaaa HUlXmaaaaaaa bQwqmaaaaaaaa Wmaaaaaaaaa Emmaaaaaaaaaa zurtmaaaaaaaaaaa mNmaaaaaaaaaaaa olnmWmaaaaaaaaaaaaa Qwmaaaaaaaaaaaaaa QZhkmaaaaaaaaaaaaaaa vqwrmmaaaaaaaaaaaaaaaa Imaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'zo';\r\ncorrect_answer = 'ozmaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'cUS j E NlYz j Tc HR P p';\r\ncorrect_answer = 'UScmaa jmaaa Emaaaa lYzNmaaaaa jmaaaaaa cTmaaaaaaa RHmaaaaaaaa Pmaaaaaaaaa pmaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'FAMfT ain J z oEo aDttb';\r\ncorrect_answer = 'AMfTFmaa ainmaaa Jmaaaa zmaaaaa oEomaaaaaa aDttbmaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'NPm t gwad PVVG d MGLk Yvmy SXgK f A xPB zrnY Pz Ga';\r\ncorrect_answer = 'PmNmaa tmaaa wadgmaaaa VVGPmaaaaa dmaaaaaa GLkMmaaaaaaa vmyYmaaaaaaaa XgKSmaaaaaaaaa fmaaaaaaaaaa Amaaaaaaaaaaa PBxmaaaaaaaaaaaa rnYzmaaaaaaaaaaaaa zPmaaaaaaaaaaaaaa aGmaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'VRVJO kxPa';\r\ncorrect_answer = 'RVJOVmaa xPakmaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'dwR MWqM wBHyj va dwCF eod sHzt ft zP SASy GD uvh';\r\ncorrect_answer = 'wRdmaa WqMMmaaa BHyjwmaaaa avmaaaaa wCFdmaaaaaa eodmaaaaaaa Hztsmaaaaaaaa tfmaaaaaaaaa Pzmaaaaaaaaaa ASySmaaaaaaaaaaa DGmaaaaaaaaaaaa uvhmaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'W UvuC AEg Hsqo r mdzgu';\r\ncorrect_answer = 'Wmaa UvuCmaaa AEgmaaaa sqoHmaaaaa rmaaaaaa dzgummaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'rDIH peGn';\r\ncorrect_answer = 'DIHrmaa eGnpmaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'Lr EV XM S Drre IDu sXbwK AFMP DS ASJ A x cXjtk w fz sD vut jg';\r\ncorrect_answer = 'rLmaa EVmaaa MXmaaaa Smaaaaa rreDmaaaaaa IDumaaaaaaa XbwKsmaaaaaaaa AFMPmaaaaaaaaa SDmaaaaaaaaaa ASJmaaaaaaaaaaa Amaaaaaaaaaaaa xmaaaaaaaaaaaaa Xjtkcmaaaaaaaaaaaaaa wmaaaaaaaaaaaaaaa zfmaaaaaaaaaaaaaaaa Dsmaaaaaaaaaaaaaaaaa utvmaaaaaaaaaaaaaaaaaa gjmaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'ALNn';\r\ncorrect_answer = 'ALNnmaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'w YCcE Cx t';\r\ncorrect_answer = 'wmaa CcEYmaaa xCmaaaa tmaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'KYgHu kur tf Qrz D sSr mOo BTW Y dlsw VGXN SQg GuRb X BU IL';\r\ncorrect_answer = 'YgHuKmaa urkmaaa ftmaaaa rzQmaaaaa Dmaaaaaa Srsmaaaaaaa Oommaaaaaaaa TWBmaaaaaaaaa Ymaaaaaaaaaa lswdmaaaaaaaaaaa GXNVmaaaaaaaaaaaa QgSmaaaaaaaaaaaaa uRbGmaaaaaaaaaaaaaa Xmaaaaaaaaaaaaaaa UBmaaaaaaaaaaaaaaaa ILmaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'xFC oTW YBfHj XfpPw bDD';\r\ncorrect_answer = 'FCxmaa oTWmaaa BfHjYmaaaa fpPwXmaaaaa DDbmaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'O B ZYpNk IfEYR Kmcy i IYo WiP T YNL k eM rhIRJ t AYnT';\r\ncorrect_answer = 'Omaa Bmaaa YpNkZmaaaa IfEYRmaaaaa mcyKmaaaaaa imaaaaaaa IYomaaaaaaaa iPWmaaaaaaaaa Tmaaaaaaaaaa NLYmaaaaaaaaaaa kmaaaaaaaaaaaa eMmaaaaaaaaaaaaa hIRJrmaaaaaaaaaaaaaa tmaaaaaaaaaaaaaaa AYnTmaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'e ttpp yZ Xi NSFfx cbpW TtT Ufl';\r\ncorrect_answer = 'emaa tpptmaaa Zymaaaa iXmaaaaa SFfxNmaaaaaa bpWcmaaaaaaa tTTmaaaaaaaa Uflmaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'at uj EE W k NhW cJo YJzf Ba Ei J CYG BS RsMWI oEr';\r\ncorrect_answer = 'atmaa ujmaaa EEmaaaa Wmaaaaa kmaaaaaa hWNmaaaaaaa Jocmaaaaaaaa JzfYmaaaaaaaaa aBmaaaaaaaaaa Eimaaaaaaaaaaa Jmaaaaaaaaaaaa YGCmaaaaaaaaaaaaa SBmaaaaaaaaaaaaaa sMWIRmaaaaaaaaaaaaaaa oErmaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'YJK WRiRy BR nsj jR aq oOBiB LM jho PIoh Jd ZVD MKJo GQa ZQ JQoI C TjW rGBxs eu';\r\ncorrect_answer = 'JKYmaa RiRyWmaaa RBmaaaa sjnmaaaaa Rjmaaaaaa aqmaaaaaaa oOBiBmaaaaaaaa MLmaaaaaaaaa hojmaaaaaaaaaa IohPmaaaaaaaaaaa dJmaaaaaaaaaaaa VDZmaaaaaaaaaaaaa KJoMmaaaaaaaaaaaaaa QaGmaaaaaaaaaaaaaaa QZmaaaaaaaaaaaaaaaa QoIJmaaaaaaaaaaaaaaaaa Cmaaaaaaaaaaaaaaaaaa jWTmaaaaaaaaaaaaaaaaaaa GBxsrmaaaaaaaaaaaaaaaaaaaa eumaaaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'KhQ RzIxv W y BZ';\r\ncorrect_answer = 'hQKmaa zIxvRmaaa Wmaaaa ymaaaaa ZBmaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'O uQT kTpvQ we MprM KeyHB o PWskJ wV uMppp V mzPt LO GNAr E k A y w';\r\ncorrect_answer = 'Omaa uQTmaaa TpvQkmaaaa ewmaaaaa prMMmaaaaaa eyHBKmaaaaaaa omaaaaaaaa WskJPmaaaaaaaaa Vwmaaaaaaaaaa uMpppmaaaaaaaaaaa Vmaaaaaaaaaaaa zPtmmaaaaaaaaaaaaa OLmaaaaaaaaaaaaaa NArGmaaaaaaaaaaaaaaa Emaaaaaaaaaaaaaaaa kmaaaaaaaaaaaaaaaaa Amaaaaaaaaaaaaaaaaaa ymaaaaaaaaaaaaaaaaaaa wmaaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'Qem sv v CsIJ';\r\ncorrect_answer = 'emQmaa vsmaaa vmaaaa sIJCmaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'WDE mKpD umWx';\r\ncorrect_answer = 'DEWmaa KpDmmaaa umWxmaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'IwiK tHUzG fff WGW p aiNRF XMK TYZV dQ b CrES';\r\ncorrect_answer = 'IwiKmaa HUzGtmaaa fffmaaaa GWWmaaaaa pmaaaaaa aiNRFmaaaaaaa MKXmaaaaaaaa YZVTmaaaaaaaaa Qdmaaaaaaaaaa bmaaaaaaaaaaa rESCmaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'Cjm nX RuiM sjZXi wlhnC F x Xp Ith p GkYwR baO pSI';\r\ncorrect_answer = 'jmCmaa Xnmaaa uiMRmaaaa jZXismaaaaa lhnCwmaaaaaa Fmaaaaaaa xmaaaaaaaa pXmaaaaaaaaa Ithmaaaaaaaaaa pmaaaaaaaaaaa kYwRGmaaaaaaaaaaaa aObmaaaaaaaaaaaaa SIpmaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'njtB MhagV fXgz yd nm bVtIX';\r\ncorrect_answer = 'jtBnmaa hagVMmaaa Xgzfmaaaa dymaaaaa mnmaaaaaa VtIXbmaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'vfzy IoIHU';\r\ncorrect_answer = 'fzyvmaa IoIHUmaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'wP TzEWi nR o Gvn tfg IRzp c tD OEf dtoM N ma k Vo O FrJm sl';\r\ncorrect_answer = 'Pwmaa zEWiTmaaa Rnmaaaa omaaaaa vnGmaaaaaa fgtmaaaaaaa IRzpmaaaaaaaa cmaaaaaaaaa Dtmaaaaaaaaaa OEfmaaaaaaaaaaa toMdmaaaaaaaaaaaa Nmaaaaaaaaaaaaa ammaaaaaaaaaaaaaa kmaaaaaaaaaaaaaaa oVmaaaaaaaaaaaaaaaa Omaaaaaaaaaaaaaaaaa rJmFmaaaaaaaaaaaaaaaaaa lsmaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'asmW tJKE OBeUn rNP TeIAr skn h Eh a JgLi J d a d';\r\ncorrect_answer = 'asmWmaa JKEtmaaa OBeUnmaaaa NPrmaaaaa eIArTmaaaaaa knsmaaaaaaa hmaaaaaaaa Ehmaaaaaaaaa amaaaaaaaaaa gLiJmaaaaaaaaaaa Jmaaaaaaaaaaaa dmaaaaaaaaaaaaa amaaaaaaaaaaaaaa dmaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'Au';\r\ncorrect_answer = 'Aumaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'hOM y vw KabmF rxfLL WcPy cO ORrjt bp ks gkz MpP NrLbG c b BNEMq zfQIt vcEp Eqh frbVt';\r\ncorrect_answer = 'OMhmaa ymaaa wvmaaaa abmFKmaaaaa xfLLrmaaaaaa cPyWmaaaaaaa Ocmaaaaaaaa ORrjtmaaaaaaaaa pbmaaaaaaaaaa skmaaaaaaaaaaa kzgmaaaaaaaaaaaa pPMmaaaaaaaaaaaaa rLbGNmaaaaaaaaaaaaaa cmaaaaaaaaaaaaaaa bmaaaaaaaaaaaaaaaa NEMqBmaaaaaaaaaaaaaaaaa fQItzmaaaaaaaaaaaaaaaaaa cEpvmaaaaaaaaaaaaaaaaaaa Eqhmaaaaaaaaaaaaaaaaaaaa rbVtfmaaaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'Djl lWo Qsbrt Y i Act ZwK h cbDrl Jtukm VOmEk J NQluv fBGok siU Iky z JM DM Edtb';\r\ncorrect_answer = 'jlDmaa Wolmaaa sbrtQmaaaa Ymaaaaa imaaaaaa Actmaaaaaaa wKZmaaaaaaaa hmaaaaaaaaa bDrlcmaaaaaaaaaa tukmJmaaaaaaaaaaa OmEkVmaaaaaaaaaaaa Jmaaaaaaaaaaaaa QluvNmaaaaaaaaaaaaaa BGokfmaaaaaaaaaaaaaaa iUsmaaaaaaaaaaaaaaaa Ikymaaaaaaaaaaaaaaaaa zmaaaaaaaaaaaaaaaaaa MJmaaaaaaaaaaaaaaaaaaa MDmaaaaaaaaaaaaaaaaaaaa Edtbmaaaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'DYwO bAv lw qoszQ bp Qh SCaAL UKWa bAHNo';\r\ncorrect_answer = 'YwODmaa Avbmaaa wlmaaaa oszQqmaaaaa pbmaaaaaa hQmaaaaaaa CaALSmaaaaaaaa UKWamaaaaaaaaa AHNobmaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":4945898,"edited_by":4945898,"edited_at":"2026-01-31T12:14:26.000Z","deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2026-01-31T12:12:55.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-31T12:12:09.000Z","updated_at":"2026-09-15T09:03:55.000Z","published_at":"2026-01-31T12:12:09.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given a string sentence that consist of words separated by spaces. Each word consists of lowercase and uppercase letters only.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe would like to convert the sentence to \\\"Goat Latin\\\" (a made-up language similar to Pig Latin.) The rules of Goat Latin are as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf a word begins with a vowel ('a', 'e', 'i', 'o', or 'u'), append \\\"ma\\\" to the end of the word.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the word \\\"apple\\\" becomes \\\"applema\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf a word begins with a consonant (i.e., not a vowel), remove the first letter and append it to the end, then add \\\"ma\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the word \\\"goat\\\" becomes \\\"oatgma\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAdd one letter 'a' to the end of each word per its word index in the sentence, starting with 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the first word gets \\\"a\\\" added to the end, the second word gets \\\"aa\\\" added to the end, and so on.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e the final sentence representing the conversion from sentence to Goat Latin\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e sentence = \\\"I speak Goat Latin\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \\\"Imaa peaksmaaa oatGmaaaa atinLmaaaaa\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e sentence = \\\"The quick brown fox jumped over the lazy dog\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \\\"heTmaa uickqmaaa rownbmaaaa oxfmaaaaa umpedjmaaaaaa overmaaaaaaa hetmaaaaaaaa azylmaaaaaaaaa ogdmaaaaaaaaaa\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConstraints:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1 \u0026lt;= sentence.length \u0026lt;= 150\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esentence consists of English letters and spaces.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esentence has no leading or trailing spaces.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAll the words in sentence are separated by a single space.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1092,"title":"Decimation","description":"When dealing to the Roman Army, the term decimate meant that the entire unit would be broken up into groups of ten soldiers, and lots would be drawn.  The person who was unlucky enough to draw the short straw would be executed by the other nine members of his group.\r\n\r\nThe bloodthirsty Roman Centurion Carnage Maximus decided to apply this to his prisoners, with a few gruesome differences.  Rather than kill every tenth prisoner and allow the rest to live, he is going to leave only one prisoner alive and kill all of the others.  Instead of killing every tenth prisoner, he chooses a number (kill_every).  If kill_every=3, he kills every third prisoner.  If kill_every=5, he kills every fifth prisoner.  He always chooses a number between 2 and the number of prisoners he has, and this process will be repeated until there is only one prisoner left.  For example, if there are 10 prisoners, and kill_every=3\r\n\r\nFirst iteration: 1 2 3 4 5 6 7 8 9 10\r\n\r\n1-2-3 4-5-6 7-8-9 10\r\n\r\nPrisoners 3, 6 and 9 will be killed.\r\n\r\nSecond iteration: 1 2 4 5 7 8 10\r\n\r\nBecause Prisoner 10 was counted during the first iteration, the executions\r\nwill proceed as such: 10-1-2 4-5-7 8-10, so prisoners 2 and 7 will be killed\r\n\r\nThird iteration: 1 4 5 8 10\r\n8-10-1 4-5-8 10, so prisoners 1 and 8 executed.\r\n\r\nFourth Iteration:  10-4-5 10\r\nPrisoner 5 is executed.\r\n\r\nFifth iteration:  10-4 10\r\nPrisoner 10 is executed\r\n\r\nSince the sole survivor is prisoner 4, he is released.\r\n\r\nYou are an unlucky prisoner caught by Carnage Maximum.  Prior to lining up the prisoners, he reveals the number of prisoners he has and his value of kill_every for the day.  Your job is to figure out which prisoner you need to be in order to survive.  Write a MATLAB script that takes the values of num_prisoners and kill_every.  The output will be survivor, which is the position of the person who survives.  If you write your script quickly enough, that person will be you.\r\n\r\nGood luck!","description_html":"\u003cp\u003eWhen dealing to the Roman Army, the term decimate meant that the entire unit would be broken up into groups of ten soldiers, and lots would be drawn.  The person who was unlucky enough to draw the short straw would be executed by the other nine members of his group.\u003c/p\u003e\u003cp\u003eThe bloodthirsty Roman Centurion Carnage Maximus decided to apply this to his prisoners, with a few gruesome differences.  Rather than kill every tenth prisoner and allow the rest to live, he is going to leave only one prisoner alive and kill all of the others.  Instead of killing every tenth prisoner, he chooses a number (kill_every).  If kill_every=3, he kills every third prisoner.  If kill_every=5, he kills every fifth prisoner.  He always chooses a number between 2 and the number of prisoners he has, and this process will be repeated until there is only one prisoner left.  For example, if there are 10 prisoners, and kill_every=3\u003c/p\u003e\u003cp\u003eFirst iteration: 1 2 3 4 5 6 7 8 9 10\u003c/p\u003e\u003cp\u003e1-2-3 4-5-6 7-8-9 10\u003c/p\u003e\u003cp\u003ePrisoners 3, 6 and 9 will be killed.\u003c/p\u003e\u003cp\u003eSecond iteration: 1 2 4 5 7 8 10\u003c/p\u003e\u003cp\u003eBecause Prisoner 10 was counted during the first iteration, the executions\r\nwill proceed as such: 10-1-2 4-5-7 8-10, so prisoners 2 and 7 will be killed\u003c/p\u003e\u003cp\u003eThird iteration: 1 4 5 8 10\r\n8-10-1 4-5-8 10, so prisoners 1 and 8 executed.\u003c/p\u003e\u003cp\u003eFourth Iteration:  10-4-5 10\r\nPrisoner 5 is executed.\u003c/p\u003e\u003cp\u003eFifth iteration:  10-4 10\r\nPrisoner 10 is executed\u003c/p\u003e\u003cp\u003eSince the sole survivor is prisoner 4, he is released.\u003c/p\u003e\u003cp\u003eYou are an unlucky prisoner caught by Carnage Maximum.  Prior to lining up the prisoners, he reveals the number of prisoners he has and his value of kill_every for the day.  Your job is to figure out which prisoner you need to be in order to survive.  Write a MATLAB script that takes the values of num_prisoners and kill_every.  The output will be survivor, which is the position of the person who survives.  If you write your script quickly enough, that person will be you.\u003c/p\u003e\u003cp\u003eGood luck!\u003c/p\u003e","function_template":"function survivor=decimate(num_prisoners,kill_every)\r\nsurvivor=4;\r\nend","test_suite":"%%\r\nassert(isequal(decimate(10,3),4))\r\n%%\r\nassert(isequal(decimate(1024,3),676))\r\n%%\r\nassert(isequal(decimate(2012,50),543))\r\n%%\r\nassert(isequal(decimate(30,5),3))\r\n%%\r\nassert(isequal(decimate(10,10),8))\r\n%%\r\nassert(isequal(decimate(2048,2),1))","published":true,"deleted":false,"likes_count":20,"comments_count":14,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":328,"test_suite_updated_at":"2012-12-04T21:28:04.000Z","rescore_all_solutions":false,"group_id":13,"created_at":"2012-12-04T19:47:49.000Z","updated_at":"2026-09-15T02:14:07.000Z","published_at":"2012-12-04T19:53:55.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen dealing to the Roman Army, the term decimate meant that the entire unit would be broken up into groups of ten soldiers, and lots would be drawn. The person who was unlucky enough to draw the short straw would be executed by the other nine members of his group.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe bloodthirsty Roman Centurion Carnage Maximus decided to apply this to his prisoners, with a few gruesome differences. Rather than kill every tenth prisoner and allow the rest to live, he is going to leave only one prisoner alive and kill all of the others. Instead of killing every tenth prisoner, he chooses a number (kill_every). If kill_every=3, he kills every third prisoner. If kill_every=5, he kills every fifth prisoner. He always chooses a number between 2 and the number of prisoners he has, and this process will be repeated until there is only one prisoner left. For example, if there are 10 prisoners, and kill_every=3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFirst iteration: 1 2 3 4 5 6 7 8 9 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1-2-3 4-5-6 7-8-9 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrisoners 3, 6 and 9 will be killed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSecond iteration: 1 2 4 5 7 8 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBecause Prisoner 10 was counted during the first iteration, the executions will proceed as such: 10-1-2 4-5-7 8-10, so prisoners 2 and 7 will be killed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThird iteration: 1 4 5 8 10 8-10-1 4-5-8 10, so prisoners 1 and 8 executed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFourth Iteration: 10-4-5 10 Prisoner 5 is executed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFifth iteration: 10-4 10 Prisoner 10 is executed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince the sole survivor is prisoner 4, he is released.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are an unlucky prisoner caught by Carnage Maximum. Prior to lining up the prisoners, he reveals the number of prisoners he has and his value of kill_every for the day. Your job is to figure out which prisoner you need to be in order to survive. Write a MATLAB script that takes the values of num_prisoners and kill_every. The output will be survivor, which is the position of the person who survives. If you write your script quickly enough, that person will be you.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood luck!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":364,"title":"Matrix spiral","description":"Make a spiral in a (n*n) matrix. The spiral has to start in the top left, and has to rotate clockwise to the center. The spiral has to have a padding of zeros between itself.\r\n\r\nThe (n*n) matrix is filled with zeros except for the spiral, that has to be made of 11 (elevens, for visual reference).\r\nThe final matrix has to have the same or more zeros than elevens.\r\n\r\nExample:\r\nn=8\r\n\r\nA =\r\n\r\n    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11     0    11\r\n     0     0    11     0     0    11     0    11\r\n     0     0    11     0    11    11     0    11\r\n     0     0    11     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0","description_html":"\u003cp\u003eMake a spiral in a (n*n) matrix. The spiral has to start in the top left, and has to rotate clockwise to the center. The spiral has to have a padding of zeros between itself.\u003c/p\u003e\u003cp\u003eThe (n*n) matrix is filled with zeros except for the spiral, that has to be made of 11 (elevens, for visual reference).\r\nThe final matrix has to have the same or more zeros than elevens.\u003c/p\u003e\u003cp\u003eExample:\r\nn=8\u003c/p\u003e\u003cp\u003eA =\u003c/p\u003e\u003cpre\u003e    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11     0    11\r\n     0     0    11     0     0    11     0    11\r\n     0     0    11     0    11    11     0    11\r\n     0     0    11     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0\u003c/pre\u003e","function_template":"function A = Matrix_Spiral(n)\r\n  A = n;\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct =[0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n%%\r\nn = 2;\r\ny_correct =[11    11\r\n     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n%%\r\nn = 3;\r\ny_correct =[11    11    11\r\n     0     0    11\r\n     0     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n%%\r\nn = 4;\r\ny_correct =[11    11    11    11\r\n     0     0     0    11\r\n     0     0    11    11\r\n     0     0     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n\r\n%%\r\nn = 5;\r\ny_correct =[11    11    11    11    11\r\n     0     0     0     0    11\r\n     0     0    11     0    11\r\n     0     0    11    11    11\r\n     0     0     0     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n%%\r\nn = 10;\r\ny_correct =[11    11    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11     0    11\r\n     0     0    11     0     0     0     0    11     0    11\r\n     0     0    11     0    11    11     0    11     0    11\r\n     0     0    11     0    11     0     0    11     0    11\r\n     0     0    11     0    11    11    11    11     0    11\r\n     0     0    11     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n\r\n%%\r\nn = 17;\r\ny_correct =[11    11    11    11    11    11    11    11    11    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11    11    11    11    11    11    11    11     0    11\r\n     0     0    11     0     0     0     0     0     0     0     0     0     0     0    11     0    11\r\n     0     0    11     0    11    11    11    11    11    11    11    11    11     0    11     0    11\r\n     0     0    11     0    11     0     0     0     0     0     0     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11    11    11    11    11     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11     0     0     0    11     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11     0    11     0    11     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11     0    11    11    11     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11     0     0     0     0     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11    11    11    11    11    11    11     0    11     0    11\r\n     0     0    11     0    11     0     0     0     0     0     0     0     0     0    11     0    11\r\n     0     0    11     0    11    11    11    11    11    11    11    11    11    11    11     0    11\r\n     0     0    11     0     0     0     0     0     0     0     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11    11    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))","published":true,"deleted":false,"likes_count":5,"comments_count":3,"created_by":872,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":98,"test_suite_updated_at":"2012-02-20T12:29:13.000Z","rescore_all_solutions":false,"group_id":18,"created_at":"2012-02-20T12:17:08.000Z","updated_at":"2026-04-28T18:06:26.000Z","published_at":"2012-02-20T12:29:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a spiral in a (n*n) matrix. The spiral has to start in the top left, and has to rotate clockwise to the center. The spiral has to have a padding of zeros between itself.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe (n*n) matrix is filled with zeros except for the spiral, that has to be made of 11 (elevens, for visual reference). The final matrix has to have the same or more zeros than elevens.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: n=8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA =\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    11    11    11    11    11    11    11    11\\n     0     0     0     0     0     0     0    11\\n     0     0    11    11    11    11     0    11\\n     0     0    11     0     0    11     0    11\\n     0     0    11     0    11    11     0    11\\n     0     0    11     0     0     0     0    11\\n     0     0    11    11    11    11    11    11\\n     0     0     0     0     0     0     0     0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":3084,"title":"Scrabble Scores - 11","description":"This problem builds on the previous problem, wherein you were provided a letter of an existing word on the board and from which you played a word to find the highest scoring word. See the previous problem for more details.\r\n\r\nNow, you will be provided a multiplier character array that represents the fifteen possible squares that can be played on, ranging from seven above the existing letter (in which case the existing letter is the last letter in an eight-letter word) to seven below the existing letter (in which case the existing letter is the first letter in an eight-letter word) with the existing letter fixed in the 8th position. The multipliers are the same as in previous problems:\r\n\r\n * D: double word\r\n * T: triple word\r\n * Q: quadruple word\r\n * d: double letter\r\n * t: triple letter\r\n * q: quadruple letter\r\n\r\nThe center multiplier square will be left blank, since it's already covered by a tile. Write a routine to determine the highest scoring word(s) based on the multiplier squares.\r\n\r\nOnce again, you will be provided a cell array of strings containing all possible words based on the existing letter and the letters on your tray. In addition to providing the highest score, also provide the word(s) that achieve that score in a cell array. See the test suite for examples. Due to high-scoring tiles, the highest score may not be achieved by the longest word(s).\r\n\r\nRelated problems:\r\n\r\nPrevious problem: 10 - \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3082-scrabble-scores-10 Word score optimization (known letter)\u003e. Next problem: 12 - \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12 Word score optimization (first word)\u003e.","description_html":"\u003cp\u003eThis problem builds on the previous problem, wherein you were provided a letter of an existing word on the board and from which you played a word to find the highest scoring word. See the previous problem for more details.\u003c/p\u003e\u003cp\u003eNow, you will be provided a multiplier character array that represents the fifteen possible squares that can be played on, ranging from seven above the existing letter (in which case the existing letter is the last letter in an eight-letter word) to seven below the existing letter (in which case the existing letter is the first letter in an eight-letter word) with the existing letter fixed in the 8th position. The multipliers are the same as in previous problems:\u003c/p\u003e\u003cpre\u003e * D: double word\r\n * T: triple word\r\n * Q: quadruple word\r\n * d: double letter\r\n * t: triple letter\r\n * q: quadruple letter\u003c/pre\u003e\u003cp\u003eThe center multiplier square will be left blank, since it's already covered by a tile. Write a routine to determine the highest scoring word(s) based on the multiplier squares.\u003c/p\u003e\u003cp\u003eOnce again, you will be provided a cell array of strings containing all possible words based on the existing letter and the letters on your tray. In addition to providing the highest score, also provide the word(s) that achieve that score in a cell array. See the test suite for examples. Due to high-scoring tiles, the highest score may not be achieved by the longest word(s).\u003c/p\u003e\u003cp\u003eRelated problems:\u003c/p\u003e\u003cp\u003ePrevious problem: 10 - \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3082-scrabble-scores-10\"\u003eWord score optimization (known letter)\u003c/a\u003e. Next problem: 12 - \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12\"\u003eWord score optimization (first word)\u003c/a\u003e.\u003c/p\u003e","function_template":"function [score,max_word] = scrabble_scores_11(words,mult,existing_letter)\r\n\r\nscore = 0;\r\nmax_word = {''};\r\n\r\nend","test_suite":"%%\r\nexisting_letter = 's'; %the word must contain this letter, which is in an already played word\r\ntray_letters = 'aethilm'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including the first letter with your tray letters\r\nwords = {'ae','ah','ai','al','am','as','at','eh','el','em','es','et','ha','he','hi','hm','is','it','la','li','ma','me','mi','sh','si','ta','te','ti','ahi','ahs','ail','aim','ais','ait','ale','als','alt','ami','ash','ate','eat','elm','els','ems','est','eta','eth','hae','ham','has','hat','hem','hes','het','hie','him','his','hit','ism','its','lah','lam','las','lat','lea','lei','let','lie','lis','lit','mae','mas','mat','meh','mel','met','mil','mis','sae','sal','sat','sea','sei','sel','set','sha','she','sim','sit','tae','tam','tas','tea','tel','tes','the','tie','til','tis','ahem','ahis','ails','aims','aits','ales','alit','alme','alms','alts','amie','amis','ates','east','eath','eats','elhi','elms','emit','etas','eths','haem','haes','haet','hail','hale','halm','halt','hame','hams','hast','hate','hats','heal','heat','heil','helm','hems','hest','hets','hies','hila','hilt','hims','hist','hits','ilea','isle','item','lahs','lame','lams','lase','lash','last','late','lath','lati','lats','leas','leis','lest','lets','lias','lies','lima','lime','list','lite','lits','maes','mail','male','malt','mash','mast','mate','math','mats','meal','meat','mels','melt','mesa','mesh','meta','meth','mile','mils','milt','mise','mist','mite','sail','sale','salt','same','sate','sati','seal','seam','seat','semi','seta','sham','shea','shim','sial','silt','sima','site','sith','slam','slat','slim','slit','smit','stem','tael','tail','tale','tali','tame','tams','tase','teal','team','teas','tela','tels','thae','them','this','ties','tile','tils','time','aisle','alist','almeh','almes','amies','email','emits','haems','haets','hails','hales','halms','halts','hames','haste','hates','heals','heats','heils','heist','helms','hemal','hilts','islet','istle','items','laith','lames','lathe','lathi','laths','leash','least','limas','limes','litas','lites','lithe','maile','mails','maist','males','malts','mates','maths','meals','meats','melts','metal','meths','metis','miles','milts','mites','saith','salmi','satem','selah','setal','shale','shalt','shame','sheal','shiel','slate','slime','smalt','smelt','smile','smite','smith','stale','steal','steam','stela','stile','stime','taels','tails','tales','tames','tamis','teals','teams','telia','tesla','thali','tiles','times','almehs','emails','halest','halite','hamlet','haslet','hiemal','lamest','lathes','lathis','latish','mailes','mashie','mesial','metals','misate','miseat','saithe','saltie','samiel','samite','samlet','sheila','shelta','smalti','stelai','tahsil','thalis','theism','atheism','halites','hamlets','heliast'};\r\nmult = ' T   d   d   T '; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\nmax_score_corr = 39;\r\nmax_word_corr = {'hamlets'};\r\n[max_score,max_word] = scrabble_scores_11(words,mult,existing_letter);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(max_word,max_word_corr))\r\n\r\n\r\n%%\r\nind = randi(4);\r\nexisting_letter = 's'; %the word must contain this letter, which is in an already played word\r\ntray_letters = 'aethilm'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including the first letter with your tray letters\r\nwords = {'ae','ah','ai','al','am','as','at','eh','el','em','es','et','ha','he','hi','hm','is','it','la','li','ma','me','mi','sh','si','ta','te','ti','ahi','ahs','ail','aim','ais','ait','ale','als','alt','ami','ash','ate','eat','elm','els','ems','est','eta','eth','hae','ham','has','hat','hem','hes','het','hie','him','his','hit','ism','its','lah','lam','las','lat','lea','lei','let','lie','lis','lit','mae','mas','mat','meh','mel','met','mil','mis','sae','sal','sat','sea','sei','sel','set','sha','she','sim','sit','tae','tam','tas','tea','tel','tes','the','tie','til','tis','ahem','ahis','ails','aims','aits','ales','alit','alme','alms','alts','amie','amis','ates','east','eath','eats','elhi','elms','emit','etas','eths','haem','haes','haet','hail','hale','halm','halt','hame','hams','hast','hate','hats','heal','heat','heil','helm','hems','hest','hets','hies','hila','hilt','hims','hist','hits','ilea','isle','item','lahs','lame','lams','lase','lash','last','late','lath','lati','lats','leas','leis','lest','lets','lias','lies','lima','lime','list','lite','lits','maes','mail','male','malt','mash','mast','mate','math','mats','meal','meat','mels','melt','mesa','mesh','meta','meth','mile','mils','milt','mise','mist','mite','sail','sale','salt','same','sate','sati','seal','seam','seat','semi','seta','sham','shea','shim','sial','silt','sima','site','sith','slam','slat','slim','slit','smit','stem','tael','tail','tale','tali','tame','tams','tase','teal','team','teas','tela','tels','thae','them','this','ties','tile','tils','time','aisle','alist','almeh','almes','amies','email','emits','haems','haets','hails','hales','halms','halts','hames','haste','hates','heals','heats','heils','heist','helms','hemal','hilts','islet','istle','items','laith','lames','lathe','lathi','laths','leash','least','limas','limes','litas','lites','lithe','maile','mails','maist','males','malts','mates','maths','meals','meats','melts','metal','meths','metis','miles','milts','mites','saith','salmi','satem','selah','setal','shale','shalt','shame','sheal','shiel','slate','slime','smalt','smelt','smile','smite','smith','stale','steal','steam','stela','stile','stime','taels','tails','tales','tames','tamis','teals','teams','telia','tesla','thali','tiles','times','almehs','emails','halest','halite','hamlet','haslet','hiemal','lamest','lathes','lathis','latish','mailes','mashie','mesial','metals','misate','miseat','saithe','saltie','samiel','samite','samlet','sheila','shelta','smalti','stelai','tahsil','thalis','theism','atheism','halites','hamlets','heliast'};\r\nswitch ind\r\n\tcase 1\r\n\t\tmult = ' T   d   d   T '; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 39;\r\n\t\tmax_word_corr = {'hamlets'};\r\n\tcase 2\r\n\t\tmult = 'T  D  d d  D  T'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 32;\r\n\t\tmax_word_corr = {'atheism'};\r\n\tcase 3\r\n\t\tmult = 'Q  t  T T  t  Q'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 153;\r\n\t\tmax_word_corr = {'halest'};\r\n\tcase 4\r\n\t\tmult = 'Q t T d d T t Q'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 60;\r\n\t\tmax_word_corr = {'heliast'};\r\nend\r\n[max_score,max_word] = scrabble_scores_11(words,mult,existing_letter);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(max_word,max_word_corr))\r\n\r\n\r\n%%\r\nind = randi(4);\r\nexisting_letter = 't'; %the word must contain this letter, which is in an already played word\r\ntray_letters = 'eodnirl'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including the first letter with your tray letters\r\nwords = {'de','do','ed','el','en','er','et','id','in','it','li','lo','ne','no','od','oe','oi','on','or','re','te','ti','to','del','den','die','din','dit','doe','dol','don','dor','dot','eld','end','eon','ern','ion','ire','led','lei','let','lid','lie','lin','lit','lot','net','nil','nit','nod','nor','not','ode','oil','old','ole','one','ore','ort','red','rei','ret','rid','rin','rod','roe','rot','ted','tel','ten','tie','til','tin','tod','toe','ton','tor','deil','deli','delt','deni','dent','diel','diet','dine','dino','dint','diol','dire','dirl','dirt','dite','doer','doit','dole','dolt','done','dore','dote','edit','enol','idle','idol','inro','into','ired','iron','lend','leno','lent','lido','lied','lien','lier','line','lino','lint','lion','lire','lite','lode','loid','loin','lone','lord','lore','lorn','loti','nerd','nide','nite','node','nodi','noel','noil','noir','nori','note','olde','orle','redo','rein','rend','reno','rent','ride','riel','rile','rind','riot','rite','rode','roil','role','rote','roti','rotl','tein','tend','tern','tide','tied','tier','tile','tine','tire','tirl','tiro','toed','toil','told','tole','tone','tore','tori','torn','trio','trod','diner','doter','droit','drone','elint','eloin','enrol','ident','idler','indol','inert','inlet','inter','intro','irone','lento','lined','liner','lirot','liter','litre','loden','loner','nerol','niter','nitre','nitro','noted','noter','oiled','oiler','olden','older','oldie','olein','oriel','redon','relit','reoil','riled','ronde','teind','teloi','tenor','tilde','tiled','tiler','tined','tired','toile','toled','tondi','toned','toner','trend','tried','trine','triol','trode','trone','dentil','dinero','dotier','editor','entoil','indole','ironed','linted','linter','loiter','neroli','norite','orient','retold','rident','rioted','rodent','roiled','rondel','tinder','tirled','toiled','toiler','tonier','trined','triode','lentoid','retinol','tendril','trindle'};\r\nswitch ind\r\n\tcase 1\r\n\t\tmult = ' T   d   d   T '; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 27;\r\n\t\tmax_word_corr = {'tendril','trindle'};\r\n\tcase 2\r\n\t\tmult = 'T  D  d d  D  T'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 18;\r\n\t\tmax_word_corr = {'retinol','tendril','trindle'};\r\n\tcase 3\r\n\t\tmult = 'Q  t  T T  t  Q'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 81;\r\n\t\tmax_word_corr = {'retinol'};\r\n\tcase 4\r\n\t\tmult = 'Q t T d d T t Q'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 90;\r\n\t\tmax_word_corr = {'lentoid'};\r\nend\r\n[max_score,max_word] = scrabble_scores_11(words,mult,existing_letter);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(max_word,max_word_corr))\r\n\r\n\r\n%% anti-cheating test case 3\r\nind = randi(4);\r\nexisting_letter = 'n'; %the word must contain this letter, which is in an already played word\r\ntray_letters = 'dmvxeao'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including the first letter with your tray letters\r\nwords = {'ad','ae','am','an','ax','da','de','do','ed','em','en','ex','ma','me','mo','na','ne','no','od','oe','om','on','ox','ado','and','ane','ave','avo','axe','dam','dan','den','dev','dex','doe','dom','don','emo','end','eon','mad','mae','man','max','med','men','moa','mod','mon','nae','nam','nav','nod','nom','oda','ode','oma','one','ova','van','vex','voe','vox','aeon','amen','axed','axon','dame','damn','dean','demo','deva','dome','dona','done','dove','exam','exon','made','mane','mano','mead','mean','mend','meno','moan','mode','move','moxa','name','nave','nema','node','noma','nome','nova','odea','omen','oven','oxen','vane','vena','vend','admen','amend','anode','axmen','axone','daven','demon','devon','doven','maned','maven','maxed','menad','monad','monde','moved','named','nomad','novae','vaned','venom','daemon','moaned'};\r\nswitch ind\r\n\tcase 1\r\n\t\tmult = ' T   d   d   T '; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 20;\r\n\t\tmax_word_corr = {'axone'};\r\n\tcase 2\r\n\t\tmult = 'T  D  d d  D  T'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 30;\r\n\t\tmax_word_corr = {'axmen'};\r\n\tcase 3\r\n\t\tmult = 'Q  t  T T  t  Q'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 108;\r\n\t\tmax_word_corr = {'axone'};\r\n\tcase 4\r\n\t\tmult = 'Q t T d d T t Q'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 45;\r\n\t\tmax_word_corr = {'axmen'};\r\nend\r\n[max_score,max_word] = scrabble_scores_11(words,mult,existing_letter);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(max_word,max_word_corr))\r\n\r\n\r\n%% anti-cheating test case 4\r\nind = randi(4);\r\nexisting_letter = 'z'; %the word must contain this letter, which is in an already played word\r\ntray_letters = 'aehcmdi'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including the first letter with your tray letters\r\nwords = {'ad','ae','ah','ai','am','da','de','ed','eh','em','ha','he','hi','hm','id','ma','me','mi','za','ace','adz','ahi','aid','aim','ami','cad','cam','chi','dah','dam','die','dim','edh','had','hae','ham','hem','hic','hid','hie','him','ice','ich','mac','mad','mae','med','meh','mic','mid','zed','aced','ache','acid','acme','adze','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','cazh','cedi','chad','chai','cham','chem','chez','chia','chid','dace','dame','daze','dice','dime','each','emic','hade','haed','haem','hame','haze','head','hide','hied','iced','idea','idem','mace','mach','made','maid','maze','mead','mech','mica','mice','zeda','ached','aimed','amice','amide','azide','chide','chime','demic','hazed','hemic','maced','mache','maize','mazed','media','medic','miche','chimed','haemic','miched','zaideh'};\r\nswitch ind\r\n\tcase 1\r\n\t\tmult = ' T   d   d   T '; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 24;\r\n\t\tmax_word_corr = {'hazed'};\r\n\tcase 2\r\n\t\tmult = 'T  D  d d  D  T'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 40;\r\n\t\tmax_word_corr = {'zaideh'};\r\n\tcase 3\r\n\t\tmult = 'Q  t  T T  t  Q'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 162;\r\n\t\tmax_word_corr = {'cazh','hazed'};\r\n\tcase 4\r\n\t\tmult = 'Q t T d d T t Q'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 84;\r\n\t\tmax_word_corr = {'zaideh'};\r\nend\r\n[max_score,max_word] = scrabble_scores_11(words,mult,existing_letter);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(max_word,max_word_corr))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":7,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":"2015-03-17T13:10:14.000Z","rescore_all_solutions":false,"group_id":40,"created_at":"2015-03-15T00:22:34.000Z","updated_at":"2026-07-15T09:52:04.000Z","published_at":"2015-03-17T01:47:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem builds on the previous problem, wherein you were provided a letter of an existing word on the board and from which you played a word to find the highest scoring word. See the previous problem for more details.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNow, you will be provided a multiplier character array that represents the fifteen possible squares that can be played on, ranging from seven above the existing letter (in which case the existing letter is the last letter in an eight-letter word) to seven below the existing letter (in which case the existing letter is the first letter in an eight-letter word) with the existing letter fixed in the 8th position. The multipliers are the same as in previous problems:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ * D: double word\\n * T: triple word\\n * Q: quadruple word\\n * d: double letter\\n * t: triple letter\\n * q: quadruple letter]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe center multiplier square will be left blank, since it's already covered by a tile. Write a routine to determine the highest scoring word(s) based on the multiplier squares.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnce again, you will be provided a cell array of strings containing all possible words based on the existing letter and the letters on your tray. In addition to providing the highest score, also provide the word(s) that achieve that score in a cell array. See the test suite for examples. Due to high-scoring tiles, the highest score may not be achieved by the longest word(s).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRelated problems:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrevious problem: 10 -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3082-scrabble-scores-10\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWord score optimization (known letter)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Next problem: 12 -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWord score optimization (first word)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1231,"title":"PACMAT Easy","description":"The Classic PACMAN game brought to Cody.\r\n\r\nPACMAT_Easy is the simple case of clearing the board of Yellow Dots while not bumping into the non-moving ghosts.\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/PACMAT_300.jpg\u003e\u003e\r\n\r\nTo aid in development of your routine, a PACMAT.m file that creates a video has been posted at \u003chttps://sites.google.com/site/razapor/matlab_cody/PACMAT_Easy.m?attredirects=0\u0026d=1 PACMAT_Easy.m\u003e. (Right click, 'save link as'). Using patches (not sprites).\r\n\r\n\r\nAn example video of the first Player \u003chttps://sites.google.com/site/razapor/matlab_cody/pac_s314_motMP4_v004.mp4?attredirects=0\u0026d=1 PACMAT_Easy_Video\u003e  (MP4: Left click and Windows Media Player)\r\n\r\nAlfonso Nieto-Castanon's 298 \u003chttps://sites.google.com/site/razapor/matlab_cody/PACMAT_Easy_ANC_298.mp4?attredirects=0\u0026d=1 PACMAT Video\u003e\r\n\r\nAlfonso employed a Local Optimum Monte-Carlo approach to find a best solution. Solution #8 is the very compact non-apriori PACMAT solver.\r\n\r\n*Inputs:* Map   Definitions: -1=Wall, 0=Empty, 1=Dot, 2=PACMAT, \u003e2=Ghost\r\n\r\n*Output:* Direction  Definitions: 1-Up, 2-Right, 3-Down, 4-Left, 0-No move\r\n\r\n*Scoring:* Total # of Moves to Clear the Yellow Dots\r\n\r\n\r\n*Near Future:* Ghosts will move with various algorithms.\r\n\r\n*Far Future:* Asteroids and Space Invaders","description_html":"\u003cp\u003eThe Classic PACMAN game brought to Cody.\u003c/p\u003e\u003cp\u003ePACMAT_Easy is the simple case of clearing the board of Yellow Dots while not bumping into the non-moving ghosts.\u003c/p\u003e\u003cimg src=\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_300.jpg\"\u003e\u003cp\u003eTo aid in development of your routine, a PACMAT.m file that creates a video has been posted at \u003ca href=\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_Easy.m?attredirects=0\u0026amp;d=1\"\u003ePACMAT_Easy.m\u003c/a\u003e. (Right click, 'save link as'). Using patches (not sprites).\u003c/p\u003e\u003cp\u003eAn example video of the first Player \u003ca href=\"https://sites.google.com/site/razapor/matlab_cody/pac_s314_motMP4_v004.mp4?attredirects=0\u0026amp;d=1\"\u003ePACMAT_Easy_Video\u003c/a\u003e  (MP4: Left click and Windows Media Player)\u003c/p\u003e\u003cp\u003eAlfonso Nieto-Castanon's 298 \u003ca href=\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_Easy_ANC_298.mp4?attredirects=0\u0026amp;d=1\"\u003ePACMAT Video\u003c/a\u003e\u003c/p\u003e\u003cp\u003eAlfonso employed a Local Optimum Monte-Carlo approach to find a best solution. Solution #8 is the very compact non-apriori PACMAT solver.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInputs:\u003c/b\u003e Map   Definitions: -1=Wall, 0=Empty, 1=Dot, 2=PACMAT, \u003e2=Ghost\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e Direction  Definitions: 1-Up, 2-Right, 3-Down, 4-Left, 0-No move\u003c/p\u003e\u003cp\u003e\u003cb\u003eScoring:\u003c/b\u003e Total # of Moves to Clear the Yellow Dots\u003c/p\u003e\u003cp\u003e\u003cb\u003eNear Future:\u003c/b\u003e Ghosts will move with various algorithms.\u003c/p\u003e\u003cp\u003e\u003cb\u003eFar Future:\u003c/b\u003e Asteroids and Space Invaders\u003c/p\u003e","function_template":"function  [newdir]=pacmat(map)\r\n newdir=randi(4);\r\nend\r\n","test_suite":"%%\r\nfeval(@assignin,'caller','score',2000);\r\n%%\r\nmap=[...\r\n      repmat('a',1,28);\r\n      'accccccccccccaacccccccccccca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acccccccccccccccccccccccccca';\r\n      'acaaaacaacaaaaaaaacaacaaaaca';\r\n      'acaaaacaacaaaaaaaacaacaaaaca';\r\n      'accccccaaccccaaccccaacccccca';\r\n      'aaaaaacaaaaabaabaaaaacaaaaaa';\r\n      'aaaaaacaaaaabaabaaaaacaaaaaa';\r\n      'aaaaaacaabbbbbbbbbbaacaaaaaa';\r\n      'aaaaaacaabaaabbaaabaacaaaaaa';\r\n      'aaaaaacaabalbbbblabaacaaaaaa';\r\n      'bbbbbbcbbbabbbbbbabbbcbbbbbb';\r\n      'aaaaaacaabalbbbblabaacaaaaaa';\r\n      'aaaaaacaabaaaaaaaabaacaaaaaa';\r\n      'aaaaaacaabbbbbbbbbbaacaaaaaa';\r\n      'aaaaaacaabaaaaaaaabaacaaaaaa';\r\n      'aaaaaacaabaaaaaaaabaacaaaaaa';\r\n      'accccccccccccaacccccccccccca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acccaacccccccbdcccccccaaccca';\r\n      'aaacaacaacaaaaaaaacaacaacaaa';\r\n      'aaacaacaacaaaaaaaacaacaacaaa';\r\n      'accccccaaccccaaccccaacccccca';\r\n      'acaaaaaaaaaacaacaaaaaaaaaaca';\r\n      'acaaaaaaaaaacaacaaaaaaaaaaca';\r\n      'acccccccccccccccccccccccccca';\r\n      repmat('a',1,28);];\r\n  \r\n  map=map-'b';\r\n  [nr, nc]=size(map);\r\n  mapdelta=[-1 nr 1 -nr]; % Valid as long as not on an edge\r\n  tunnel=find(map(:,1)==0); % tunnelptr\r\n  tunnel=[tunnel tunnel+nr*(nc-1)]; % Entrance/Exit Tunnel\r\n  [pmr, pmc]=find(map==2); % pi 24 row  pj 15 column of map\r\n   ptrpac=find(map==2);\r\n\r\n lives=1; % Lives\r\n  movepac=0;\r\nwhile lives \u0026\u0026 any(mod(map(:),10)==1) \u0026\u0026 movepac\u003c5000 \u0026\u0026 ~isempty(find(map(:)==2))\r\n   while ~isempty(find(map(:)==2)) \u0026\u0026 movepac\u003c5000\r\n     movepac=movepac+1;\r\n\r\n if isempty(find(map==1,1)),break;end % \r\n [curdir]=pacmat(map);\r\n  if curdir==0,continue;end\r\n\r\n if map(ptrpac+mapdelta(curdir))==-1\r\n     % Do nothing - Ran into a Wall\r\n    elseif map(ptrpac+mapdelta(curdir))\u003e2 % ran into ghost\r\n      map(ptrpac)=0; % remove PAC from the board\r\n      lives=0;\r\n      break; % Lose\r\n    else % legal move\r\n      map(ptrpac)=0; % Eat Dot and clear PAC\r\n      ptrpac=ptrpac+mapdelta(curdir);\r\n      if ptrpac==tunnel(1),ptrpac=tunnel(2)-nr;end\r\n      if ptrpac==tunnel(2),ptrpac=tunnel(1)+nr;end\r\n      map(ptrpac)=2;\r\n    end\r\n  end % PAC Move while\r\n  if isempty(find(map==1,1)),break;end % \r\n   if lives==0,break;end\r\n   lives=lives-1;\r\n end % while alive\r\n\r\nfprintf('moves %i\\n',movepac)\r\n\r\nassert(lives\u003e0)\r\nassert(isempty(find(map==1)))\r\n\r\n\r\nfeval( @assignin,'caller','score',floor(min( 2000,movepac )) );","published":true,"deleted":false,"likes_count":4,"comments_count":4,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":33,"created_at":"2013-01-30T04:55:54.000Z","updated_at":"2026-08-12T16:08:25.000Z","published_at":"2013-01-30T05:48:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Classic PACMAN game brought to Cody.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePACMAT_Easy is the simple case of clearing the board of Yellow Dots while not bumping into the non-moving ghosts.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo aid in development of your routine, a PACMAT.m file that creates a video has been posted at\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_Easy.m?attredirects=0\u0026amp;d=1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePACMAT_Easy.m\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. (Right click, 'save link as'). Using patches (not sprites).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn example video of the first Player\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/pac_s314_motMP4_v004.mp4?attredirects=0\u0026amp;d=1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePACMAT_Easy_Video\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (MP4: Left click and Windows Media Player)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAlfonso Nieto-Castanon's 298\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_Easy_ANC_298.mp4?attredirects=0\u0026amp;d=1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePACMAT Video\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAlfonso employed a Local Optimum Monte-Carlo approach to find a best solution. Solution #8 is the very compact non-apriori PACMAT solver.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Map Definitions: -1=Wall, 0=Empty, 1=Dot, 2=PACMAT, \u0026gt;2=Ghost\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Direction Definitions: 1-Up, 2-Right, 3-Down, 4-Left, 0-No move\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Total # of Moves to Clear the Yellow Dots\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNear Future:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Ghosts will move with various algorithms.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFar Future:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Asteroids and Space 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\"}]}"},{"id":44630,"title":"Guess the number I'm thinking of (Part 1)","description":"In this game you are competing against two other people to guess the number that I'm thinking of.\r\nI randomly choose an integer between one and ten (inclusive). I don't provide any clues about the number.\r\nYour first opponent tries to guess the number. They guess randomly.\r\nYour second opponent tries to guess the number. They also guess randomly.\r\nYou try to guess the number. But you guess strategically.\r\nThe winner is the person who guesses my chosen number, or the person who guesses closest to my chosen number. This represents a \"win\".\r\nIf two contestants are equally close, they may share the win, with such a result being declared a \"draw\". (It is a loss for the remaining contestant.) A draw is worth half as much as a win.\r\nEach person hears the guesses stated by any preceding competitors, so you will be aware of the two prior guesses (provided to you as the vector guessesOfOpponents). Moreover, each guess must be unique.\r\nIf everyone guessed randomly, each person should have an equal chance of winning.\r\nIt might seem that you're at a disadvantage, having the last opportunity to guess. But actually you have the advantage of extra knowledge.\r\nBy guessing strategically, you should be able to achieve a success rate of 45% or more, in which\r\nsuccess rate = (wins + draws/2) / games\r\n\r\nRELATED PROBLEM:  \r\nProblem 52323. Guess the number I'm thinking of (Part 2)","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 484px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 242px; transform-origin: 407px 242px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIn this game you are competing against two other people to guess the number that I'm thinking of.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 160px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 80px; transform-origin: 391px 80px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eI randomly choose an\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003einteger\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e between\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eone\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eten\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e (inclusive). I don't provide any clues about the number.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYour first opponent tries to guess the number. They guess randomly.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYour second opponent tries to guess the number. They also guess randomly.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou try to guess the number. But you guess\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estrategically\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20px; text-align: left; transform-origin: 363px 20px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe winner is the person who guesses my chosen number, or the person who guesses closest to my chosen number. This represents a \"win\".\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20px; text-align: left; transform-origin: 363px 20px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIf two contestants are equally close, they may share the win, with such a result being declared a \"draw\". (It is a loss for the remaining contestant.) A draw is worth half as much as a win.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eEach person hears the guesses stated by any preceding competitors, so you will be aware of the two prior guesses (provided to you as the vector\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eguessesOfOpponents\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e). Moreover, each guess must be unique.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIf everyone guessed randomly, each person should have an equal chance of winning.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIt might seem that you're at a disadvantage, having the last opportunity to guess. But actually you have the advantage of extra knowledge.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eBy guessing strategically, you should be able to\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eachieve a success rate of 45% or more\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, in which\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003esuccess rate = (wins + draws/2) / games\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eRELATED PROBLEM:  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 10px; transform-origin: 391px 10px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52323\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 52323. Guess the number I'm thinking of (Part 2)\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = myGuess(guessesOfOpponents)\r\n    y = 42;\r\nend","test_suite":"%% Anti-hacking test\r\nassessFunctionAbsence({'rng', 'RandStream'}, 'FileName','myGuess.m')\r\n\r\n%% Ensure unique guesses of integers, which are in-range\r\nfor j = 1 : 1000\r\n    numberToBeGuessed = randi(10);\r\n    gOO = randperm(10, 2);\r\n    mG = myGuess(gOO);\r\n    assert( mG \u003e= 1  \u0026  mG \u003c= 10 , 'Out of requested range.' )\r\n    u = unique( floor([gOO mG]) );\r\n    assert( length(u) == 3 , 'Your guess must not have been already chosen.' )\r\nend;\r\n\r\n%% maxIts: 20000 = Too small; 30000 = Not quite big enough; 35000 = Just big enough (usually!); 50000 = Big enough (usually!); 100000 = Big enough, plus safety margin \u0026 efficiency incentive (but waste of resources)\r\nmaxIts = 100000;    \r\ntic\r\nfor j = 1 : 10\r\n    WDL = [0 0 0];\r\n    for itn = 1 : maxIts\r\n        numberToBeGuessed = randi(10);\r\n        gOO = randperm(10, 2);\r\n        diffs = abs( [gOO myGuess(gOO)] - numberToBeGuessed );\r\n        winningContestant = find( min(diffs)==diffs );\r\n        if any( winningContestant == 3 ),\r\n            if length(winningContestant) == 1,\r\n                % Win\r\n                WDL(1) = WDL(1) + 1;  \r\n            else\r\n                % Draw\r\n                WDL(2) = WDL(2) + 1;  \r\n            end;\r\n        else\r\n            % Loss\r\n            WDL(3) = WDL(3) + 1;  \r\n        end;\r\n    end;\r\n    successRate = (WDL(1) + WDL(2)/2) / maxIts\r\n    assert( successRate \u003e= 0.45 )\r\nend;\r\ntoc","published":true,"deleted":false,"likes_count":13,"comments_count":6,"created_by":64439,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":83,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2018-05-04T14:00:17.000Z","updated_at":"2026-08-18T14:22:47.000Z","published_at":"2018-05-05T12:29:22.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this game you are competing against two other people to guess the number that I'm thinking of.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI randomly choose an\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einteger\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e between\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eone\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eten\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (inclusive). I don't provide any clues about the number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour first opponent tries to guess the number. They guess randomly.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour second opponent tries to guess the number. They also guess randomly.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou try to guess the number. But you guess\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estrategically\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe winner is the person who guesses my chosen number, or the person who guesses closest to my chosen number. This represents a \\\"win\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf two contestants are equally close, they may share the win, with such a result being declared a \\\"draw\\\". (It is a loss for the remaining contestant.) A draw is worth half as much as a win.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach person hears the guesses stated by any preceding competitors, so you will be aware of the two prior guesses (provided to you as the vector\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eguessesOfOpponents\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e). Moreover, each guess must be unique.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf everyone guessed randomly, each person should have an equal chance of winning.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt might seem that you're at a disadvantage, having the last opportunity to guess. But actually you have the advantage of extra knowledge.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBy guessing strategically, you should be able to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eachieve a success rate of 45% or more\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, in which\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esuccess rate = (wins + draws/2) / games\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRELATED PROBLEM:  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52323\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 52323. Guess the number I'm thinking of (Part 2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":196,"title":"love is an n-letter word","description":"Given a list of *N words*, return the *N-letter word* (choosing one letter from each word) with the property of having the least distance between each pair of two consecutive letters (if there are multiple optimal solutions return any one of them).\r\n\r\nExample: s1 = {'abcd','bcde','cdef','defg'}; should return s2 = 'dddd'; (with total letter-distance = 0)\r\n\r\nExample: s1={'aldfejk','czoa','vwy','abcde'}; should return s2='love'; (with total letter-distance = 27: _|'l'-'o'|_=3 + _|'o'-'v'|_=7 + _|'v'-'e'|_=17 ; compare for example to the possible word 'aave' which has a total letter-distance of 38)\r\n\r\n\r\n\r\n","description_html":"\u003cp\u003eGiven a list of \u003cb\u003eN words\u003c/b\u003e, return the \u003cb\u003eN-letter word\u003c/b\u003e (choosing one letter from each word) with the property of having the least distance between each pair of two consecutive letters (if there are multiple optimal solutions return any one of them).\u003c/p\u003e\u003cp\u003eExample: s1 = {'abcd','bcde','cdef','defg'}; should return s2 = 'dddd'; (with total letter-distance = 0)\u003c/p\u003e\u003cp\u003eExample: s1={'aldfejk','czoa','vwy','abcde'}; should return s2='love'; (with total letter-distance = 27: \u003ci\u003e\u003ctt\u003e'l'-'o'\u003c/tt\u003e\u003c/i\u003e=3 + \u003ci\u003e\u003ctt\u003e'o'-'v'\u003c/tt\u003e\u003c/i\u003e=7 + \u003ci\u003e\u003ctt\u003e'v'-'e'\u003c/tt\u003e\u003c/i\u003e=17 ; compare for example to the possible word 'aave' which has a total letter-distance of 38)\u003c/p\u003e","function_template":"function s2 = gobbledigook(s1)\r\n  s2 = '';\r\nend","test_suite":"%%\r\ns1 = {'abcd','bcde','cdef','defg'}; \r\nassert(isequal(gobbledigook(s1),'dddd'))\r\ns2_correct = 'dddd';\r\n%%\r\ns1 = {'aldfejk','czoa','vwy','abcde'}; \r\nassert(isequal(gobbledigook(s1),'love'))\r\ns2_correct = 'love';\r\n%%\r\ns1 = {'some','help','check','viterbi','algorithm'}; \r\nassert(isequal(gobbledigook(s1),'eeeeg'))\r\ns2_correct = 'eeeeg';\r\n%%\r\ns1 = {'ldjfac','deamv','fka','idlw','pqmfjavs'}; \r\nassert(isequal(gobbledigook(s1),'lmklm')|isequal(gobbledigook(s1),'aaadf'))\r\ns2_correct = 'lmklm';\r\ns2_correct = 'aaadf';\r\n%% \r\n% avoids look-up table hack\r\ns1 = cellfun(@(x)char('a'-1+randi(26,1,5)),cell(1,7),'uniformoutput',false);\r\nassert(all(any(bsxfun(@eq,gobbledigook(s1),cell2mat(cellfun(@(x)x',s1,'uniformoutput',false)))))\u0026all(sum(abs(diff(double(gobbledigook(s1)))))\u003c=sum(abs(diff(double(cell2mat(cellfun(@(x)x(randi(numel(x),1,1000))',s1,'uniformoutput',false))),1,2)),2)));","published":true,"deleted":false,"likes_count":6,"comments_count":5,"created_by":43,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":67,"test_suite_updated_at":"2012-03-08T02:36:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-31T08:36:36.000Z","updated_at":"2026-07-15T17:19:22.000Z","published_at":"2012-03-08T03:14:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a list of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN words\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN-letter word\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (choosing one letter from each word) with the property of having the least distance between each pair of two consecutive letters (if there are multiple optimal solutions return any one of them).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: s1 = {'abcd','bcde','cdef','defg'}; should return s2 = 'dddd'; (with total letter-distance = 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: s1={'aldfejk','czoa','vwy','abcde'}; should return s2='love'; (with total letter-distance = 27:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'l'-'o'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e=3 +\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'o'-'v'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e=7 +\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'v'-'e'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e=17 ; compare for example to the possible word 'aave' which has a total letter-distance of 38)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44345,"title":"MATLAB Counter","description":"Write a function f = counter(x0,b) to construct a counter handle f that counts with an initial value x0 and a step size b. \r\n\r\nE.g.,\r\n\r\n  \u003e\u003e f = counter(0,1)  % Initialize a counter f() with initial_count = 0 and step_size = 1\r\n  \u003e\u003e f()\r\n  ans =\r\n       0\r\n  \u003e\u003e f()\r\n  ans =\r\n       1\r\n  \u003e\u003e f()\r\n  ans =\r\n       2\r\n\r\n\r\n","description_html":"\u003cp\u003eWrite a function f = counter(x0,b) to construct a counter handle f that counts with an initial value x0 and a step size b.\u003c/p\u003e\u003cp\u003eE.g.,\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e\u0026gt;\u0026gt; f = counter(0,1)  % Initialize a counter f() with initial_count = 0 and step_size = 1\r\n\u0026gt;\u0026gt; f()\r\nans =\r\n     0\r\n\u0026gt;\u0026gt; f()\r\nans =\r\n     1\r\n\u0026gt;\u0026gt; f()\r\nans =\r\n     2\r\n\u003c/pre\u003e","function_template":"function y = counter(x,b)\r\n  y = x;\r\nend","test_suite":"%%\r\nassessFunctionAbsence({'regexp','regexpi','regexprep','str2num'},'FileName','counter.m')\r\n\r\n%%\r\nf = counter(0,1);\r\nassert(isequal(f(),0))\r\nassert(isequal(f(),1))\r\nassert(isequal(2,f()))\r\nassert(isequal(3,f()))\r\n\r\n%%\r\nf = counter(1,0);\r\nassert(isequal(f(),1))\r\nassert(isequal(f(),1))\r\nassert(isequal(1,f()))\r\nassert(isequal(1,f()))\r\n\r\n%%\r\nf = counter(10,2);\r\nassert(isequal(f(),10))\r\nassert(isequal(f(),12))\r\nassert(isequal(14,f()))\r\nassert(isequal(16,f()))\r\n\r\n%%\r\nf = counter(0,5);\r\ny_correct = [0, 5, 10, 15, 20, 55];\r\nassert(isequal([f() f() f() f() f() f()+f()],y_correct))\r\n\r\n%%\r\nx0 = randi(10);\r\nb = randi(10);\r\nf = counter(x0,b);\r\ny_correct = x0 + (0:1000)*b;\r\nassert(isequal(arrayfun(@(n)f(),0:1000),y_correct))","published":true,"deleted":false,"likes_count":23,"comments_count":9,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":305,"test_suite_updated_at":"2017-10-17T00:19:49.000Z","rescore_all_solutions":false,"group_id":34,"created_at":"2017-09-24T01:58:21.000Z","updated_at":"2026-05-28T04:25:58.000Z","published_at":"2017-10-16T01:45:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function f = counter(x0,b) to construct a counter handle f that counts with an initial value x0 and a step size b.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eE.g.,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e f = counter(0,1)  % Initialize a counter f() with initial_count = 0 and step_size = 1\\n\u003e\u003e f()\\nans =\\n     0\\n\u003e\u003e f()\\nans =\\n     1\\n\u003e\u003e f()\\nans =\\n     2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":81,"title":"Mandelbrot Numbers","description":"The \u003chttp://en.wikipedia.org/wiki/Mandelbrot_set Mandelbrot Set\u003e is built around a simple iterative equation.\r\n\r\n z(1)   = c\r\n z(n+1) = z(n)^2 + c\r\n\r\nFor any complex c, we can continue this iteration until either\r\nabs(z(n+1)) \u003e 2 or n == lim, then return the iteration count n.\r\n\r\n* If c = 0   and lim = 3, then z = [0 0 0] and n = 3.\r\n* If c = 1   and lim = 5, then z = [1 2], and n = length(z) or 2.\r\n* If c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\r\n\r\nFor a matrix of complex numbers C, return a corresponding matrix N such\r\nthat each element of N is the iteration count n for each complex number c\r\nin the matrix C, subject to the iteration count limit of lim.\r\n\r\nIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\r\n\r\nCleve Moler has a whole chapter on the Mandelbrot set in his book Experiments\r\nwith MATLAB: \u003chttp://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf \r\nChapter 10, Mandelbrot Set (PDF)\u003e","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 296.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 148.083px; transform-origin: 407px 148.083px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.5px 8px; transform-origin: 12.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://en.wikipedia.org/wiki/Mandelbrot_set\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMandelbrot Set\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133px 8px; transform-origin: 133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is built around a simple iterative equation.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 44px 8.5px; transform-origin: 44px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e z(1)   = c\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e z(n+1) = z(n)^2 + c\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379.5px 8px; transform-origin: 379.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor any complex c, we can continue this iteration until either abs(z(n+1)) \u0026gt; 2 or n == lim, then return the iteration count n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 142.5px 8px; transform-origin: 142.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 0 and lim = 3, then z = [0 0 0] and n = 3.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 176.5px 8px; transform-origin: 176.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 1 and lim = 5, then z = [1 2], and n = length(z) or 2.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 226.5px 8px; transform-origin: 226.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377px 8px; transform-origin: 377px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a matrix of complex numbers C, return a corresponding matrix N such that each element of N is the iteration count n for each complex number c in the matrix C, subject to the iteration count limit of lim.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 149.5px 8px; transform-origin: 149.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127px 8px; transform-origin: 127px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCleve Moler has a whole chapter on the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/exm/chapters/mandelbrot.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMandelbrot set\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38px 8px; transform-origin: 38px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in his book \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/moler/exm/chapters.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eExperiments with MATLAB\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function N = mandelbrot(C,lim)\r\n  N = ones(size(C));\r\nend","test_suite":"%%\r\nC = 0;\r\nlim = 5;\r\nN_correct = 5;\r\nassert(isequal(mandelbrot(C,lim),N_correct))\r\n\r\n%%\r\nC = [0 0.5; 1 4];\r\nlim = 5;\r\nN_correct = [5 4; 2 1];\r\nassert(isequal(mandelbrot(C,lim),N_correct))\r\n\r\n%%\r\ni = sqrt(-1);\r\nC = [i 1 -2*i -2];\r\nlim = 10;\r\nN_correct = [10 2 1 10];\r\nassert(isequal(mandelbrot(C,lim),N_correct))","published":true,"deleted":false,"likes_count":17,"comments_count":9,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1783,"test_suite_updated_at":"2012-01-26T03:21:20.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:28.000Z","updated_at":"2026-10-20T11:26:19.000Z","published_at":"2012-01-18T01:00:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Mandelbrot_set\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot Set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is built around a simple iterative equation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ z(1)   = c\\n z(n+1) = z(n)^2 + c]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor any complex c, we can continue this iteration until either abs(z(n+1)) \u0026gt; 2 or n == lim, then return the iteration count n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 0 and lim = 3, then z = [0 0 0] and n = 3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 1 and lim = 5, then z = [1 2], and n = length(z) or 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a matrix of complex numbers C, return a corresponding matrix N such that each element of N is the iteration count n for each complex number c in the matrix C, subject to the iteration count limit of lim.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCleve Moler has a whole chapter on the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/exm/chapters/mandelbrot.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in his book \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/moler/exm/chapters.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eExperiments with MATLAB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42580,"title":"Conic equation","description":"A conic of revolution (around the |z| axis) can be defined by the equation\r\n\r\n   s^2 – 2*R*z + (k+1)*z^2 = 0\r\n\r\nwhere |s^2=x^2+y^2|, |R| is the vertex radius of curvature, and |k| is the conic constant: |k\u003c-1| for a hyperbola, |k=-1| for a parabola, |-1\u003ck\u003c0| for a tall ellipse, |k=0| for a sphere, and |k\u003e0| for a short ellipse.\r\n\r\nWrite a function |z=conic(s,R,k)| to calculate height |z| as a function of radius |s| for given |R| and |k|.  Choose the branch of the solution that gives |z=s^2/(2*R)+...| for small values of |s|.  This defines a concave surface for |R\u003e0| and a convex surface for |R\u003c0|.  \r\n\r\nThe trick is to get full machine precision for all values of |s| and |R|.  The test suite will require a relative error less than |4*eps|, where |eps| is the machine precision.\r\n\r\nHint (added 2015/09/03): the straightforward solution is \r\n\r\n   z = (R-sqrt(R^2-(k+1)*s^2))/(k+1), \r\n\r\nbut this does not work if |k=-1|, gives the wrong branch of the solution if |R\u003c0|, and is subject to severe roundoff error if |s^2| is small compared to |R^2|.  It is possible, however, to find a mathematically equivalent form of the solution that solves all three problems at once.\r\n","description_html":"\u003cp\u003eA conic of revolution (around the \u003ctt\u003ez\u003c/tt\u003e axis) can be defined by the equation\u003c/p\u003e\u003cpre\u003e   s^2 – 2*R*z + (k+1)*z^2 = 0\u003c/pre\u003e\u003cp\u003ewhere \u003ctt\u003es^2=x^2+y^2\u003c/tt\u003e, \u003ctt\u003eR\u003c/tt\u003e is the vertex radius of curvature, and \u003ctt\u003ek\u003c/tt\u003e is the conic constant: \u003ctt\u003ek\u0026lt;-1\u003c/tt\u003e for a hyperbola, \u003ctt\u003ek=-1\u003c/tt\u003e for a parabola, \u003ctt\u003e-1\u0026lt;k\u0026lt;0\u003c/tt\u003e for a tall ellipse, \u003ctt\u003ek=0\u003c/tt\u003e for a sphere, and \u003ctt\u003ek\u0026gt;0\u003c/tt\u003e for a short ellipse.\u003c/p\u003e\u003cp\u003eWrite a function \u003ctt\u003ez=conic(s,R,k)\u003c/tt\u003e to calculate height \u003ctt\u003ez\u003c/tt\u003e as a function of radius \u003ctt\u003es\u003c/tt\u003e for given \u003ctt\u003eR\u003c/tt\u003e and \u003ctt\u003ek\u003c/tt\u003e.  Choose the branch of the solution that gives \u003ctt\u003ez=s^2/(2*R)+...\u003c/tt\u003e for small values of \u003ctt\u003es\u003c/tt\u003e.  This defines a concave surface for \u003ctt\u003eR\u0026gt;0\u003c/tt\u003e and a convex surface for \u003ctt\u003eR\u0026lt;0\u003c/tt\u003e.\u003c/p\u003e\u003cp\u003eThe trick is to get full machine precision for all values of \u003ctt\u003es\u003c/tt\u003e and \u003ctt\u003eR\u003c/tt\u003e.  The test suite will require a relative error less than \u003ctt\u003e4*eps\u003c/tt\u003e, where \u003ctt\u003eeps\u003c/tt\u003e is the machine precision.\u003c/p\u003e\u003cp\u003eHint (added 2015/09/03): the straightforward solution is\u003c/p\u003e\u003cpre\u003e   z = (R-sqrt(R^2-(k+1)*s^2))/(k+1), \u003c/pre\u003e\u003cp\u003ebut this does not work if \u003ctt\u003ek=-1\u003c/tt\u003e, gives the wrong branch of the solution if \u003ctt\u003eR\u0026lt;0\u003c/tt\u003e, and is subject to severe roundoff error if \u003ctt\u003es^2\u003c/tt\u003e is small compared to \u003ctt\u003eR^2\u003c/tt\u003e.  It is possible, however, to find a mathematically equivalent form of the solution that solves all three problems at once.\u003c/p\u003e","function_template":"function z=conic(s,R,k)\r\nz=0;\r\nend","test_suite":"%%\r\nR=5;\r\nk=-1;\r\ns=-5:5;\r\nz=[25 16 9 4 1 0 1 4 9 16 25]/10;\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=-5;\r\nk=-1;\r\ns=-5:5;\r\nz=-[25 16 9 4 1 0 1 4 9 16 25]/10;\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=6;\r\nk=0;\r\ns=0:0.125:2;\r\nz=[0 0.001302224649086391 0.005210595859100573 ...\r\n   0.01173021649825800 0.02086962844930099 ...\r\n   0.03264086885999461 0.04705955010467117 ...\r\n   0.06414496470811713 0.08392021690038396 ...\r\n   0.1064123829368584 0.1316527028472488 ...\r\n   0.1596768068881667 0.1905249806888747 ...\r\n   0.2242424739260392 0.2608798583755018 ...\r\n   0.3004934424110011 0.3431457505076198];\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=6800;\r\nk=-2;\r\ns=10.^(-9:9);\r\nz=[7.352941176470588e-23 7.352941176470588e-21 ...\r\n   7.352941176470588e-19 7.352941176470588e-17 ...\r\n   7.352941176470588e-15 7.352941176470588e-13 ...\r\n   7.352941176470548e-11 7.352941176466613e-9 ...\r\n   7.352941176073046e-7 0.00007352941136716365 ...\r\n   0.007352937201052538 0.7352543677216725 ...\r\n   73.13611097583313 5292.973166264779 93430.93334894173 ...\r\n   993223.1197327390 9.993202311999733e6 9.99932002312e7 ...\r\n   9.9999320002312e8];\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=exp(1);\r\nk=pi;\r\ns=10.^(-7:0);\r\nz=[1.839397205857214e-15 1.839397205857469e-13 ...\r\n   1.839397205882986e-11 1.839397208434684e-09 ...\r\n   1.839397463604480e-07 0.00001839422981299153 ...\r\n   0.001841981926630790 0.2212216213343403];\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nt=fileread('conic.m');\r\nassert(isempty(findstr(t,'roots')))\r\nassert(isempty(findstr(t,'fzero')))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":245,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":37,"created_at":"2015-08-26T21:39:35.000Z","updated_at":"2026-05-25T04:09:40.000Z","published_at":"2015-08-26T22:21:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA conic of revolution (around the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e axis) can be defined by the equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   s^2 – 2*R*z + (k+1)*z^2 = 0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es^2=x^2+y^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the vertex radius of curvature, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the conic constant:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u0026lt;-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a hyperbola,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek=-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a parabola,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-1\u0026lt;k\u0026lt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a tall ellipse,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek=0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a sphere, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u0026gt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a short ellipse.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez=conic(s,R,k)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to calculate height\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as a function of radius\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for given\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Choose the branch of the solution that gives\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez=s^2/(2*R)+...\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for small values of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. This defines a concave surface for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u0026gt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and a convex surface for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u0026lt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe trick is to get full machine precision for all values of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The test suite will require a relative error less than\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e4*eps\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eeps\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the machine precision.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint (added 2015/09/03): the straightforward solution is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   z = (R-sqrt(R^2-(k+1)*s^2))/(k+1),]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ebut this does not work if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek=-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, gives the wrong branch of the solution if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u0026lt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and is subject to severe roundoff error if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is small compared to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. It is possible, however, to find a mathematically equivalent form of the solution that solves all three problems at once.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44963,"title":"Mask Generation Function (MGF1) for PKCS #1 Standard utilizing Optimal Asymmetric Encryption Padding for RSA Cryptography","description":"Create Mask Generation Function (MGF1) from PKCS #1 v2.2 standard (B.2.1 page 50) at below link. Input will be character array (mgfSeed) which will need to be converted to octet array using UTF-8 representation. Output must be octet array (uint8) of length, maskLen (input). Hashing must use SHA-1 (160 - 20 byte).\r\n\r\nFor example:\r\n\r\n  mgfSeed = 'I like to swim.';%input\r\n  maskLen = 20;%input\r\n  mask = [170,251,101,210,23,101,10,242,193,163,174,148,104,138,228,245,52,234,0,195];%output\r\n\r\n\r\n\u003chttps://www.emc.com/collateral/white-papers/h11300-pkcs-1v2-2-rsa-cryptography-standard-wp.pdf\u003e","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 194px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 97px; transform-origin: 407px 97px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCreate Mask Generation Function (MGF1) from PKCS #1 v2.2 standard (B.2.1) at below link. Input will be character array (mgfSeed) which will need to be converted to octet array using UTF-8 representation. Output must be octet array (uint8) of length, maskLen (input). Hashing must use SHA-1 (160 - 20 byte).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 60px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 30px; transform-origin: 404px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003emgfSeed = \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); \"\u003e'I like to swim.'\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e;\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration: none; text-decoration-color: rgb(2, 128, 9); \"\u003e%input\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003emaskLen = 20;\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration: none; text-decoration-color: rgb(2, 128, 9); \"\u003e%input\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003emask = [170,251,101,210,23,101,10,242,193,163,174,148,104,138,228,245,52,234,0,195];\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration: none; text-decoration-color: rgb(2, 128, 9); \"\u003e%output\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSee: https://www.foo.be/docs/opensst/ref/pkcs/pkcs-1/pkcs-1v2-1d1.pdf\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function mask = mgf(mgfSeed,maskLen)\r\n    mask = []%octet array of length maskLen\r\nend","test_suite":"%%\r\nmgfSeed = 'I like to swim.';\r\nmaskLen = 20;\r\nmask = [170,251,101,210,23,101,10,242,193,163,174,148,104,138,228,245,52,234,0,195];\r\nassert(isequal(mgf(mgfSeed,maskLen),mask))\r\n%%\r\nmgfSeed = 'People who succeed have momentum. The more they succeed, the more they want to succeed and the more they find a way to succeed. Similarly, when someone is failing, the tendency is to get on a downward spiral that can even become a self-fulfilling prophecy.';\r\nmaskLen = 825;\r\nmask = [40    55   251    83   143   211    49    16    87    56   109   116    17   188    72    54   231    67   125   182   223    53   149    36   246   233    71   113   113    29   176    61    74    77   205   167   179    99   172   172   212   249    53   148    13    89   253     3    85     0   155   181    94    15     8   122   120    92    29   229   229    46   192   162   252   119   243    94    52    12   133    98   161   249   152    68    69    22 156   155   229   132    30   163   102    90   217   160    36    53   185   128    74   224   105   214   134    90   188   101    98   220    43   162   251   183    72    54   219     4    44   185   199   193    31    42   129   112    74    25    81   133    70   156    38   225   243    24    50   132    79   130    42    72   145   158   105   253   190    62    73   107    95   133    78   238   214    39    88   245    40    46   166   201   173   209   234   194     3   117   226    32   176    12   139    83   211    67   101    99   174   126   103   130    83    56   157    52    76    21   189    99   217    43   150    92   219   148   173   138   184   183   203    62   231   125    42    79    29   248    30    26   127    50     9    31   219   212   160   157   243    15    52   217     7   144    43   241    70    98   247   231   174   111    96    91   108    59   164   146    77   180   212   155   165    18   150   198   100   233   255   129    44   170   150   243   244   126   203   255   231    28    94    77    58   198   147    84   212   248    36    34   107   210    77    79    80   224    24   126    88   125   255    11   124   227    44   253   242   234    59   176   108   146   170   132    20   128   230   141   187    81   139    26   119    47   159     8   182    40    94   213   107   223    21   187    35     1    40   145   154    92   218   252    46   201   203    65    48    94   118   110     5   158   212    19   129     9    59   124    19   190   201    55   141   124   210    85   240    34   150    81   154    11     3   116   204    37    73    39   169   234    50   241   131    94     9   133     0   209   190   171   206    93   165   145   142   117   230    34   245   223   205   153   227   202     3   218    56   163   203   137    46   114    78   248   196   136    19   177   126    95   231   213   251   130    39    57    59   228   251    73    48     9   109    11   172   152   223   120   153   108   233    76   117   219     8     6   124    44     7   249   116    43   198    98    55   235    52    47   146   239    76   142    88    19    64   169   209   206   255   101    91   197    36   180   253    52    54    63   198    63   113    58    43   229   141    59     4   147    34   200     7   184   108   176   153    95    94    18   235   178   160    51    63   154   227    39   231    71   246   109    13   199   185   220   180    50   146    85   194   176   175   159   103   177    47   149   252   182    33   224   226     1   232   167    94    93   202    55    60   201   228   107   135   142    22   165   168   124   219   216    34   230   174   179    66    67    91    92   186    30    48     9   177   192   254   190   236    52    84   114   255     3    81   150   112   131    49   157    48   243   218    11   132    40    13    68   214   159    36   109   152   219    32   219   193   182    69    37   104   217   115    54   158    79    90     3   223   116   127     8    28   233   223   194    30   241   180    45   209    77   180   184    52   132   164    49   206    50    57   149   118   105    44    25   212   141   253   150    45   244    73   203    10   137   161   118    49   165   248   105   215    58    90    67   180    78    22   135   102   173   139    62    31    63    82   187    78    47     2   176   144    83    22   143    31   155     8   160    12   252   164    52   159   102   113    95   132    49   168   194   137    32   131   189   139    77   143   248    36    30   154   239   163   149    86     9   178   122     6   248    25   208   211   142    59    23    72    43   158   195   244   232   229   245   148    49   163    28    81    93   106    33   239   249    26   220    73    65   112   249   254   251    91   106   204   113    10    59    34   114   189   185   188   181   100   185    22   188   221   187   109   170    35    57   181   234   157   230   206   169    97   140    51   170   128   215   188    14    50   190   167    41   173    19    10    98   165    12    77    49    21    33   147    93    84   163   106   151   234    76   252    91   165   248   223   136    85   124   174    90   188   130   174    83    92   181   134    65    91   105    15   103    91    15    27   201   162    58    84   164    33   137    63     0    84     0    78   180    31   218    47    84    43    13    35   122   117   205    59    81   146    97    14];\r\nassert(isequal(mgf(mgfSeed,maskLen),mask))\r\n%%\r\nmgfSeed = 'First, have a definite, clear practical ideal; a goal, an objective. Second, have the necessary means to achieve your ends; wisdom, money, materials, and methods.';\r\nmaskLen = 300;\r\nmask = [96   185   223   209   149    51   224   128   249   139    57   249   190    69   199   132    37    24    75   127    98    59   231   206    13    83    79   111   181   220   204   120    27   178   155   116   155    11   157   112    10   195   106     4   127   146   101   112   197    29    54    45    14    78    16   100     1   111   156    44   138   141   219   101   171     1   126   254    60    82   214    63    13    94   227   238    64   173    93   142     3   224    63    76     8   190   105     8    77   113   250   243   249    82    56   124   129   116   121   131   207   116    80   185    72   184   244   232   236   127    37   195   236   163   176   245    65    48   169   131    19    36   208   178   184   150   188    50   221    83   132   241    73   205    23     9    41    74    65   251    10    21   133   150   101    15    42   153   164   197   136    19   113   134   153   247    10   161   221   184   195   215   253   149   223    83   180   148   198     4    53   112   114    39    18   132   254   170   130    61     6   158   224   166    76   187   190   128    14   251   158   218   192    68    46   210   199   231   120    57   212    10   107     2    50    37   110    30    87    48     2   134    81   165   107    95   250   206    98    26    45   102   173    46    85   103   137     4   140   154   236   142   125   211    28   164    94    41     8    70   215    10    13   140   139    97   205    60   212   205    35   175   235   158    88   165    40    41   187   215    72   172    97   159   119    79    80    31   128   121   108    94   219   216    77   209   184   244    90   238   182   207   244    52   248     6   220   175   117   122   236   228   219    42    49   196   186    12    19    95];\r\nassert(isequal(mgf(mgfSeed,maskLen),mask))","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2019-09-06T22:10:21.000Z","updated_at":"2026-05-25T02:42:38.000Z","published_at":"2019-09-06T22:31:17.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate Mask Generation Function (MGF1) from PKCS #1 v2.2 standard (B.2.1) at below link. Input will be character array (mgfSeed) which will need to be converted to octet array using UTF-8 representation. Output must be octet array (uint8) of length, maskLen (input). Hashing must use SHA-1 (160 - 20 byte).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[mgfSeed = 'I like to swim.';%input\\nmaskLen = 20;%input\\nmask = [170,251,101,210,23,101,10,242,193,163,174,148,104,138,228,245,52,234,0,195];%output]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee: https://www.foo.be/docs/opensst/ref/pkcs/pkcs-1/pkcs-1v2-1d1.pdf\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44765,"title":"Lights Out 11 - 5x5, with wrapping, x moves","description":"\u003chttps://en.wikipedia.org/wiki/Lights_Out_(game) Lights Out\u003e is a logic game wherein all lights need to be turned off to complete each board. See \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44751-lights-out-1-5x5-3-moves the first problem in the series\u003e for an introduction.\r\n\r\nThis problem contains boards that each require any number of moves to solve. However, now wrapping of the lights occurs. For example, if \r\n\r\n board = [1 0 0 0 1  \r\n          1 1 1 0 1  \r\n          0 1 1 1 0  \r\n          1 1 1 0 0  \r\n          0 0 0 1 1]\r\n\r\nthe answer is:\r\n\r\n moves = [2 4 13 25]\r\n\r\nPrev.: \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44764 5x5, wrapping, 6 moves\u003e — \r\nNext: \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44766 5x5, 3 stages, \u003c7 moves\u003e","description_html":"\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Lights_Out_(game)\"\u003eLights Out\u003c/a\u003e is a logic game wherein all lights need to be turned off to complete each board. See \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44751-lights-out-1-5x5-3-moves\"\u003ethe first problem in the series\u003c/a\u003e for an introduction.\u003c/p\u003e\u003cp\u003eThis problem contains boards that each require any number of moves to solve. However, now wrapping of the lights occurs. For example, if\u003c/p\u003e\u003cpre\u003e board = [1 0 0 0 1  \r\n          1 1 1 0 1  \r\n          0 1 1 1 0  \r\n          1 1 1 0 0  \r\n          0 0 0 1 1]\u003c/pre\u003e\u003cp\u003ethe answer is:\u003c/p\u003e\u003cpre\u003e moves = [2 4 13 25]\u003c/pre\u003e\u003cp\u003ePrev.: \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44764\"\u003e5x5, wrapping, 6 moves\u003c/a\u003e — \r\nNext: \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44766\"\u003e5x5, 3 stages, \u0026lt;7 moves\u003c/a\u003e\u003c/p\u003e","function_template":"function moves = lights_out_11(board) % 5x5 board, with wrapping, any number of moves\r\n moves = board;\r\nend","test_suite":"%% \r\n board = [1 0 0 0 1  \r\n          1 1 1 0 1  \r\n          0 1 1 1 0  \r\n          1 1 1 0 0  \r\n          0 0 0 1 1];\r\nmoves = lights_out_11(board); % [2 4 13 25]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1);\r\nb1(1,5) = 1; b1(5,1) = 1; b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b2; b2,b1,b2,b3,b3; b3,b2,b1,b2,b3; b3,b3,b2,b1,b2; b2,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\n\r\n%% \r\n board = [1 1 0 1 1  \r\n          1 0 0 0 1  \r\n          0 0 0 0 0  \r\n          1 0 0 0 1  \r\n          1 1 0 1 1];\r\nmoves = lights_out_11(board); % [1 5 21 25]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1);\r\nb1(1,5) = 1; b1(5,1) = 1; b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b2; b2,b1,b2,b3,b3; b3,b2,b1,b2,b3; b3,b3,b2,b1,b2; b2,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\n\r\n%% \r\n board = [0 1 0 1 0  \r\n          1 0 1 0 1  \r\n          0 1 0 1 0  \r\n          1 0 1 0 1  \r\n          0 1 0 1 0];\r\nmoves = lights_out_11(board); % [2 6 8 12 14 18 20 24]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1);\r\nb1(1,5) = 1; b1(5,1) = 1; b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b2; b2,b1,b2,b3,b3; b3,b2,b1,b2,b3; b3,b3,b2,b1,b2; b2,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\n\r\n%% \r\n board = [1 1 0 0 0  \r\n          0 1 0 1 1  \r\n          0 0 0 0 1  \r\n          0 0 0 1 1  \r\n          1 0 0 1 1];\r\nmoves = lights_out_11(board); % [3 7 17 21 23:25]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1);\r\nb1(1,5) = 1; b1(5,1) = 1; b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b2; b2,b1,b2,b3,b3; b3,b2,b1,b2,b3; b3,b3,b2,b1,b2; b2,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\n\r\n%% \r\n board = [0 1 1 1 0  \r\n          1 1 0 1 1  \r\n          1 0 1 0 1  \r\n          1 1 0 1 1  \r\n          0 1 1 1 0];\r\nmoves = lights_out_11(board); % [7:9 12:14 17:19]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1);\r\nb1(1,5) = 1; b1(5,1) = 1; b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b2; b2,b1,b2,b3,b3; b3,b2,b1,b2,b3; b3,b3,b2,b1,b2; b2,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\n\r\n%% \r\n board = [0 1 1 1 0  \r\n          0 1 1 1 0  \r\n          0 1 1 1 0  \r\n          0 1 1 1 0  \r\n          0 1 1 1 0];\r\nmoves = lights_out_11(board); % [11:15]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1);\r\nb1(1,5) = 1; b1(5,1) = 1; b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b2; b2,b1,b2,b3,b3; b3,b2,b1,b2,b3; b3,b3,b2,b1,b2; b2,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\n\r\n%% \r\n board = [1 1 1 0 0  \r\n          0 0 1 0 0  \r\n          1 1 1 1 1  \r\n          1 0 0 1 0  \r\n          1 1 0 1 0];\r\nmoves = lights_out_11(board); % [9 11 14 21 23 25]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1);\r\nb1(1,5) = 1; b1(5,1) = 1; b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b2; b2,b1,b2,b3,b3; b3,b2,b1,b2,b3; b3,b3,b2,b1,b2; b2,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\n\r\n%% \r\n board = [1 1 0 1 1  \r\n          1 1 0 1 1  \r\n          0 0 1 0 0  \r\n          1 1 0 1 1  \r\n          1 1 0 1 1];\r\nmoves = lights_out_11(board); % on your own\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1);\r\nb1(1,5) = 1; b1(5,1) = 1; b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b2; b2,b1,b2,b3,b3; b3,b2,b1,b2,b3; b3,b3,b2,b1,b2; b2,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\n\r\n%% \r\n board = [0 0 1 0 1  \r\n          0 0 1 0 1  \r\n          0 0 1 0 1  \r\n          0 0 1 0 1  \r\n          0 0 1 0 1];\r\nmoves = lights_out_11(board);\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1);\r\nb1(1,5) = 1; b1(5,1) = 1; b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b2; b2,b1,b2,b3,b3; b3,b2,b1,b2,b3; b3,b3,b2,b1,b2; b2,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\n\r\n%% \r\n board = [1 0 0 0 1  \r\n          0 1 1 1 0  \r\n          0 1 1 1 0  \r\n          0 1 1 1 0  \r\n          1 0 0 0 1];\r\nmoves = lights_out_11(board);\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1);\r\nb1(1,5) = 1; b1(5,1) = 1; b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b2; b2,b1,b2,b3,b3; b3,b2,b1,b2,b3; b3,b3,b2,b1,b2; b2,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":624,"created_at":"2018-10-31T16:37:46.000Z","updated_at":"2026-05-25T02:30:59.000Z","published_at":"2019-05-02T12:20:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Lights_Out_(game)\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLights Out\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a logic game wherein all lights need to be turned off to complete each board. See\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44751-lights-out-1-5x5-3-moves\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ethe first problem in the series\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for an introduction.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem contains boards that each require any number of moves to solve. However, now wrapping of the lights occurs. For example, if\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ board = [1 0 0 0 1  \\n          1 1 1 0 1  \\n          0 1 1 1 0  \\n          1 1 1 0 0  \\n          0 0 0 1 1]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe answer is:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ moves = [2 4 13 25]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrev.:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44764\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e5x5, wrapping, 6 moves\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e — Next:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44766\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e5x5, 3 stages, \u0026lt;7 moves\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44263,"title":"Multivariate polynomials - emulate symbolic form","description":"In \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44262-multivariate-polynomials-overload-multiplication Problem 44262\u003e I asked you to create a class |mPoly| with overloaded multiplication, so a product of two polynomials can be expressed in the form |p = p1*p2|. However, the method of constructing these polynomials is still somewhat unintuitive. In the \u003chttps://www.mathworks.com/products/symbolic.html Symbolic Math Toolbox\u003e, one can simply define some variables,\r\n\r\n  syms x y z\r\n\r\nand then create a polynomial:\r\n\r\n  p = 2*x*y + 3*x^5*z;\r\n\r\nWe would like to do something like that here. As a start, create a class |mPolySym| with properties |exponents| and |coefficients|, and |varnames|,  where the first two properties are the same as in previous problems and |varnames| is a \u003chttps://www.mathworks.com/help/matlab/characters-and-strings.html string array\u003e. The constructor should accept a numeric, char or string input, e.g.,\r\n\r\n  x = mPolySym('x')\r\n\r\n  x = \r\n\r\n  mPolySym with properties:\r\n\r\n        varnames: \"x\"\r\n       exponents: 1\r\n    coefficients: 1\r\n\r\n  r = mPolySym(pi)\r\n\r\n  r = \r\n\r\n  mPolySym with properties:\r\n\r\n        varnames: [0×0 string]\r\n       exponents: 1\r\n    coefficients: 3.1416\r\n\r\nAlso modify the method |mtimes| from the previous problem so it can multiply polynomials with different variable names.","description_html":"\u003cp\u003eIn \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44262-multivariate-polynomials-overload-multiplication\"\u003eProblem 44262\u003c/a\u003e I asked you to create a class \u003ctt\u003emPoly\u003c/tt\u003e with overloaded multiplication, so a product of two polynomials can be expressed in the form \u003ctt\u003ep = p1*p2\u003c/tt\u003e. However, the method of constructing these polynomials is still somewhat unintuitive. In the \u003ca href = \"https://www.mathworks.com/products/symbolic.html\"\u003eSymbolic Math Toolbox\u003c/a\u003e, one can simply define some variables,\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003esyms x y z\r\n\u003c/pre\u003e\u003cp\u003eand then create a polynomial:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ep = 2*x*y + 3*x^5*z;\r\n\u003c/pre\u003e\u003cp\u003eWe would like to do something like that here. As a start, create a class \u003ctt\u003emPolySym\u003c/tt\u003e with properties \u003ctt\u003eexponents\u003c/tt\u003e and \u003ctt\u003ecoefficients\u003c/tt\u003e, and \u003ctt\u003evarnames\u003c/tt\u003e,  where the first two properties are the same as in previous problems and \u003ctt\u003evarnames\u003c/tt\u003e is a \u003ca href = \"https://www.mathworks.com/help/matlab/characters-and-strings.html\"\u003estring array\u003c/a\u003e. The constructor should accept a numeric, char or string input, e.g.,\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ex = mPolySym('x')\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ex = \r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003emPolySym with properties:\r\n\u003c/pre\u003e\u003cpre\u003e        varnames: \"x\"\r\n       exponents: 1\r\n    coefficients: 1\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003er = mPolySym(pi)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003er = \r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003emPolySym with properties:\r\n\u003c/pre\u003e\u003cpre\u003e        varnames: [0×0 string]\r\n       exponents: 1\r\n    coefficients: 3.1416\u003c/pre\u003e\u003cp\u003eAlso modify the method \u003ctt\u003emtimes\u003c/tt\u003e from the previous problem so it can multiply polynomials with different variable names.\u003c/p\u003e","function_template":"classdef mPolySym\r\n    properties\r\n        varnames\r\n        exponents\r\n        coefficients\r\n    end\r\n    \r\n    methods\r\n        function p = mPolySym(s)\r\n        end\r\n        \r\n        function p = mtimes(p1,p2)\r\n        end            \r\n    end\r\n    \r\nend\r\n\r\n","test_suite":"%% Test mPolySym\r\nfiletext = fileread('mPolySym.m');\r\nassert(~contains(filetext,'regexp'))\r\n\r\n\r\n%%\r\nr = randi(1000);\r\nx = mPolySym(r);\r\nassert(isempty(x.varnames))\r\nassert(isequal(x.exponents,0))\r\nassert(isequal(x.coefficients,r))\r\n\r\n%%\r\nr = randi(1000);\r\nx = mPolySym('x');\r\ny = r*x;\r\nassert(isequal(y.varnames,\"x\"))\r\nassert(isequal(y.exponents,1))\r\nassert(isequal(y.coefficients,r))\r\nassert(isequal(r*x,x*r))\r\n\r\n%%\r\nx = mPolySym('x');\r\ny = mPolySym(\"y\");\r\nz = mPolySym('z');\r\nw = x*y*z;\r\nassert(isequal(w.varnames,[\"x\" \"y\" \"z\"]))\r\nassert(isequal(w.exponents,[1 1 1]))\r\nassert(isequal(w.coefficients,1))\r\n\r\n%%\r\nm = randi(5);\r\nn = randi(4);\r\nx = mPolySym(\"x\");\r\ny = mPolySym(\"y\");\r\np = [repmat(x,1,m) repmat(y,1,n)];\r\np = p(randperm(length(p)));\r\nr = randi(1000);\r\np_prod = r;\r\nfor ii=1:length(p)\r\n    p_prod = p_prod*p(ii);\r\nend\r\ns = randi(1000);\r\np_prod = p_prod*s;\r\nassert(isequal(p_prod.varnames,[\"x\" \"y\"]))\r\nassert(isequal(p_prod.exponents,[m n]))\r\nassert(isequal(p_prod.coefficients,r*s))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":1011,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-07-14T23:13:17.000Z","updated_at":"2026-05-25T00:58:31.000Z","published_at":"2017-07-14T23:13:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44262-multivariate-polynomials-overload-multiplication\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 44262\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e I asked you to create a class\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emPoly\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with overloaded multiplication, so a product of two polynomials can be expressed in the form\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = p1*p2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. However, the method of constructing these polynomials is still somewhat unintuitive. In the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/products/symbolic.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSymbolic Math Toolbox\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, one can simply define some variables,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[syms x y z]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand then create a polynomial:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[p = 2*x*y + 3*x^5*z;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe would like to do something like that here. As a start, create a class\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emPolySym\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with properties\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexponents\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecoefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003evarnames\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where the first two properties are the same as in previous problems and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003evarnames\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/characters-and-strings.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003estring array\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The constructor should accept a numeric, char or string input, e.g.,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x = mPolySym('x')\\n\\nx = \\n\\nmPolySym with properties:\\n\\n        varnames: \\\"x\\\"\\n       exponents: 1\\n    coefficients: 1\\n\\nr = mPolySym(pi)\\n\\nr = \\n\\nmPolySym with properties:\\n\\n        varnames: [0×0 string]\\n       exponents: 1\\n    coefficients: 3.1416]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAlso modify the method\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emtimes\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from the previous problem so it can multiply polynomials with different variable names.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2511,"title":" BLOCK x3 (Version 4) ","description":"Always in this series ( \u003chttp://www.mathworks.com/matlabcentral/cody/problems/2451-block-x3-version-1/ 2451\u003e, \u003chttp://www.mathworks.com/matlabcentral/cody/problems/2484-block-x3-version-3/ 2484\u003e, and \u003chttp://www.mathworks.com/matlabcentral/cody/problems/2478-block-x3-version-2 2478\u003e ).\r\n\r\nNow we are in color (1 for red  and 2 for white).\r\nYour task is always to count the  *minimum number* of movements required to align the 3 blocks in each colors (vertically or horizontally).\r\n\r\n\r\n\r\n\u003c\u003chttp://4.bp.blogspot.com/-iveYgRwOmLs/Udk9ZctxnUI/AAAAAAAA3Uw/Z9XNHw6f-f4/s400/pack+2+level+2-1.png\u003e\u003e\r\n\r\n* [0 0 0 0 0 0 0;\r\n*  0 0 1 2 0 0 0;\r\n*  0 0 0 0 0 0 0;\r\n*  0 0 1 2 0 0 0;\r\n*  0 0 1 2 0 0 0;\r\n*  0 0 0 0 0 0 0;\r\n*  0 0 0 0 0 0 0]\r\n\r\nIn this example you can move down the first two blocks ( *in two moves* ).\r\n\r\n\r\nNote that blocks can be *swapped* . \r\n\r\n\r\nIn this second example :\r\n\r\n\u003c\u003chttp://1.bp.blogspot.com/-XJP6Mn4X9Ws/Udk9bHEKx_I/AAAAAAAA3Vo/V_Ar3oF9gYw/s400/pack+2+level+2-7.png\u003e\u003e\r\n\r\n* [0 0 0 0 0 0 0;\r\n*  0 0 0 0 0 0 0;\r\n*  0 0 1 2 0 0 0;\r\n*  0 0 2 1 0 0 0;\r\n*  0 0 1 2 0 0 0;\r\n*  0 0 0 0 0 0 0;\r\n*  0 0 0 0 0 0 0]\r\n\r\nHere you win in only *one move* by swapping the two central blocks.\r\n\r\nGood luck !","description_html":"\u003cp\u003eAlways in this series ( \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/2451-block-x3-version-1/\"\u003e2451\u003c/a\u003e, \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/2484-block-x3-version-3/\"\u003e2484\u003c/a\u003e, and \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/2478-block-x3-version-2\"\u003e2478\u003c/a\u003e ).\u003c/p\u003e\u003cp\u003eNow we are in color (1 for red  and 2 for white).\r\nYour task is always to count the  \u003cb\u003eminimum number\u003c/b\u003e of movements required to align the 3 blocks in each colors (vertically or horizontally).\u003c/p\u003e\u003cimg src = \"http://4.bp.blogspot.com/-iveYgRwOmLs/Udk9ZctxnUI/AAAAAAAA3Uw/Z9XNHw6f-f4/s400/pack+2+level+2-1.png\"\u003e\u003cul\u003e\u003cli\u003e[0 0 0 0 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 1 2 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 0 0 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 1 2 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 1 2 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 0 0 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 0 0 0 0 0]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eIn this example you can move down the first two blocks ( \u003cb\u003ein two moves\u003c/b\u003e ).\u003c/p\u003e\u003cp\u003eNote that blocks can be \u003cb\u003eswapped\u003c/b\u003e .\u003c/p\u003e\u003cp\u003eIn this second example :\u003c/p\u003e\u003cimg src = \"http://1.bp.blogspot.com/-XJP6Mn4X9Ws/Udk9bHEKx_I/AAAAAAAA3Vo/V_Ar3oF9gYw/s400/pack+2+level+2-7.png\"\u003e\u003cul\u003e\u003cli\u003e[0 0 0 0 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 0 0 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 1 2 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 2 1 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 1 2 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 0 0 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 0 0 0 0 0]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eHere you win in only \u003cb\u003eone move\u003c/b\u003e by swapping the two central blocks.\u003c/p\u003e\u003cp\u003eGood luck !\u003c/p\u003e","function_template":"function y = block3_4(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [0 0 0 0 0 0 0;0 0 0 0 0 0 0;0 0 1 2 0 0 0;0 0 0 0 0 0 0;0 0 1 2 0 0 0;0 0 1 2 0 0 0;0 0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(block3_4(x),y_correct))\r\n\r\n\r\n%%\r\nx = [0 0 0 0 0 0 0;0 0 0 0 0 0 0;0 0 0 2 1 0 0;0 0 0 1 2 0 0;0 0 0 2 1 0 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0];\r\ny_correct = 1;\r\nassert(isequal(block3_4(x),y_correct))\r\n\r\n\r\n%%\r\nx = [0 0 0 0 0 0 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0;0 0 2 1 2 0 0;0 0 1 2 1 0 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0];\r\ny_correct = 1;\r\nassert(isequal(block3_4(x),y_correct))\r\n\r\n\r\n%%\r\nx = [0 0 0 0 0 0 0;0 0 0 0 0 0 0;0 0 1 0 1 1 0;0 0 2 2 0 2 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(block3_4(x),y_correct))\r\n\r\n\r\n%%\r\nx = [0 0 0 0 0 0 0;0 0 0 0 0 0 0;0 0 1 1 2 0 0;0 0 2 2 1 0 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0];\r\ny_correct = 1;\r\nassert(isequal(block3_4(x),y_correct))\r\n\r\n%%\r\nx = [0 0 0 0 0 0 0;0 0 0 0 0 0 0;0 0 1 1 0 0 0;0 0 2 2 0 0 0;0 0 2 1 0 0 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(block3_4(x),y_correct))\r\n\r\n%%\r\nx = [0 0 0 0 0 0 0;0 0 0 1 0 0 0;0 0 2 0 1 0 0;0 0 1 0 2 0 0;0 0 0 2 0 0 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0];\r\ny_correct = 3;\r\nassert(isequal(block3_4(x),y_correct))\r\n\r\n%%\r\nx = [0 0 0 0 0 0 0;0 0 0 1 0 0 0;0 0 1 2 1 0 0;0 0 2 0 2 0 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(block3_4(x),y_correct))\r\n\r\n%%\r\nx = [0 0 0 0 0 0 0;0 0 0 1 0 0 0;0 0 0 1 0 0 0;0 0 1 2 0 0 0;0 0 2 0 0 0 0;0 0 2 0 0 0 0;0 0 0 0 0 0 0];\r\ny_correct = 1;\r\nassert(isequal(block3_4(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":5390,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-08-15T07:15:35.000Z","updated_at":"2026-05-25T00:45:42.000Z","published_at":"2014-08-15T07:17:45.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.png\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/media/image2.png\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAlways in this series (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/2451-block-x3-version-1/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e2451\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/2484-block-x3-version-3/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e2484\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/2478-block-x3-version-2\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e2478\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNow we are in color (1 for red and 2 for white). Your task is always to count the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eminimum number\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of movements required to align the 3 blocks in each colors (vertically or horizontally).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[0 0 0 0 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 1 2 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 0 0 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 1 2 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 1 2 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 0 0 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 0 0 0 0 0]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this example you can move down the first two blocks (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ein two moves\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote that blocks can be\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eswapped\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this second example :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[0 0 0 0 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 0 0 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 1 2 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 2 1 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 1 2 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 0 0 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 0 0 0 0 0]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere you win in only\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eone move\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e by swapping the two central blocks.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood luck 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\"},{\"partUri\":\"/media/image2.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\"}]}"},{"id":2451,"title":"BLOCK x3 (Version 1)","description":"\r\n\u003chttps://play.google.com/store/apps/details?id=com.noodlecake.blockblock BLOCK x3\u003e is a simple, fun and relaxing puzzle game.\r\n\r\nThe basics are easy. Solve the puzzles by getting *3 blocks* in a row or column. \r\n\r\nThe puzzle is coded a 6x6 matrix and the 3 blocks are indicated by 1 (and 0 for free space).\r\n\r\nIn this example :\r\n\r\n\u003c\u003chttp://1.bp.blogspot.com/-GbZ-AMjylSs/Udk6kRyp4uI/AAAAAAAA3Pk/3jdWrVSqQpc/s400/pack+1+level+1-1.png\u003e\u003e\r\n \r\n \r\n\r\n* [0 0 0 0 0 0\r\n* \r\n* 0 0 1 0 0 0\r\n* \r\n* 0 0 1 0 0 0\r\n* \r\n* 0 0 0 0 0 0\r\n* \r\n* 0 0 1 0 0 0\r\n* \r\n* 0 0 0 0 0 0]\r\n\r\nYou line up 3 blocks in one move by dragging the last block to the top (you can move a block in the free space only horizontally or vertically.)\r\n\r\n\r\n\r\nThe goal in this first problem is to give the *smallest number* of moves to solve the puzzle.\r\n\r\n\r\n\r\n","description_html":"\u003cp\u003e\u003ca href = \"https://play.google.com/store/apps/details?id=com.noodlecake.blockblock\"\u003eBLOCK x3\u003c/a\u003e is a simple, fun and relaxing puzzle game.\u003c/p\u003e\u003cp\u003eThe basics are easy. Solve the puzzles by getting \u003cb\u003e3 blocks\u003c/b\u003e in a row or column.\u003c/p\u003e\u003cp\u003eThe puzzle is coded a 6x6 matrix and the 3 blocks are indicated by 1 (and 0 for free space).\u003c/p\u003e\u003cp\u003eIn this example :\u003c/p\u003e\u003cimg src = \"http://1.bp.blogspot.com/-GbZ-AMjylSs/Udk6kRyp4uI/AAAAAAAA3Pk/3jdWrVSqQpc/s400/pack+1+level+1-1.png\"\u003e\u003cul\u003e\u003cli\u003e[0 0 0 0 0 0\u003c/li\u003e\u003cli\u003e\u003c/li\u003e\u003cli\u003e0 0 1 0 0 0\u003c/li\u003e\u003cli\u003e\u003c/li\u003e\u003cli\u003e0 0 1 0 0 0\u003c/li\u003e\u003cli\u003e\u003c/li\u003e\u003cli\u003e0 0 0 0 0 0\u003c/li\u003e\u003cli\u003e\u003c/li\u003e\u003cli\u003e0 0 1 0 0 0\u003c/li\u003e\u003cli\u003e\u003c/li\u003e\u003cli\u003e0 0 0 0 0 0]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eYou line up 3 blocks in one move by dragging the last block to the top (you can move a block in the free space only horizontally or vertically.)\u003c/p\u003e\u003cp\u003eThe goal in this first problem is to give the \u003cb\u003esmallest number\u003c/b\u003e of moves to solve the puzzle.\u003c/p\u003e","function_template":"function y = block3(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [0 0 0 0 0 0;0 0 0 0 0 0;0 0 1 0 0 0;0 0 1 0 0 0;0 0 0 1 0 0;0 0 0 0 0 0];\r\ny_correct = 1;\r\nassert(isequal(block3(x),y_correct))\r\n%%\r\nx = [0 0 0 0 0 0;0 0 0 0 0 0;0 0 1 0 0 0;0 1 0 0 0 0;0 0 1 0 0 0;0 0 0 0 0 0];\r\ny_correct = 1;\r\nassert(isequal(block3(x),y_correct))\r\n%%\r\nx = [0 0 0 0 0 0;0 0 0 0 0 0;0 0 1 0 0 0;0 0 0 1 0 0;0 0 0 0 1 0;0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(block3(x),y_correct))\r\n%%\r\nx = [0 0 0 0 0 0;0 0 1 0 0 0;0 0 0 0 0 0;0 0 1 0 0 0;0 0 0 0 0 0;0 0 1 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(block3(x),y_correct))\r\n%%\r\nx = [0 0 0 0 0 0;0 0 0 0 0 0;0 1 0 1 1 0;0 0 0 0 0 0;0 0 0 0 0 0;0 0 0 0 0 0];\r\ny_correct = 1;\r\nassert(isequal(block3(x),y_correct))\r\n%%\r\nx = [0 0 0 0 0 0;0 0 0 0 0 0;0 0 0 1 1 0;0 0 0 0 0 0;0 0 1 0 0 0;0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(block3(x),y_correct))\r\n%%\r\nx = [0 0 0 0 0 0;0 0 0 0 0 0;0 0 0 1 1 0;0 0 0 1 0 0;0 0 0 0 0 0;0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(block3(x),y_correct))\r\n%%\r\nx = [0 0 0 0 0 0;0 0 0 0 0 0;0 0 0 1 0 0;0 0 0 1 1 0;0 0 0 0 0 0;0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(block3(x),y_correct))\r\n%%\r\nx = [0 0 0 0 0 0;0 0 1 0 1 0;0 0 0 0 0 0;0 0 0 0 0 0;0 0 0 1 0 0;0 0 0 0 0 0];\r\ny_correct = 3;\r\nassert(isequal(block3(x),y_correct))\r\n%%\r\nx = [0 0 0 0 0 0;0 0 1 0 1 0;0 0 1 0 0 0;0 0 0 0 0 0;0 0 0 0 0 0;0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(block3(x),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":5390,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2014-07-20T00:15:18.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-07-19T23:58:55.000Z","updated_at":"2026-05-25T00:43:28.000Z","published_at":"2014-07-20T00:15:18.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.png\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://play.google.com/store/apps/details?id=com.noodlecake.blockblock\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eBLOCK x3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a simple, fun and relaxing puzzle game.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe basics are easy. 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\"}]}"},{"id":2478,"title":"BLOCK x3 (Version 2)","description":"An extension to problem 2451 ( \u003chttps://www.mathworks.com/matlabcentral/cody/problems/2451-block-x3-version-1\u003e ).\r\n\r\nIt is based on an android game - BLOCK x3. The objective is to align the 1's in the matrix using minimum movements. The valid movements are  horizontal and vertical (by one step). A zero (0) indicates an empty space. Your task is to count minimum number of movements required to align the three 1's vertically or horizontally.\r\n\r\nNew challenge in this problem : There are some static elements which can not be moved and can not be included in the alignment. These elements are indicated by 2. This makes the problem a bit challenging.\r\n\r\nExample:\r\n\r\n\r\n  Input =[0 0 0 0 0 0 0 0;\r\n          0 0 1 0 1 0 0 0;\r\n          0 0 0 2 1 0 0 0;\r\n          0 0 0 0 0 0 0 0]\r\n  \r\n  Output = 2;\r\n","description_html":"\u003cp\u003eAn extension to problem 2451 ( \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/2451-block-x3-version-1\"\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/2451-block-x3-version-1\u003c/a\u003e ).\u003c/p\u003e\u003cp\u003eIt is based on an android game - BLOCK x3. The objective is to align the 1's in the matrix using minimum movements. The valid movements are  horizontal and vertical (by one step). A zero (0) indicates an empty space. Your task is to count minimum number of movements required to align the three 1's vertically or horizontally.\u003c/p\u003e\u003cp\u003eNew challenge in this problem : There are some static elements which can not be moved and can not be included in the alignment. These elements are indicated by 2. This makes the problem a bit challenging.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eInput =[0 0 0 0 0 0 0 0;\r\n        0 0 1 0 1 0 0 0;\r\n        0 0 0 2 1 0 0 0;\r\n        0 0 0 0 0 0 0 0]\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eOutput = 2;\r\n\u003c/pre\u003e","function_template":"function y = blockx3_2(x)\r\n\r\nend","test_suite":"%%\r\n\r\nx =  [0 0 0 0 0 0 0 0;\r\n      0 0 1 0 1 0 0 0;\r\n      0 0 0 2 1 0 0 0;\r\n      0 0 0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(blockx3_2(x),y_correct));\r\n\r\n\r\n%%\r\nx =  [0 0 0 0 0 0 0 0;\r\n      0 0 1 0 1 0 0 0;\r\n      0 0 0 2 0 0 0 0;\r\n      0 0 1 0 0 0 0 0];\r\ny_correct = 3;\r\nassert(isequal(blockx3_2(x),y_correct))\r\n\r\n%%\r\nx =  [1 1 0 0 0 0 0 0;\r\n      1 2 0 0 0 0 0 0;\r\n      0 0 0 0 0 0 0 0;\r\n      0 0 0 0 0 0 0 0];\r\ny_correct = 3;\r\nassert(isequal(blockx3_2(x),y_correct))\r\n\r\n%%\r\nx =  [0 0 0 1 0 0 0 0;\r\n      0 0 1 2 1 0 0 0;\r\n      0 0 0 0 0 0 0 0;\r\n      0 0 0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(blockx3_2(x),y_correct))\r\n\r\n\r\n%%\r\nx =  [0 0 0 1 0 0 0 0;\r\n      0 0 1 2 0 0 0 0;\r\n      0 0 1 0 0 0 0 0;\r\n      0 0 0 0 0 0 0 0]\r\ny_correct = 1;\r\nassert(isequal(blockx3_2(x),y_correct))\r\n\r\n\r\n%%\r\nx =  [0 0 0 1 0 0 0 0;\r\n      0 0 1 2 0 0 0 0;\r\n      0 0 0 0 0 0 0 1;\r\n      0 0 0 0 0 0 0 0]\r\ny_correct = 6;\r\nassert(isequal(blockx3_2(x),y_correct))\r\n\r\n\r\n%%\r\nx =  [0 0 0 1 0 0 0 0;\r\n      0 0 0 2 0 0 0 0;\r\n      0 0 0 1 0 0 0 0;\r\n      0 0 0 1 0 0 0 0]\r\ny_correct = 4;\r\nassert(isequal(blockx3_2(x),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":17203,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2014-08-03T08:43:51.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-08-03T08:31:00.000Z","updated_at":"2026-05-25T00:44:08.000Z","published_at":"2014-08-03T08:31:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn extension to problem 2451 (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/2451-block-x3-version-1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/2451-block-x3-version-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt; ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt is based on an android game - BLOCK x3. The objective is to align the 1's in the matrix using minimum movements. The valid movements are horizontal and vertical (by one step). A zero (0) indicates an empty space. Your task is to count minimum number of movements required to align the three 1's vertically or horizontally.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNew challenge in this problem : There are some static elements which can not be moved and can not be included in the alignment. These elements are indicated by 2. This makes the problem a bit challenging.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Input =[0 0 0 0 0 0 0 0;\\n        0 0 1 0 1 0 0 0;\\n        0 0 0 2 1 0 0 0;\\n        0 0 0 0 0 0 0 0]\\n\\nOutput = 2;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60746,"title":"List Ormiston prime pairs","description":"The numbers 1913 and 1931 form the first Ormiston prime pair. The numbers are consecutive primes, and they are anagrams of each other—that is, the digits of one number can be arranged to give the second number. 347 and 743 are not an Ormiston prime pair: they are anagrams of each other, but they are not consecutive primes. \r\nWrite a function that produces the nth Ormiston prime pair.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe numbers 1913 and 1931 form the first Ormiston prime pair. The numbers are consecutive primes, and they are anagrams of each other—that is, the digits of one number can be arranged to give the second number. 347 and 743 are not an Ormiston prime pair: they are anagrams of each other, but they are not consecutive primes. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that produces the nth Ormiston prime pair.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = OrmistonPrimePair(n)\r\n  p = primes(n); \r\n  y = isequal(sort(p(n)),sort(p(n+1)));\r\nend","test_suite":"%%\r\nn = 1;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [1913 1931];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 18;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [55313 55331];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 54;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [131413 131431];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 126;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [343337 343373];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 180;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [481513 481531];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1080;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [2744279 2744297];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1818;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [4696613 4696631];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 5436;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [14589013 14589031];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 7290;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [19592813 19592831];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 10800;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [29470879 29470897];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 17496;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [48654979 48654997];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 11111;\r\ny = OrmistonPrimePair(n);\r\nsmf_correct = 81182;\r\nsmf = sum([max(factor(y(1)+1)) max(factor(y(2)+1))]);\r\nassert(isequal(smf,smf_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2024-10-09T05:13:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-10-09T05:13:08.000Z","updated_at":"2026-06-06T01:40:24.000Z","published_at":"2024-10-09T05:13:23.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe numbers 1913 and 1931 form the first Ormiston prime pair. The numbers are consecutive primes, and they are anagrams of each other—that is, the digits of one number can be arranged to give the second number. 347 and 743 are not an Ormiston prime pair: they are anagrams of each other, but they are not consecutive primes. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that produces the nth Ormiston prime pair.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61292,"title":"The Singularity - Event Horizon (Absolute Zero)","description":"Inspired by Problem61291\r\nMô tả:\r\nBầy đàn gồm M agents phải di chuyển xuyên qua không gian 5D Hyper-Torus ( kích thước mỗi chiều L = 100 ) từ Node 1 đến Target Node. Để sống sót, thuật toán của bạn phải tuân thủ nghiêm ngặt các định luật vật lí sau:\r\n1. Hình học Torus 5D: Khoảng cách giữa 2 điểm là khoảng cách Chebyshev trên mặt Torus:\r\n        d = max(min( | x_i - y_i |,100 - | x_i - y_i | )) cho i = 1..5.\r\n2. Động lực học Pulse: Chi phí năng lượng tại thời điểm cập bến t bị nhân bởi hệ số \r\n        Pulse(t) = 1 + 2 sin^2(pi*t/2). Lưu ý: V_{swarm} = 20.\r\n3. Kẻ săn mồi ( Dynamic Predator ): Predator xuất phát từ pred_start với V_p = 15. Nếu tại bất kì node trung gian nào, Predator có thể đến trước hoặc cùng lúc với bầy đàn ( t_p \u003c= t_s ), bầy đàn sẽ bị tiêu diệt ( Energy = -1 ).\r\n4. Cấm quay đầu ( No-Revisit Rule ): Để tránh việc \"câu giờ\" đợi nhịp Pulse thấp, bầy đàn không được phép đi qua 1 node quá một lần trong cùng 1 hành trình.\r\n5. Hệ số bão hòa \u0026 Thuế Entropy: *Sat  = M + 0.125 x M x ( M - 1 ).\r\n6. Cộng hưởng Spin: Nếu tọa độ thứ 5(ω) của node đến gần sát một số nguyên ( sai số \u003c 0.05 ), một hình phạt Spin = 50 x (step + 1) sẽ được cộng vào chi phí","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 405px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 202.5px; transform-origin: 468.5px 202.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInspired by \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://ww2.mathworks.cn/matlabcentral/cody/groups/97667/problems/61291\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); \"\u003e\u003cspan style=\"\"\u003eProblem61291\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eMô tả:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBầy đàn gồm \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e agents phải di chuyển xuyên qua không gian 5D Hyper-Torus ( kích thước mỗi chiều \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 100 ) từ Node 1 đến Target Node. Để sống sót, thuật toán của bạn phải tuân thủ nghiêm ngặt các định luật vật lí sau:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHình học Torus 5D\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Khoảng cách giữa 2 điểm là khoảng cách Chebyshev trên mặt Torus:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        d = max(min( | x_i - y_i |,100 - | x_i - y_i | )) cho i = 1..5.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eĐộng lực học Pulse\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Chi phí năng lượng tại thời điểm cập bến \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003et\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e bị nhân bởi hệ số \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        Pulse(t) = 1 + 2 sin^2(pi*t/2). Lưu ý: V_{swarm} = 20.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eKẻ săn mồi ( Dynamic Predator ):\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Predator xuất phát từ pred_start với V_p = 15. Nếu tại bất kì node trung gian nào, Predator có thể đến trước hoặc cùng lúc với bầy đàn ( t_p \u0026lt;= t_s ), bầy đàn sẽ bị tiêu diệt ( Energy = -1 ).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCấm quay đầu ( No-Revisit Rule ):\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Để tránh việc \"câu giờ\" đợi nhịp Pulse thấp, bầy đàn không được phép đi qua 1 node quá một lần trong cùng 1 hành trình.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e5. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHệ số bão hòa \u0026amp; Thuế Entropy\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: *Sat  = \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e + 0.125 x M x ( M - 1 ).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e6. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCộng hưởng Spin\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Nếu tọa độ thứ 5(ω) của node đến gần sát một số nguyên ( sai số \u0026lt; 0.05 ), một hình phạt Spin = 50 x (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e + 1) sẽ được cộng vào chi phí\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [max_energy, best_path] = solve_event_horizon_v3(nodes, pred_start, params)\r\n    V_p = 15;%\r\nend","test_suite":"%% PHASE 1: THE PULSE TIMING TRAP\r\nclear n p;\r\np.M = 1; p.target = 2; p.ATP_total = 2000;\r\nn(1).coord = [0,0,0,0,0.5]; n(1).res = 1;\r\nn(2).coord = [30,0,0,0,0.5]; n(2).res = 10; \r\nn(3).coord = [10,0,0,0,0.5]; n(3).res = 0.1;\r\n[e1, s1] = solve_event_horizon_v3(n, 0, p);\r\nassert(~isempty(s1) \u0026\u0026 length(s1{1}) == 3, 'FAILED T1: Phải đi vòng qua Node 3 để khớp t=2.0s.');\r\n\r\n%% PHASE 2: HYPER-TORUS WRAP-AROUND \r\nclear n p; p.M = 1; p.ATP_total = 2000; p.target = 2;\r\nbase.res = 1; base.coord = [0,0,0,0,0.5];\r\n\r\n% Test 2: Chiều 1\r\nn2 = repmat(base, 1, 2); n2(2).coord(1) = 90;\r\n[e2, ~] = solve_event_horizon_v3(n2, 0, p);\r\nassert(abs(e2 - 1980) \u003c 1e-3, 'FAILED T2: Lỗi Torus chiều 1');\r\n\r\n% Test 3: Chiều 5\r\nn3 = repmat(base, 1, 2); n3(2).coord(5) = 95.5; \r\n[e3, ~] = solve_event_horizon_v3(n3, 0, p);\r\nassert(e3 \u003e 1990, 'FAILED T3: Lỗi Torus chiều 5');\r\n\r\n%% PHASE 4: PREDATOR INTERCEPT \r\nclear n p; p.M = 1; p.ATP_total = 5000; p.target = 2;\r\nn(1).coord = [0,0,0,0,0.5]; n(1).res = 1;\r\nn(2).coord = [40,0,0,0,0.5]; n(2).res = 1; \r\n\r\nn(3).coord = [0,20,0,0,0.5]; n(3).res = 0.1; \r\n\r\nn(4).coord = [0,60,0,0,0.5]; \r\n\r\n[e7, s7] = solve_event_horizon_v3(n, 4, p);\r\n\r\nassert(~isempty(s7) \u0026\u0026 e7 \u003e 0, 'FAILED T7: Vẫn không tìm thấy đường an toàn');\r\n\r\n%% TEST 20: THE OMEGA LABYRINTH (Bản Chuẩn Hóa 100%)\r\nclear n p;\r\n% 1. Cấu hình cố định để Solver và Testcase đồng bộ\r\np.M = 10; \r\np.target = 5; \r\np.ATP_total = 10000;\r\nV_s = 20; \r\nV_p = 15; % Hằng số Predator\r\n\r\n% 2. Tạo 5 Nodes với tọa độ NẰM TRONG KHOẢNG [0, 100]\r\n% Node 1: Xuất phát\r\nn(1).coord = [10, 10, 10, 10, 0.5]; n(1).res = 1;\r\n% Node 2: Predator (Kẻ săn mồi đứng đây)\r\nn(2).coord = [30, 10, 10, 10, 0.5]; n(2).res = 1;\r\n% Node 3: Node trung gian (Đường vòng an toàn)\r\nn(3).coord = [10, 50, 10, 10, 0.5]; n(3).res = 0.5;\r\n% Node 4: Node rác\r\nn(4).coord = [80, 80, 80, 80, 0.5]; n(4).res = 1;\r\n% Node 5: Đích\r\nn(5).coord = [50, 50, 10, 10, 0.5]; n(5).res = 0.5;\r\n\r\n% 3. Chạy Solver\r\n[user_e, user_path] = solve_event_horizon_v3(n, 2, p);\r\n\r\n% 4. CHẶN LỖI CRASH (Nếu Solver trả về rỗng)\r\nassert(~isempty(user_path) \u0026\u0026 ~isempty(user_path{1}), 'Solver không tìm thấy bất kỳ con đường nào!');\r\n\r\n% 5. KIỂM TRA LOGIC SINH TỒN\r\npath = user_path{1};\r\nt_run = 0; is_captured = false;\r\nSat = p.M + 0.125 * p.M * (p.M - 1);\r\ne_val = p.ATP_total;\r\n\r\nfor k = 1:length(path)-1\r\n    u = path(k); v = path(k+1);\r\n    df = abs(n(u).coord - n(v).coord);\r\n    % Chuẩn hóa khoảng cách Torus chuẩn 100%\r\n    d = max(min(df, 100 - df));\r\n    \r\n    t_run = t_run + d/V_s;\r\n    \r\n    % Kiểm tra Predator (Node 2) có bắt được tại Node v không\r\n    df_p = abs(n(2).coord - n(v).coord);\r\n    dp = max(min(df_p, 100 - df_p));\r\n    \r\n    if dp/V_p \u003c= t_run + 1e-9\r\n        is_captured = true; break;\r\n    end\r\n    \r\n    % Tính năng lượng để đối chiếu\r\n    pulse = 1 + 2 * (sin(t_run * pi / 2)^2);\r\n    cost = (d * n(v).res * Sat * pulse) * (1.15^(k-1));\r\n    if abs(n(v).coord(5) - round(n(v).coord(5))) \u003c 0.05\r\n        cost = cost + 50 * k;\r\n    end\r\n    e_val = e_val - cost;\r\nend\r\n\r\n% ASSERTION CUỐI CÙNG\r\nassert(~is_captured, 'Omega Phase: Swarm captured! Code của bạn đang phớt lờ Predator.');\r\nassert(abs(user_e - e_val) \u003c 1e-5, 'Omega Phase: Năng lượng tính toán không khớp!');\r\n%% PHASE 5: SPIN SENSITIVITY \r\nclear n p; p.M = 20; p.target = 2; p.ATP_total = 10000;\r\nn(1).coord = [0,0,0,0,0.5]; n(2).coord = [10,0,0,0,1.02]; n(2).res = 1; \r\n[e12, ~] = solve_event_horizon_v3(n, 0, p);\r\nassert(abs(e12 - 8600) \u003c 1e-4, 'FAILED T12: Spin Penalty không kích hoạt đúng ngưỡng.');\r\n\r\nn(2).coord(5) = 1.06;\r\n[e13, ~] = solve_event_horizon_v3(n, 0, p);\r\nassert(abs(e13 - 8650) \u003c 1e-4, 'FAILED T13: Spin Penalty kích hoạt sai mục tiêu.');","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":5076265,"edited_by":5076265,"edited_at":"2026-03-23T17:47:36.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2026-03-23T17:47:36.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-22T19:51:08.000Z","updated_at":"2026-06-06T20:25:40.000Z","published_at":"2026-03-22T19:51:08.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInspired by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://ww2.mathworks.cn/matlabcentral/cody/groups/97667/problems/61291\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem61291\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMô tả:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBầy đàn gồm \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e agents phải di chuyển xuyên qua không gian 5D Hyper-Torus ( kích thước mỗi chiều \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 100 ) từ Node 1 đến Target Node. Để sống sót, thuật toán của bạn phải tuân thủ nghiêm ngặt các định luật vật lí sau:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHình học Torus 5D\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Khoảng cách giữa 2 điểm là khoảng cách Chebyshev trên mặt Torus:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        d = max(min( | x_i - y_i |,100 - | x_i - y_i | )) cho i = 1..5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eĐộng lực học Pulse\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Chi phí năng lượng tại thời điểm cập bến \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e bị nhân bởi hệ số \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        Pulse(t) = 1 + 2 sin^2(pi*t/2). Lưu ý: V_{swarm} = 20.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eKẻ săn mồi ( Dynamic Predator ):\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Predator xuất phát từ pred_start với V_p = 15. Nếu tại bất kì node trung gian nào, Predator có thể đến trước hoặc cùng lúc với bầy đàn ( t_p \u0026lt;= t_s ), bầy đàn sẽ bị tiêu diệt ( Energy = -1 ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e4. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCấm quay đầu ( No-Revisit Rule ):\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Để tránh việc \\\"câu giờ\\\" đợi nhịp Pulse thấp, bầy đàn không được phép đi qua 1 node quá một lần trong cùng 1 hành trình.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e5. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHệ số bão hòa \u0026amp; Thuế Entropy\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: *Sat  = \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e + 0.125 x M x ( M - 1 ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e6. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCộng hưởng Spin\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Nếu tọa độ thứ 5(ω) của node đến gần sát một số nguyên ( sai số \u0026lt; 0.05 ), một hình phạt Spin = 50 x (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e + 1) sẽ được cộng vào chi phí\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61046,"title":"Decipher Message Using Prime of Primitive Root of Two Sequence Key","description":"Provided a message with all characters \u003c= 255 (ascii) as an input, decode the padded message (removing the random character pad), XORing input converted to binary vector (8 bits each) with the inputted prime having primitive root of two as the key. The key is the repeated sequence of 2^x modulo prime key input starting from x=0 until the cycle repeats (unpadded zero binary represented vector of the repeated sequence). After XORing, remove the padded front and return the character array as output.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 105px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 52.5px; transform-origin: 408px 52.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 52.5px; text-align: left; transform-origin: 385px 52.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eProvided a message with all characters \u0026lt;= 255 (ascii) as an input, decode the padded message (removing the random character pad), XORing input converted to binary vector (8 bits each) with the inputted prime having primitive root of two as the key. The key is the repeated sequence of 2^x modulo prime key input starting from x=0 until the cycle repeats (unpadded zero binary represented vector of the repeated sequence). After XORing, remove the padded front and return the character array as output.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function d = deCipher(x,key)\r\n  d=xor(x,key);\r\nend\r\n","test_suite":"%%\r\nx=[39   212    74    83   164    14     3   175    39   212    74    83   164    14     3   175    39   212    74    83   164   14     3   175    39   212    74    83   164    14     3   175    39   212    74    83   164    14     3   175    39   212   74    83   164    14     3   175    39   212    74    83   164    14     3   175    39   212    74    83   164    14     3   19   242    77   208   208    52   219   130    53   242    82   200   207    60   218];\r\nassert(isequal(deCipher(x,19),'I love to swim!'));\r\n%%\r\nx=double('şl‘……‘ŒŒœŚøùè©ădurŢŠª«Ădõ³f ÈijĨĻ™isœ´Ŕ~ê‚ĪŢŞjhĻľŒĒďċĈÓ»ŃÃÜĮîĜŐËīōï´ÖŜąđo‹tŚļŸ‰Ķ¦ĺąˆ®ŝšŊň˜Ç´ļōďƅł¶ÕľŐĔşºśŔ“dk’ĢŠŏĽžá³ÐqfʯĬŕĔăĢċĠŋÆÄĮōĈėĠŽĠ')-100;\r\nassert(isequal(deCipher(x,797),'abcdefghijklmnopqrstuvwxyz !@#$%^\u0026*()_+ 0123456789 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!@#$%^\u0026*()_+ 0123456789 ABCDEFGHIJKLMNOPQRSTUVWXYZ';\r\ny=repmat(y,1,100);\r\nrng(2718);\r\ny=y(randperm(length(y)));\r\nassert(isequal(deCipher(x,16067),y));\r\n%%\r\nx=double('“ŀŝřřŝŠšŁţšőšĖþ¸xĤŒ‘ÇãŖ±äÿĨÚİIJŐÉÝz¦vgy•üňłŃijŐÑî‡kv¾äŅ߶Ħu…ðjĺ½igÄÀŞŜřÞÁ£ŋùdfä©kŇðoꊠ¸ÓĤ«ċ•jâ¯ċpg·Đ¦Õŀ}qĻĻg«ŸlÉĉŞÒġ•ÔÆķ¯»™èÁĜŀ¿ĻęÎ{möġæĽ½ÐĤ°ÉÈĔØœđÀġh‡āĠřu˂ċĜÊĂÕĨęâş×ř¼‹­É¯µĦϦøÓĨăøÌ|¿×ÎÔåá×´Òœİfý–™kĬµijş©×Ţç|īdºĩ€¤ıŖÇýqʂèívĜŔij¼˜ĎĂŝÐřšļnzČmŊãÂĺŅŒûįçıċkõĨ÷ĆÒףĦd…‹ċĮàÿĈĹňÙŐIJÒĊ탂ú›ĭðā‹ôȵ')-100;\r\ny='Men go abroad to wonder at the heights of mountains, at the huge waves of the sea, at the long courses of the rivers, at the vast compass of the ocean, at the circular motions of the stars, and they pass by themselves without wondering.';\r\nassert(isequal(deCipher(x,16067),y));\r\n%%\r\nx=double('˜īņŒŒņ³ÓdÓÅℐjīĭÃÚŔŘśÏĻ|f}Ŏu´ÇŕōæĵòöĬĝoÑ®²vÝř»ěíijĥvÍŌæ󼍑ò¶ĬqipˆÄwŜšğ’¥Ôŗ÷ovĀ{·Ň÷²ŅŒÎéªw‚ŗš²Øqśxr®ď¹”ĩiuóöe«ÖwÇńēÌĠ£ÝÆıÂeœúrśļ‚Īė“«lüĎįā|Ðì½Ý…ŜáĄď¾Œ«žåąŎyÄ¿ĐޖæàåŚÇŠÅŝ¡n½iñĔnê‹Ŀāó µ° ÔÅ÷’ËfÄŋüwùݙ£ħ¹ľęž‘ņĻ¤óu‚ħ‚òʼnÞðÖîí¿ĜŜĀl˜ğĿţ½ĚœĦ¯iĒµĒÕ¦ĿğţŃľöìśzûĽľėã¢İĨuПĈêÏłĘĀŋÙņħÓŗò´­ùšħòij“ñœowĽāÜĥĐÏā½ĸĈđ®Ńšô{‘řăğğôĶŇñeíp‡ģĭą—«°')-100;\r\ny='No man can be judged a criminal until he is found guilty; nor can society take from him the public protection until it has been proved that he has violated the conditions on which it was granted. What right, then, but that of power, can authorize the punishment of a citizen so long as there remains any doubt of his guilt?';\r\nassert(isequal(deCipher(x,16067),y));\r\n%%\r\nx=double('ÆõĘĜĜĘĕĔôĖĔĄĔţĻ}½ñćĒ–ģdıĺíŸå籌˜¿sò¼àĹč÷öæą„īÒ®Ã{ıКºŜ»ŽĦ­Ń·ijˆá¥ğţĝÅ¥ÞŇĺ²kï¼·Ŏā½Ņ…uÍĺy¾uĊšjʬċrn¶ċ¼”Ľ|uôĻuÀŸtÆĒġŠčœÕÆĻ©e†ö~ĉŃsĩČÇ¿gĻčłúºœø´Ì…ŗØœĔÂŝ«ŒëąŘ¸ÄºčĎÊāàåŕÇĖÏţÂØz„³iúĚ³ĵ„ŀÿīÏ´µãӄìÓ×´Òŝí|ø—™rĨªòń~á')-100;\r\ny='When one door closes, another opens; but we often look so long and so regretfully upon the closed door that we do not see the one which has opened for us.';\r\nassert(isequal(deCipher(x,16067),y));\r\n%%\r\nx=double('Ŋy”  ”™˜xš˜ˆ˜ß·āŁm‹ňĎĚŸè­¶qģik‰ĐĔŃïĿĮŀŜµ‘{zj‰Ĉ§ŎIJĿ÷­ŒĖĶÿoÌÔĺÕĽ»µ¦†ÅwŘŕĠÄÁÎŇľkyĩ§³ŋļ²Ą¡ ¸Ôݾv·ĈŽ³Ö©ċvg¯ċzÄĴ|rûö¦¸ØÀÏĖęÏŌ‰ØŸı¨ªÔçyĚIJ¿Ļęβ¾÷ėĤł°œðµÊÈĔÏœĒÂōs‰êčĊd߂ğģ£çÛĪęÜŞÈňn„q„n¦ñČ³ç…ŃÿíÌ|¯ØÌÙð΄zÒşòƒùÛà€éxŝšp¡Îŗİ}óf}êuÁĽō“ð{‹kįóxĚŞô¼£ćĴĎeĔŚŀrkēiĄÐ¹ĻĉřöòòæśyûĩĩčŚíŀd¢‘ņĮÉôĔĿ')-100;\r\ny='What is ominous is the ease with which some people go from saying that they don''t like something to saying that the government should forbid it. When you go down that road, don''t expect freedom to survive very long.';\r\nassert(isequal(deCipher(x,16067),y));\r\n%%\r\nx=[{'ī˜Ďė¨ŒŇ³ī˜Ďė¨ŒŇ³ī˜Ďė¨ŒŇ³ī˜Ďė¨ŒŇ³ī˜Ďė¨ŒŇ³ī˜Ďė¨ŒŇ³ī˜Ďė¨ŒŇ³ī˜Ďė¨Ğ'} ...\r\n    {'pţÅÜw'}    {'âñwnš»¾Śâñwnš»¾Śâñwnš»¾Śâñwnš»¾Śâñwnš»¾Śâñwnš»¾Śâñwnš»¾ŚâñwnšĜ'}...\r\n    {'Ł’ĔčÂŘŝ¹Ł’ĔčÂŘŝ¹Ł’ĔčÂŘŝ¹Ł’Ĕņ'}    {' ijµ¬ģy|Ę ijµ¬ģy|Ę ijµ¬ģy|Ę ijµ¬ģy|Ę ijµ¬ģy|Ę ijµ¬ģy|Ę ijµ¬ģy|Ę ijµ¬ģyė'} ...\r\n    {'Ƶijĺ…ïêŽĆµijĺ…ïêŽĆµijń'}    {'‰ĺ¬µĊpeđ‰ĺ¬µĊpeđ‰ĺ¬µĊpeđ‰ĺ¬µĊpeđ‰ĺ¬µĊpeđ‰ĺ¬µĊpeđ‰ĺ¬µz'}  ...\r\n    {'âñwnš»¾Śâñwnš»¾Śâñwnš»¾Śâñwnš»¾Śâñwnš»¾Śâñś'}    {'²ġ‡œ'}    {'oŜÊã솓çoŜÊã솓çoŜÊã솓çoŜÊã솓çoŜÊã솓çoŜÊã솓çoŜÊãìĕ'} ...\r\n    {'üÏřŐ~'}  {'Øë}dśÁ´ŠĂ'}    {'ÿÌŚœ|ĖģwÿÌŚœ|ĖģwÿÌŚœ|Ě'}    {'îÝŋŢmćĒfîÝŋŢmćĒfĀ'}   ...\r\n    {'Ĉ»ĭĴ‹ñäĈ»ĭĴ‹ñäĈ»ĭĴ‹ñäĈ»ĭĴ‹ñäĈ»ĭĴ‹ñäĈ»ĭĴ‹ñäy'}    {'ĿŒĚē¼Ŗţ·ĿŒĚē¼Ŗţn'} ...\r\n    {'Øë}dśÁ´ŠØë}dśÁ´ŠØë}dśÁ´ŠØë}dśÁ´ŠØë}dśÁ´ŠØë}dśÁ´ŠØë}ś'}    {'ßìzsŜ¶ÃŗßìzsŜ¶ÃŗßìzsŜ¶ÃŗßìzsŜ¶ÃŗßìzŘ'} ...\r\n    {'ªę–ĩÓÆIJªę–ĩÓÆIJªę–ĩÓÆIJªę–ĩÓÆIJªę–ĩÓÆIJªÖ'}    {'ņuóúÅē'}    {'ÝîxqŞ´ÁŕÝîxqŞ´ÁŕÝîxqŞ´ÁŕÝîxqŞ´ÁŕÝîxŗ'} ...\r\n    {'dŗÑØ獈ìdŗÑØ獈ìdŗÑØ獈ìdŗÑØ獈ìdŗÑØ獈ìdŗÑØ獈ìdŗÑØ獈ìdŗÑØ獈p'}    {'vŅãÊõŸšþvŅãÊõŸšþvŅãÊõŸšþvŅãÊõŸšþvŅãÊõŸšþvŅãÊõŸšþvŅãÊõŸšþvŅãÊj'}  ...\r\n    {'xŋÝÄû¡”ĀxŋÝÄû¡”ĀxŋÝÄû¡”ĀxŋÝÄû¡”ĀxŋÝÄû¡”ĀxŋÝÄû¡”ĀxŋÝŢ'}    {'ñâńŝrĈčiñâńŝrĈē'}    {'ńwñøÇĭĨÌńwñøÇĭĨÌńwñøÇĭĨÌńwñøÇĭĨÌńwñøÇĭĨÌńwñøÇĭĨÌńwñøÇĭĨÌńwñøÇĭĐ'}];\r\ny='ABCDEFGHIJKLMNOPQRSTUVWXYZ';\r\nfor k=1:26\r\n  assert(isequal(deCipher(double(x{k})-100,19),y(k)));\r\nend\r\n%%\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":145982,"edited_by":145982,"edited_at":"2025-10-23T11:07:00.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2025-10-23T01:21:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-10-22T22:43:16.000Z","updated_at":"2026-06-06T06:03:32.000Z","published_at":"2025-10-23T01:21:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProvided a message with all characters \u0026lt;= 255 (ascii) as an input, decode the padded message (removing the random character pad), XORing input converted to binary vector (8 bits each) with the inputted prime having primitive root of two as the key. The key is the repeated sequence of 2^x modulo prime key input starting from x=0 until the cycle repeats (unpadded zero binary represented vector of the repeated sequence). After XORing, remove the padded front and return the character array as output.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59079,"title":"The Hacker Parole Problem","description":"The hacker parole problem\r\n\r\n100 hackers have been imprisoned, but have been given a way to get parole.\r\nEach of the 100 prisoners has been given a number.  There is also a room with 100 numbered boxes.  Each box contains a number.  Each prisoner goes into the room and has 50 tries to find their number in a box.\r\nIf all 100 prisoners can find their number within 50 tries, then they all get parole.  But, if one prisoner cannot find their number within 50 tries all the hackers go back to prison for another year.\r\nThe hackers meet and devise an algorithm that has better than a 30 percent chance of going free that year.\r\nThe hacker's solution\r\nIt is obvious that having each prisoner randomly open boxes will fail.  Each prisoner has a 0.5 chance of finding their number and so the chance that all 100 are able to do it is 0.5^100.  Essentially giving a 0 probablility.\r\nThe hacker solution is to have each prisoner go into the room and use their number to find a box.  They open the box, and if their number is in it they are done.  If their number is not in it, then they use the number in the box to choose another box.  They continue following the numbers and opening boxes until they find the box with their number on it.\r\nThis solution will free all the prisoners over 30% of the time.  This is because the random numbers in boxes form loops.  For example if we have five boxes and five number we might see this set of numbers stored in boxes.\r\n\r\nThe hacker holding number 3 would open box 3 and find a 4.  Then the hacker would open box 4 and find a 1.  Then the hacker would open box 1 and find a 3. \r\n\r\nThis solution works because numbers stored this way always form at least one loop.  In this case we have the following loops:\r\n\r\n3 -\u003e 4 -\u003e 1 -\u003e 3\r\n5 -\u003e 2 -\u003e 5\r\n\r\nThe hackers know that they will get their freedom if the longest loop among the 100 boxes is 50 boxes or shorter.  This happens 30% of the time, thus they get their freedom 30% of the time.\r\nTesting the solution\r\nWe want to test the hacker's algorithm by running 10,000 trials and seeing how often the hackers won their freedom.  Math says that the number should be greater than or equal to 3000 times in 10,000 trials.\r\nYour assignment is to write a function named runTrial() that takes a vector of boxes in the room and runs a trial of the hacker's algorithm. It returns whether the hackers found the number after looking at only half the boxes. The boxes are a vector that contains randomized numbers from 1:numBoxes.\r\nThe testbench will run your trial 10000 times and capture the number of times the hackers won their freedom. That number should be above 3000.\r\nThe function looks like this:\r\nfunction foundAll = runTrial(boxes)\r\n        %%  Insert your code here. I solved this problem in 11 lines inside the function\r\nend","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1078.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 539.3px; transform-origin: 408px 539.3px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10px; text-align: left; transform-origin: 384px 10px; white-space-collapse: preserve; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe hacker parole problem\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e100 hackers have been imprisoned, but have been given a way to get parole.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach of the 100 prisoners has been given a number.  There is also a room with 100 numbered boxes.  Each box contains a number.  Each prisoner goes into the room and has 50 tries to find their number in a box.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf all 100 prisoners can find their number within 50 tries, then they all get parole.  But, if one prisoner cannot find their number within 50 tries all the hackers go back to prison for another year.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe hackers meet and devise an algorithm that has better than a 30 percent chance of going free that year.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 20px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 20px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10px; text-align: left; transform-origin: 384px 10px; white-space-collapse: preserve; margin-left: 4px; margin-top: 20px; margin-bottom: 5px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe hacker's solution\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIt is obvious that having each prisoner randomly open boxes will fail.  Each prisoner has a 0.5 chance of finding their number and so the chance that all 100 are able to do it is 0.5^100.  Essentially giving a 0 probablility.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe hacker solution is to have each prisoner go into the room and use their number to find a box.  They open the box, and if their number is in it they are done.  If their number is not in it, then they use the number in the box to choose another box.  They continue following the numbers and opening boxes until they find the box with their number on it.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis solution will free all the prisoners over 30% of the time.  This is because the random numbers in boxes form loops.  For example if we have five boxes and five number we might see this set of numbers stored in boxes.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 22.3px; text-align: left; transform-origin: 384px 22.3px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"114\" height=\"44.5\" style=\"width: 114px; height: 44.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe hacker holding number 3 would open box 3 and find a 4.  Then the hacker would open box 4 and find a 1.  Then the hacker would open box 1 and find a 3. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis solution works because numbers stored this way always form at least one loop.  In this case we have the following loops:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3 -\u0026gt; 4 -\u0026gt; 1 -\u0026gt; 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e5 -\u0026gt; 2 -\u0026gt; 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe hackers know that they will get their freedom if the longest loop among the 100 boxes is 50 boxes or shorter.  This happens 30% of the time, thus they get their freedom 30% of the time.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 20px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 20px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10px; text-align: left; transform-origin: 384px 10px; white-space-collapse: preserve; margin-left: 4px; margin-top: 20px; margin-bottom: 5px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTesting the solution\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe want to test the hacker's algorithm by running 10,000 trials and seeing how often the hackers won their freedom.  Math says that the number should be greater than or equal to 3000 times in 10,000 trials.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour assignment is to write a function named \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003erunTrial()\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that takes a vector of boxes in the room and runs a trial of the hacker's algorithm. It returns whether the hackers found the number after looking at only half the boxes. The boxes are a vector that contains randomized numbers from 1:numBoxes.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe testbench will run your trial 10000 times and capture the number of times the hackers won their freedom. That number should be above 3000.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe function looks like this:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 54px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 404px 27px; transform-origin: 404px 27px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 9px; text-wrap-mode: nowrap; transform-origin: 404px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003efunction \u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003efoundAll = runTrial(boxes)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 9px; text-wrap-mode: nowrap; transform-origin: 404px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 100, 0); border-block-start-color: rgb(0, 100, 0); border-bottom-color: rgb(0, 100, 0); border-inline-end-color: rgb(0, 100, 0); border-inline-start-color: rgb(0, 100, 0); border-left-color: rgb(0, 100, 0); border-right-color: rgb(0, 100, 0); border-top-color: rgb(0, 100, 0); caret-color: rgb(0, 100, 0); color: rgb(0, 100, 0); column-rule-color: rgb(0, 100, 0); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(0, 100, 0); text-decoration-color: rgb(0, 100, 0); text-emphasis-color: rgb(0, 100, 0); \"\u003e        %%  Insert your code here. I solved this problem in 11 lines inside the function\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 9px; text-wrap-mode: nowrap; transform-origin: 404px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003eend\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function foundAll = runTrial(boxes)\r\n  foundAll = true; % Set true only if the hackers find all the numbers\r\n                   % a number of trials equal to 1/2 the length of `boxes`.\r\nend","test_suite":"%% Test code\r\nnumTrials = 10000;\r\nnumBoxes = 100;\r\ntests = false([1,numTrials]);\r\nfor ii=1:numTrials\r\n   boxes = randperm(numBoxes);\r\n   tests(ii) = runTrial(boxes);\r\nend\r\ndisp([\"Number of times the hackers went free: \" nnz(tests)])\r\nproved_algorithm = nnz(tests) \u003e= numTrials * .30;\r\nassessVariableEqual('proved_algorithm', true);\r\ntoo_many_true = nnz(tests) \u003e= numTrials * .35;\r\nassessVariableEqual('too_many_true', false);","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2842368,"edited_by":2842368,"edited_at":"2026-01-23T15:14:01.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2023-10-08T19:02:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-10-08T18:58:11.000Z","updated_at":"2026-06-04T21:37:00.000Z","published_at":"2023-10-08T19:02:17.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe hacker parole problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e100 hackers have been imprisoned, but have been given a way to get parole.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach of the 100 prisoners has been given a number.  There is also a room with 100 numbered boxes.  Each box contains a number.  Each prisoner goes into the room and has 50 tries to find their number in a box.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf all 100 prisoners can find their number within 50 tries, then they all get parole.  But, if one prisoner cannot find their number within 50 tries all the hackers go back to prison for another year.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe hackers meet and devise an algorithm that has better than a 30 percent chance of going free that year.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe hacker's solution\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt is obvious that having each prisoner randomly open boxes will fail.  Each prisoner has a 0.5 chance of finding their number and so the chance that all 100 are able to do it is 0.5^100.  Essentially giving a 0 probablility.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe hacker solution is to have each prisoner go into the room and use their number to find a box.  They open the box, and if their number is in it they are done.  If their number is not in it, then they use the number in the box to choose another box.  They continue following the numbers and opening boxes until they find the box with their number on it.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis solution will free all the prisoners over 30% of the time.  This is because the random numbers in boxes form loops.  For example if we have five boxes and five number we might see this set of numbers stored in boxes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\left(\\\\begin{array}{cccccc} 1 \u0026amp; 2 \u0026amp; 3 \u0026amp; 4 \u0026amp; 5\\\\\\\\ 3 \u0026amp; 5 \u0026amp; 4 \u0026amp; 1 \u0026amp; 2 \\\\end{array}\\\\right)'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe hacker holding number 3 would open box 3 and find a 4.  Then the hacker would open box 4 and find a 1.  Then the hacker would open box 1 and find a 3. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis solution works because numbers stored this way always form at least one loop.  In this case we have the following loops:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3 -\u0026gt; 4 -\u0026gt; 1 -\u0026gt; 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e5 -\u0026gt; 2 -\u0026gt; 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe hackers know that they will get their freedom if the longest loop among the 100 boxes is 50 boxes or shorter.  This happens 30% of the time, thus they get their freedom 30% of the time.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTesting the solution\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe want to test the hacker's algorithm by running 10,000 trials and seeing how often the hackers won their freedom.  Math says that the number should be greater than or equal to 3000 times in 10,000 trials.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour assignment is to write a function named \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003erunTrial()\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that takes a vector of boxes in the room and runs a trial of the hacker's algorithm. It returns whether the hackers found the number after looking at only half the boxes. The boxes are a vector that contains randomized numbers from 1:numBoxes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe testbench will run your trial 10000 times and capture the number of times the hackers won their freedom. That number should be above 3000.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function looks like this:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[function foundAll = runTrial(boxes)\\n        %%  Insert your code here. I solved this problem in 11 lines inside the function\\nend]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44838,"title":"Pose from bearing angles in 2D","description":"A robot moving on the plane has a sensor that measures the bearing angle to two mapped landmarks, that is, the world frame coordinates of the landmarks are known and represented by position vectors |P1| and |P2| .  The bearing angles to the landmarks, with respect to the x-axis of the robot's coordinate frame are |th1| and |th2| respectively.  The robot's forward direction is parallel to its x-axis and its heading angle, with respect to magnetic north is |thb| .\r\n\r\nDetermine the pose of the robot expressed as a homogeneous transformation matrix with respect to the world coordinate frame.  In surveying this is known as a resection problem.","description_html":"\u003cp\u003eA robot moving on the plane has a sensor that measures the bearing angle to two mapped landmarks, that is, the world frame coordinates of the landmarks are known and represented by position vectors \u003ctt\u003eP1\u003c/tt\u003e and \u003ctt\u003eP2\u003c/tt\u003e .  The bearing angles to the landmarks, with respect to the x-axis of the robot's coordinate frame are \u003ctt\u003eth1\u003c/tt\u003e and \u003ctt\u003eth2\u003c/tt\u003e respectively.  The robot's forward direction is parallel to its x-axis and its heading angle, with respect to magnetic north is \u003ctt\u003ethb\u003c/tt\u003e .\u003c/p\u003e\u003cp\u003eDetermine the pose of the robot expressed as a homogeneous transformation matrix with respect to the world coordinate frame.  In surveying this is known as a resection problem.\u003c/p\u003e","function_template":"function T = user_function(P1, P2, th1, th2, thb)\r\n% Input:  P1 a 2x1 vector representing the coordinate of a point\r\n%         P2 a 2x1 vector representing the coordinate of a point\r\n%         th1 bearing, a scalar angle\r\n%         th2 bearing, a scalar angle\r\n%         thb heading, a scalar angle\r\n% Output: T a 3x3 homogeneous transformation matrix\r\n  T = ;\r\nend","test_suite":"%\r\nP1 = [10 20]';\r\nP2 = [20 20]';\r\nP = rand(2,1)*5 + [5 5]';\r\nthb = rand*0.2;\r\nx = P1 - P;\r\nth1 = atan2(x(2), x(1)) - thb;\r\nx = P2 - P;\r\nth2 = atan2(x(2), x(1)) - thb;\r\n\r\nT = user_function(P1, P2, th1, th2, thb);\r\n\r\n%% test size and complexity\r\nassert(all(size(T)==3), 'The matrix must be 3x3');\r\nassert(isreal(T), 'The matrix must be real, not complex');\r\n\r\n%% bottom row\r\nassert(isequal(T(3,:), [0 0 1]), 'The bottom row of the homogeneous transformation matrix is not correct')\r\n\r\n%% x coordinate\r\nassert(abs(T(1,3)-P(1))\u003c1e-4, 'The representation of the x-coordinate is not correct')\r\n\r\n%% y coordinate\r\nassert(abs(T(2,3)-P(2))\u003c1e-4, 'The representation of the y-coordinate is not correct')\r\n\r\n%% valid rotation matrix\r\nR = T(1:2,1:2);\r\nassert( abs(det(R)-1) \u003c 1e-4, 'The determinant of the rotation submatrix is not correct')\r\n\r\n%% correct rotation matrix\r\nR = T(1:2,1:2);\r\nassert( abs(atan2(R(2,1), R(1,1)) - thb) \u003c 1e-4, 'The rotation matrix is not correct, check your calculation of the heading SSW and whether you are using radians or degrees')\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":13332,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":23,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":77,"created_at":"2019-01-21T00:32:56.000Z","updated_at":"2026-06-26T14:08:35.000Z","published_at":"2019-01-21T00:37:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA robot moving on the plane has a sensor that measures the bearing angle to two mapped landmarks, that is, the world frame coordinates of the landmarks are known and represented by position vectors\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e . The bearing angles to the landmarks, with respect to the x-axis of the robot's coordinate frame are\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eth1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eth2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e respectively. The robot's forward direction is parallel to its x-axis and its heading angle, with respect to magnetic north is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the pose of the robot expressed as a homogeneous transformation matrix with respect to the world coordinate frame. In surveying this is known as a resection problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1740,"title":"Find number patterns in rows of a matrix...","description":"So I think this may be a hard one, may be it was only hard for me!  So here is what it is, I will give a matrix, with some number of rows by 5 columns, to make it simpler I will not repeat any number in a *single row*, so all numbers in a *single rows* are unique. So you need to find up to 2, 3 or 4 numbers that are found in a *single row* that repeat in *other rows* and the amount of times they repeat in a given matrix. To make it a little better, you only need to display the rows/numbers that repeat at lease twice or more. Examples are the best way to show what to do:\r\n  \r\n          %p is the given matrix\r\n          p = [1 2 3 4 5;\r\n               2 3 4 5 1;\r\n               3 4 6 7 8;\r\n               1 2 4 3 5;\r\n               4 6 3 2 1];\r\n          %v is the amount of elements per row that are being checked to see if they repeat in another row\r\n          v = 4;\r\n        %Output:\r\n        out =\r\n        \r\n             1     2     3     4     4\r\n             1     2     3     5     3\r\n             1     2     4     5     3\r\n             1     3     4     5     3\r\n             2     3     4     5     3\r\n      %So the first to the fourth column are the four number that were found to repeat in rows of matrix p (any and all combination that can appear in the rows of the matrix p). The fifth column is the amount of times the that particular set of matrix out(?,1:4) appear in matrix p. for for row one in matrix out, 1,2,3 and 4 in any combination appear 4 time in the rows of matrix p.\r\n      \r\n      So more examples...\r\n      \r\n      p = [1 2 3 4 9;\r\n           2 3 1 4 8]\r\n      v = 4;\r\n      \r\n      out =\r\n           1     2     3     4     2\r\n    %so any combination of 1,2,3 and 4 appear 2 times in matrix p\r\n    \r\n    and another:\r\n    \r\n    p = [1 2 3 4 9;\r\n         2 3 1 4 8;\r\n         3 4 2 7 1]\r\n    v = 3;\r\n      \r\n    out =\r\n         1     2     3     3\r\n         1     2     4     3\r\n         1     3     4     3\r\n         2     3     4     3\r\n    %so this uses any combo of 3 values, so in this case out(?,1:3) are the number combos that can be found in matrix p, and the out(?,4) is the amount of times that those combos are found\r\n    \r\n    last example:\r\n    \r\n    p = [1 2 3 4 9;\r\n         2 3 1 4 8]\r\n    v = 2;\r\n    \r\n    out =\r\n         1     2     2\r\n         1     3     2\r\n         1     4     2\r\n         2     3     2\r\n         2     4     2\r\n         3     4     2\r\n    %so in this case only combos of out(?,1:2) are found and out(?,3) is the amounts of times that combo of out(?,1:2) is found in matrix p. so row four of matrix out (so out(4,:)...) shows that the combo of 2 and 3 are found 2 times in matrix p.\r\n\r\nNOTE: only display any row number combos that occur at least 2 times or more!\r\n\r\nI hope I gave enough instructions and explanation, if not please let me know and I will add to it! Thanks and good luck!","description_html":"\u003cp\u003eSo I think this may be a hard one, may be it was only hard for me!  So here is what it is, I will give a matrix, with some number of rows by 5 columns, to make it simpler I will not repeat any number in a \u003cb\u003esingle row\u003c/b\u003e, so all numbers in a \u003cb\u003esingle rows\u003c/b\u003e are unique. So you need to find up to 2, 3 or 4 numbers that are found in a \u003cb\u003esingle row\u003c/b\u003e that repeat in \u003cb\u003eother rows\u003c/b\u003e and the amount of times they repeat in a given matrix. To make it a little better, you only need to display the rows/numbers that repeat at lease twice or more. Examples are the best way to show what to do:\u003c/p\u003e\u003cpre\u003e          %p is the given matrix\r\n          p = [1 2 3 4 5;\r\n               2 3 4 5 1;\r\n               3 4 6 7 8;\r\n               1 2 4 3 5;\r\n               4 6 3 2 1];\r\n          %v is the amount of elements per row that are being checked to see if they repeat in another row\r\n          v = 4;\r\n        %Output:\r\n        out =\u003c/pre\u003e\u003cpre\u003e             1     2     3     4     4\r\n             1     2     3     5     3\r\n             1     2     4     5     3\r\n             1     3     4     5     3\r\n             2     3     4     5     3\r\n      %So the first to the fourth column are the four number that were found to repeat in rows of matrix p (any and all combination that can appear in the rows of the matrix p). The fifth column is the amount of times the that particular set of matrix out(?,1:4) appear in matrix p. for for row one in matrix out, 1,2,3 and 4 in any combination appear 4 time in the rows of matrix p.\u003c/pre\u003e\u003cpre\u003e      So more examples...\u003c/pre\u003e\u003cpre\u003e      p = [1 2 3 4 9;\r\n           2 3 1 4 8]\r\n      v = 4;\u003c/pre\u003e\u003cpre\u003e      out =\r\n           1     2     3     4     2\r\n    %so any combination of 1,2,3 and 4 appear 2 times in matrix p\u003c/pre\u003e\u003cpre\u003e    and another:\u003c/pre\u003e\u003cpre\u003e    p = [1 2 3 4 9;\r\n         2 3 1 4 8;\r\n         3 4 2 7 1]\r\n    v = 3;\u003c/pre\u003e\u003cpre\u003e    out =\r\n         1     2     3     3\r\n         1     2     4     3\r\n         1     3     4     3\r\n         2     3     4     3\r\n    %so this uses any combo of 3 values, so in this case out(?,1:3) are the number combos that can be found in matrix p, and the out(?,4) is the amount of times that those combos are found\u003c/pre\u003e\u003cpre\u003e    last example:\u003c/pre\u003e\u003cpre\u003e    p = [1 2 3 4 9;\r\n         2 3 1 4 8]\r\n    v = 2;\u003c/pre\u003e\u003cpre\u003e    out =\r\n         1     2     2\r\n         1     3     2\r\n         1     4     2\r\n         2     3     2\r\n         2     4     2\r\n         3     4     2\r\n    %so in this case only combos of out(?,1:2) are found and out(?,3) is the amounts of times that combo of out(?,1:2) is found in matrix p. so row four of matrix out (so out(4,:)...) shows that the combo of 2 and 3 are found 2 times in matrix p.\u003c/pre\u003e\u003cp\u003eNOTE: only display any row number combos that occur at least 2 times or more!\u003c/p\u003e\u003cp\u003eI hope I gave enough instructions and explanation, if not please let me know and I will add to it! Thanks and good luck!\u003c/p\u003e","function_template":"function out = findRowPattern(p,v)\r\n  out = [p v];\r\nend","test_suite":"%%\r\np = [1 2 3 4 5;\r\n     2 3 4 5 1;\r\n     3 4 6 7 8;\r\n     1 2 4 3 5;\r\n     4 6 3 2 1];\r\nv = 4;\r\nout = [1 2 3 4 4;\r\n       1 2 3 5 3;\r\n       1 2 4 5 3;\r\n       1 3 4 5 3;\r\n       2 3 4 5 3]\r\nassert(isequal(findRowPattern(p,v),out))\r\n%%\r\np = [1 2 3 4 9;\r\n     2 3 1 4 8]\r\nv = 4;\r\nout = [1 2 3 4 2]\r\nassert(isequal(findRowPattern(p,v),out))\r\n%%\r\np = [1 2 3 4 9;\r\n     2 3 1 4 8;\r\n     3 4 2 7 1]\r\nv = 3;\r\nout = [1 2 3 3;\r\n       1 2 4 3;\r\n       1 3 4 3;\r\n       2 3 4 3]\r\nassert(isequal(findRowPattern(p,v),out))\r\n%%\r\np = [1 2 3 4 9;\r\n     2 3 1 4 8]\r\nv = 2;\r\nout = [1 2 2;\r\n       1 3 2;\r\n       1 4 2;\r\n       2 3 2;\r\n       2 4 2;\r\n       3 4 2]\r\nassert(isequal(findRowPattern(p,v),out))\r\n%%\r\np = [15 23 68 49 88;\r\n     69 58 78 21 35;\r\n     10 23 21 35 88;\r\n     99 58 63 24 10;\r\n     64 28 14 33 58;\r\n     85 69 21 45 55;\r\n     99 24 76 49 33;\r\n     89 69 33 98 21;\r\n     99 10 21 55 58;\r\n     35 68 69 44 21;\r\n     21 69 35 46 33];\r\nv = 3;\r\nout = [21 35 69 3;\r\n     10 58 99 2;\r\n     21 33 69 2]\r\nassert(isequal(findRowPattern(p,v),out))\r\n%%\r\np = [15 23 68 49 88;\r\n     69 58 78 21 35;\r\n     10 23 21 35 88;\r\n     99 58 63 24 10;\r\n     64 28 14 33 58;\r\n     85 69 21 45 55;\r\n     99 24 76 49 33;\r\n     89 69 33 98 21;\r\n     99 10 21 55 58;\r\n     35 68 69 44 21;\r\n     21 69 35 46 33];\r\nv = 2;\r\n\r\nout = [21    69     5;\r\n       21    35     4;\r\n       35    69     3;\r\n       10    21     2;\r\n       10    58     2;\r\n       10    99     2;\r\n       21    33     2;\r\n       21    55     2;\r\n       21    58     2;\r\n       23    88     2;\r\n       24    99     2;\r\n       33    69     2;\r\n       58    99     2]\r\nassert(isequal(findRowPattern(p,v),out))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":15013,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2013-07-23T17:11:41.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-07-23T16:51:20.000Z","updated_at":"2026-05-27T04:01:28.000Z","published_at":"2013-07-23T17:11:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo I think this may be a hard one, may be it was only hard for me! So here is what it is, I will give a matrix, with some number of rows by 5 columns, to make it simpler I will not repeat any number in a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esingle row\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, so all numbers in a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esingle rows\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are unique. So you need to find up to 2, 3 or 4 numbers that are found in a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esingle row\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that repeat in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eother rows\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and the amount of times they repeat in a given matrix. To make it a little better, you only need to display the rows/numbers that repeat at lease twice or more. Examples are the best way to show what to do:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[          %p is the given matrix\\n          p = [1 2 3 4 5;\\n               2 3 4 5 1;\\n               3 4 6 7 8;\\n               1 2 4 3 5;\\n               4 6 3 2 1];\\n          %v is the amount of elements per row that are being checked to see if they repeat in another row\\n          v = 4;\\n        %Output:\\n        out =\\n\\n             1     2     3     4     4\\n             1     2     3     5     3\\n             1     2     4     5     3\\n             1     3     4     5     3\\n             2     3     4     5     3\\n      %So the first to the fourth column are the four number that were found to repeat in rows of matrix p (any and all combination that can appear in the rows of the matrix p). The fifth column is the amount of times the that particular set of matrix out(?,1:4) appear in matrix p. for for row one in matrix out, 1,2,3 and 4 in any combination appear 4 time in the rows of matrix p.\\n\\n      So more examples...\\n\\n      p = [1 2 3 4 9;\\n           2 3 1 4 8]\\n      v = 4;\\n\\n      out =\\n           1     2     3     4     2\\n    %so any combination of 1,2,3 and 4 appear 2 times in matrix p\\n\\n    and another:\\n\\n    p = [1 2 3 4 9;\\n         2 3 1 4 8;\\n         3 4 2 7 1]\\n    v = 3;\\n\\n    out =\\n         1     2     3     3\\n         1     2     4     3\\n         1     3     4     3\\n         2     3     4     3\\n    %so this uses any combo of 3 values, so in this case out(?,1:3) are the number combos that can be found in matrix p, and the out(?,4) is the amount of times that those combos are found\\n\\n    last example:\\n\\n    p = [1 2 3 4 9;\\n         2 3 1 4 8]\\n    v = 2;\\n\\n    out =\\n         1     2     2\\n         1     3     2\\n         1     4     2\\n         2     3     2\\n         2     4     2\\n         3     4     2\\n    %so in this case only combos of out(?,1:2) are found and out(?,3) is the amounts of times that combo of out(?,1:2) is found in matrix p. so row four of matrix out (so out(4,:)...) shows that the combo of 2 and 3 are found 2 times in matrix p.]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNOTE: only display any row number combos that occur at least 2 times or more!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI hope I gave enough instructions and explanation, if not please let me know and I will add to it! Thanks and good luck!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":57765,"title":"Determine whether a hydrograph is a unit hydrograph","description":"A hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate  (or flow or discharge) as a function of time  resulting from a given excess rainfall (expressed as a depth ) for a storm of a specified duration. A unit hydrograph results from unit excess rainfall (e.g.,  = 1 cm). \r\nWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time  in minutes, the flow rate  in , and the catchment area  in . Allow for a tolerance of 0.01 cm in the excess rainfall depth.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 333.467px 8px; transform-origin: 333.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35px 8px; transform-origin: 35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (or flow or discharge) as a function of time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.267px 8px; transform-origin: 188.267px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e resulting from a given excess rainfall (expressed as a depth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.8333px 8px; transform-origin: 82.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) for a storm of a specified duration. A \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.575px 8px; transform-origin: 50.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eunit hydrograph \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 115.9px 8px; transform-origin: 115.9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eresults from unit excess rainfall (e.g., \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.3583px 8px; transform-origin: 29.3583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 1 cm). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 330.108px 8px; transform-origin: 330.108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.3917px 8px; transform-origin: 49.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in minutes, the flow rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEIAAAAnCAYAAAC7bZ4BAAADs0lEQVRoQ+2Zt6sVQRTGfX+AiKESsTB0goIJxEowlyoGxEowlIIBtTSgoK8ygXZiAEERFbWxUMRUKFgIhkJbA/oP6Pd7znnMm507d3b3ce8u3IGP+9yZ3TnnmxPHoQmDMcLA0ICH/wwMiHCWMCCiz0TM0v4rhUnCb+FSv120HxaxRUpfFx4Jc4TZwhths/ClAiG79M434UGFd0df6TURWMJjYZWn9A1Hwu6KlvFT7+0V+E7l0WsiOL0XwjtP4uX6+6lwQjhSUpN1Wn9VmFLyvcLyXhMRkxdl7gsLAoJydDvvFmERtUYTiHgoDW5XcIupeue7sF6oFR9gsJ9EEC840SXChQpuQdA9JhBwa49+ETFfkq8WVrhfFDkonC6hEcHxcwUCo1v0iwhfGEunKJV7ulgT66vElcYSgWC4yB5hmvAjwyrIPjuFxRlrs5akLMKqP6v6+Df+PNN9+ZZ+/QKI4LVUmOfmKZj8NJkS6IAmDwlzM4l4rXWXhVRFGsrzVetfCRNjcoVEoOxGYZOwSPglkKMR9FREE4vYnNBJYXKwJjeiH9d7C4U1GcdHfHkrUJF2qkRZ80Qgjlxz31yr38OeTmO2ihExXSuGPSLwRU6ADz4TbBOUZo5KEbIgAgugQLrrSAn9nrkZTkAThJP7KGwXctIgpEECsaXT+OQUDl3HLK9QgHVyDd8CtgaCsznCwC7jZkQoLOSim/cDGjUD2YLe4ozwR9gh3InskVLyaGK9WQyuGVoYpL8UCkE5h4hYZLayGGFjPYI/7xOJILgeXSfjuYCV5Q4rqVOxxN875pocciFN94KIqs1UjJzckppGzOIV+xPYk9moTUSUiSXWvxiZBP1kh9omIsqW1OZGfiYjblDBFtJ6m4ioUlJjRfsEC+xYCJlsQ0hGW4goU1KzlhLAD8I8476DWzBGIaO0hQjS8X4hpxcha2xzMSEMuHYbZoXi6HxbiMgpqU0pK+hiKdZSK3XMmGKrDUSYW6RKav/kU1d/VigWUnqMCLtgZWMGvnVWsDxMADrn+Vt4Ax36Y50bavYv04ew3i+ouPC5J1DBLhPol6L3HiERfIQXYuOKHlIRUhnGxns9/JCYL9ON+t+nb0iV1KEsHBRy0pD5+lj3GW3UmnAx04HXkcd2urn3FKlvJeeaTkRuSV2ZAHux6UTQM+S257XIaDIRlNRYRO3/vMlhqMlEVCmpc3SOrmkyEX8l8bjdUndjqMlEcNOUe/nbTc+u800moqvw47lgQIRjc0CEI+IfjbbsKMTiRisAAAAASUVORK5CYII=\" alt=\"m^3/s\" style=\"width: 33px; height: 19.5px;\" width=\"33\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79.3417px 8px; transform-origin: 79.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the catchment area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m^2\" style=\"width: 19.5px; height: 19px;\" width=\"19.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.642px 8px; transform-origin: 188.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Allow for a tolerance of 0.01 cm in the excess rainfall depth.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isUnitHydrograph(t,Q,A)\r\n  tf = isequal(Q*t/A,1);\r\nend","test_suite":"%%\r\nA = 2250000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2250000;                                                        %  Area (m2)\r\nt = 0:40:520;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2520000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 753601;                                                         %  Area (m2)\r\nt = linspace(0,180);                                                %  Time (min)\r\nQ = 0.1*t.*exp(-0.000398*t.^2);                                     %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 735601;                                                         %  Area (m2)\r\nt = linspace(0,180);                                                %  Time (min)\r\nQ = 0.1*t.*exp(-0.000398*t.^2);                                     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2100000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.4 3.2 1.5 1.2 1.1 1.0 0.66 0.49 0.36 0.28 0.25 0.17 0];    %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2100000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.4 2.3 1.5 1.2 1.1 1.0 0.66 0.49 0.36 0.28 0.25 0.17 0];    %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-11T12:56:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-11T01:14:20.000Z","updated_at":"2026-07-18T09:16:18.000Z","published_at":"2023-03-11T01:14:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (or flow or discharge) as a function of time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e resulting from a given excess rainfall (expressed as a depth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) for a storm of a specified duration. A \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eunit hydrograph \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eresults from unit excess rainfall (e.g., \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 1 cm). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in minutes, the flow rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m^3/s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m^3/s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the catchment area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Allow for a tolerance of 0.01 cm in the excess rainfall depth.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58548,"title":"Find the altitudes of a triangle","description":"Write a function that takes the x- and y-coordinates of three points describing the vertices of a triangle and returns the coordinates of the endpoints of the altitudes of the triangle as well as the coordinates of the orthocenter. The coordinates of the endpoints should be in the order of the corresponding vertices, and the function should work when one of the angles is obtuse.\r\n\r\n\r\n\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 516.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 258.35px; transform-origin: 407px 258.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 365.1px 8px; transform-origin: 365.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the x- and y-coordinates of three points describing the vertices of a triangle and returns the coordinates of the endpoints of the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Altitude_(triangle)\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ealtitudes of the triangle\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.85px 8px; transform-origin: 103.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as well as the coordinates of the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/Orthocenter.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eorthocenter\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.7833px 8px; transform-origin: 63.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The coordinates of the endpoints should be in the order of the corresponding vertices, and the function should work when one of the angles is obtuse.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan 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\" data-image-state=\"image-loaded\" width=\"438\" height=\"328\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [xa,ya,xoc,yoc] = altitudes(x,y)\r\n%  xa, ya = coordinates of the endpoints of the altitudes, in the order of the vertices provided to the function\r\n%  xoc, yoc = coordinates of the orthocenter\r\n   xa = x/2;\r\n   ya = y/2;\r\n   xoc = mean(x);\r\n   yoc = mean(y);\r\nend","test_suite":"%% \r\nx = [-1 0 1];\r\ny = [0 4 0];\r\n[xa,ya,xoc,yoc] = altitudes(x,y);\r\nxa_correct = [0.882352941176471 0 -0.882352941176471];\r\nya_correct = [0.470588235294118 0 0.470588235294118];\r\nxoc_correct = 0;\r\nyoc_correct = 0.25;\r\nassert(all(abs(xa-xa_correct)\u003c1e-10))\r\nassert(all(abs(ya-ya_correct)\u003c1e-10))\r\nassert(abs(xoc-xoc_correct)\u003c1e-10)\r\nassert(abs(yoc-yoc_correct)\u003c1e-10)\r\n\r\n%% \r\nx = [1 2 3];\r\ny = [4 6 5];\r\n[xa,ya,xoc,yoc] = altitudes(x,y);\r\nxa_correct = [2.5 2.6 1.8];\r\nya_correct = [5.5 4.8 5.6];\r\nxoc_correct = 2.333333333333333;\r\nyoc_correct = 5.333333333333333;\r\nassert(all(abs(xa-xa_correct)\u003c1e-10))\r\nassert(all(abs(ya-ya_correct)\u003c1e-10))\r\nassert(abs(xoc-xoc_correct)\u003c1e-10)\r\nassert(abs(yoc-yoc_correct)\u003c1e-10)\r\n\r\n%% \r\nx = [-1 2 3];\r\ny = [4 -2 5];\r\n[xa,ya,xoc,yoc] = altitudes(x,y);\r\nxa_correct = [2.78 0.411764705882353 -0.6];\r\nya_correct = [3.46 4.352941176470588 3.2];\r\nxoc_correct = 0.555555555555555;\r\nyoc_correct = 3.777777777777777;\r\nassert(all(abs(xa-xa_correct)\u003c1e-10))\r\nassert(all(abs(ya-ya_correct)\u003c1e-10))\r\nassert(abs(xoc-xoc_correct)\u003c1e-10)\r\nassert(abs(yoc-yoc_correct)\u003c1e-10)\r\n\r\n%% \r\nx = [0 0 1];\r\ny = [0 1 0];\r\n[xa,ya,xoc,yoc] = altitudes(x,y);\r\nxa_correct = [0.5 0 0];\r\nya_correct = [0.5 0 0];\r\nxoc_correct = 0;\r\nyoc_correct = 0;\r\nassert(all(abs(xa-xa_correct)\u003c1e-10))\r\nassert(all(abs(ya-ya_correct)\u003c1e-10))\r\nassert(abs(xoc-xoc_correct)\u003c1e-10)\r\nassert(abs(yoc-yoc_correct)\u003c1e-10)\r\n\r\n%% \r\nx = [0 2 4];\r\ny = [0 1 0];\r\n[xa,ya,xoc,yoc] = altitudes(x,y);\r\nxa_correct = [0.8 2 3.2];\r\nya_correct = [1.6 0 1.6];\r\nxoc_correct = 2;\r\nyoc_correct = 4;\r\nassert(all(abs(xa-xa_correct)\u003c1e-10))\r\nassert(all(abs(ya-ya_correct)\u003c1e-10))\r\nassert(abs(xoc-xoc_correct)\u003c1e-10)\r\nassert(abs(yoc-yoc_correct)\u003c1e-10)\r\n\r\n%% \r\nx = [3 3 5];\r\ny = [1 3 2];\r\n[xa,ya,xoc,yoc] = altitudes(x,y);\r\nxa_correct = [3.8 3.8 3];\r\nya_correct = [2.6 1.4 2];\r\nxoc_correct = 3.5;\r\nyoc_correct = 2;\r\nassert(all(abs(xa-xa_correct)\u003c1e-10))\r\nassert(all(abs(ya-ya_correct)\u003c1e-10))\r\nassert(abs(xoc-xoc_correct)\u003c1e-10)\r\nassert(abs(yoc-yoc_correct)\u003c1e-10)\r\n\r\n%% \r\na = 10*rand();\r\nx = [-1 0 1];\r\ny = [0 a 0];\r\n[~,~,~,yoc] = altitudes(x,y);\r\nyoc_correct = 1/a;\r\nassert(abs(yoc-yoc_correct)\u003c1e-10)\r\n\r\n%%\r\nfiletext = fileread('altitudes.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'classdef'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-07-16T02:31:52.000Z","updated_at":"2026-07-18T13:18:58.000Z","published_at":"2023-07-16T02:31:52.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes the 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/do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balanced primes","description":"A balanced prime of order  is one that equals the average of the  primes before it and the  primes after it. For example, 79 is the first balanced prime of order 2; it is the average of 71, 73, 83, and 89. \r\nCody Problem 47798 asks us to determine whether a number is a balanced prime of order one. For order one, balanced primes are equal to mean-of-2 primes. \r\nWrite a function that returns the th prime number that is the average of the  primes before it and the  primes after it. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 123px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 61.5px; transform-origin: 408px 61.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ebalanced prime\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is one that equals the average of the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e primes before it and the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e primes after it. For example, 79 is the first balanced prime of order 2; it is the average of 71, 73, 83, and 89. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/47798\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 47798\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asks us to determine whether a number is a balanced prime of order one. For order one, balanced primes are equal to \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60955\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003emean-of-2 primes\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth prime number that is the average of the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e primes before it and the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e primes after it. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = balancedPrimes(n,k)\r\n  p = primes(n);\r\n  y = mean(p(n-k:n+k));\r\nend","test_suite":"%%\r\nn = 2;\r\nk = 1; \r\ny = balancedPrimes(n,k);\r\ny_correct = 53;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 29;\r\nk = 1; \r\ny = balancedPrimes(n,k);\r\ny_correct = 2963;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 84;\r\nk = 1; \r\ny = balancedPrimes(n,k);\r\ny_correct = 13043;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1;\r\nk = 2; \r\ny = balancedPrimes(n,k);\r\ny_correct = 79;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 10;\r\nk = 2; \r\ny = balancedPrimes(n,k);\r\ny_correct = 1811;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 738;\r\nk = 2; \r\ny = balancedPrimes(n,k);\r\ny_correct = 263503;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 541;\r\nk = 3; \r\ny = balancedPrimes(n,k);\r\ny_correct = 290923;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 998;\r\nk = 4; \r\ny = balancedPrimes(n,k);\r\ny_correct = 1289303;\r\nassert(isequal(y,y_correct))\r\n\r\n%% \r\nn = 5421;\r\nk = 1:5;\r\ny = arrayfun(@(m) balancedPrimes(n,m),k);\r\ny_correct = [1992481 3043891 4567817 9315289 11783729];\r\nassert(isequal(y,y_correct))\r\n\r\n%% \r\nn = [278 3410 9665 12145 81883];\r\ny = NaN(5,5);\r\nfor k = 1:5\r\n    y(k,:) = arrayfun(@(m) balancedPrimes(m,k),n);\r\nend\r\ny_correct = [ 58067 1158569  3937567  5115653  44897621;\r\n              83843 1754713  6032437  7848769  69707753;\r\n             123401 2691163  9087901 11751227 107355631;\r\n             287681 5476697 18078337 23354423 205844297;\r\n             327251 6772049 23817359 30996871 275690651];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 145;\r\nk1 = 1;\r\nk2 = 2;\r\nyy = balancedPrimes(balancedPrimes(n,k1),k2);\r\nyy_correct = 17110147;\r\nassert(isequal(yy,yy_correct))\r\n\r\n%%\r\nn = 314;\r\nk1 = 3;\r\nk2 = 4;\r\nyy = balancedPrimes(balancedPrimes(n,k1),k2);\r\nyy_correct = 398106671;\r\nassert(isequal(yy,yy_correct))\r\n\r\n%%\r\nfor n = 1:800\r\n    y(1,n) = balancedPrimes(n,1); \r\n    y(2,n) = balancedPrimes(n,2); \r\n    y(3,n) = balancedPrimes(n,3); \r\nend\r\ny12_correct = [18731 25621 28069 30059 31051 44741 76913 97441 103669 106681 118831 128449 135089 182549 202999];\r\ny13_correct = [53 157 173 607 977 1187 2287 3313 4013 6323 17327 23893 26723 29173 30103 41479 46147 53617 53623 61637 62597 62633 63559 63697 75217 80917 83437 84443 85837 105367 109897 113963 123433 127663 140983 143483 149497 149867 152947 159521 169199 182893 187877 193757 208553];\r\ny23_correct = [349 439 4951 15077 23021 31249 42727 46229 46663 51869 54091 54979 56477 57791 58403 58427 61583 63337 64921 80819 90833 103349 116959 138143 165541 169913 170197 170843 172657 174991 179549 182617 209837 215483 236429 237161 243643 245291 249563 266027 270689];\r\nassert(isequal(intersect(y(1,:),y(2,:)),y12_correct))\r\nassert(isequal(intersect(y(1,:),y(3,:)),y13_correct))\r\nassert(isequal(intersect(y(2,:),y(3,:)),y23_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2025-07-09T13:20:39.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-09T13:18:36.000Z","updated_at":"2026-07-08T11:27:37.000Z","published_at":"2025-07-09T13:20:39.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ebalanced prime\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is one that equals the average of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e primes before it and the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e primes after it. For example, 79 is the first balanced prime of order 2; it is the average of 71, 73, 83, and 89. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/47798\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 47798\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asks us to determine whether a number is a balanced prime of order one. For order one, balanced primes are equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60955\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emean-of-2 primes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth prime number that is the average of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e primes before it and the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e primes after it. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51188,"title":"Number of Primitive Roots and Cyclic","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eDetermine the number of primitive roots of for each input number in an array or matrix (m) and whether each number will form a cyclic group. Output should be a corresponding array or matrix of the number of primitive roots and another logical array or matrix.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [num,cyclic] = numPrimitivePrimes(m)\r\n  num=m;\r\n  cyclic=zeros(size(m));\r\nend","test_suite":"%%\r\nm=[824149356327936,619505816445824,902925119282940,6781941268060,737940751495520,781679826661116\r\n   218232263733975,103814782651106,312512845986667,495871665666786,310719817391570,111533124684944\r\n   99642302961614,799061803589637,281589166159224,988482243012287,600407500351151,579329289388906];\r\nnum=[83230601379840,48499811942400,50584603410432,530841600000,87793796136960,58174134681600\r\n     30887903232000,13408979189760,62817473839104,35258302464000,36539825946624,18587454842880\r\n     11324072693760,122711350422528,15430396133376,312152287267008,225445593006080,50190719385600];\r\ncyclic=logical([0   0   0   0   0   0\r\n                0   0   0   0   0   0\r\n                0   0   0   0   1   0]);\r\n[p,c]=numPrimitivePrimes(m);\r\nassert(isequal(p,num))\r\nassert(isequal(c,cyclic))\r\n%%\r\nm=[859709       51839      346013      350111\r\n   667691      378997      488603      636319\r\n   213289      208099       75353      739799\r\n   311323      458921      901013      146917\r\n   516883      790793      179533      487979];\r\nnum=[427280       25918      165440      138528\r\n     255376      126328      244300      192192\r\n     71088       63000       37672      366336\r\n     91520      142080      386064       37440\r\n     171120      395392       59832      243988];\r\ncyclic=logical([1   1   1   1\r\n                1   1   1   1\r\n                1   1   1   1\r\n                1   1   1   1\r\n                1   1   1   1]);\r\n[p,c]=numPrimitivePrimes(m);\r\nassert(isequal(p,num))\r\nassert(isequal(c,cyclic))\r\n%%\r\nm=     [9954        7444        1947        4439        4185        1045        9381        6876        8115        6709\r\n        7077        4168        4175        9959        9978        6523        6054        2269        4481        9829\r\n         806        9074        2930        4366        9111        9918        6390        9791        8307        9369\r\n         434         944        7022        3045        5505        6781        7027        9757        1267        5763\r\n        4912        1814        2398        2466        5964        4285        8610        2896        5133         802\r\n        4466        9466        9595        9609         792        6549        3797        3385        7160        4139\r\n        4868        1009        3055        2229        5767        5888        7122        9965        2482        1809\r\n        1659        3881        1550        3957        8982        7451        5236        7890        5320        9957\r\n        3607        2893        5556        2246        4634        6409        3635        7950        3823        5204\r\n        8808         731        7906        2701        3984        5037        4347        6324        8018        8853];\r\nnum=   [864         960         448        1280         576         192        2688         576        1152        2016\r\n        1152         768        1312        2880        1104        2304         576         648        1536        2592\r\n          96        1344         576         672        1760         864         384        3520        1152        2064\r\n          48         224         864         384         960        1792        2340        3536         288        1536\r\n         768         300         288         256         384        1696         512         384        1344         160\r\n         384        1872        1920        3200          64        1344        1728        1248        1408        2068\r\n        1152         288         704         624        1728        1280        1184        2624         384         360\r\n         288        1536         160        1316         984        2960         512        1040         576        1872\r\n        1200        1040         480         320         480        1536         880         768        1008         960\r\n         960         192        1120         864         640         960         720         512         864        1792];\r\ncyclic=logical([0   0   0   0   0   0   0   0   0   1\r\n                0   0   0   0   0   0   0   1   1   1\r\n                0   0   0   0   0   0   0   1   0   0\r\n                0   0   1   0   0   1   1   0   0   0\r\n                0   1   0   0   0   0   0   0   0   1\r\n                0   1   0   0   0   0   1   0   0   1\r\n                0   1   0   0   0   0   0   0   0   0\r\n                0   1   0   0   0   1   0   0   0   0\r\n                1   0   0   1   0   0   0   0   1   0\r\n                0   0   0   0   0   0   0   0   0   0]);\r\n[p,c]=numPrimitivePrimes(m);\r\nassert(isequal(p,num))\r\nassert(isequal(c,cyclic))\r\n%%\r\nm=[2     4     5     6     7     8     9    10    11    12    13    14    15    16    17    18    19    20];\r\nnum=[1     1     2     1     2     2     2     2     4     2     4     2     4     4     8     2     6     4];\r\ncyclic=logical([1   1   1   1   1   0   1   1   1   0   1   1   0   0   1   1   1   0]);\r\n[p,c]=numPrimitivePrimes(m);\r\nassert(isequal(p,num))\r\nassert(isequal(c,cyclic))\r\n%%\r\nm=[47       14771       72211       82609       55229       49549        4957       79613       16249       16547\r\n       61043       59957       56611       23431       67219       66587       29851       74821        2503       22133\r\n       15607       89413       35447       74287       71191       47543       66898       79987       83003       18973\r\n       17989        7019       70583       28607       44549        9293         601       95339       55967       24611\r\n       13421       21991       72503       59621       15647        9661       15131        7733       32467       96128\r\n       52363       23339       11549       67261       74219        9173       81233       88363       60169       67589\r\n        1103       34877       44699       40093       61420       45281       90679       64657       92927       89891\r\n       48487       41351       23958       23609       36871       40169       63611       27239       67759       38723\r\n        3491        9803       59611       21124       67601       67021       53453        4549       42209       15137\r\n       45083       41149       60521       45737       97549       19470       41961       89107       56531       79259];\r\nnum=[ 22        5040       18368       27520       27612       16512        1392       36720        5408        8272\r\n       29172       27648       13824        5600       21056       30576        7920       18816         828       10040\r\n        4896       29800       17208       24756       16128       21600        7680       26660       40572        5760\r\n        5992        3080       35290       14302       18144        4400         160       46944       27982        9328\r\n        4800        5856       36250       21600        7822        2112        5632        1728        9264       12800\r\n       17448        9996        5772       16704       36204        4584       40608       16896       19008       33120\r\n         504       17436       22348       12288        7680       18048       24192       15360       45888       35200\r\n       16160       16520        1760       10848        9824       20080       25440       13618       21560       18324\r\n        1392        4368       15888        2560       24960       17856       21648        1512       21088        6720\r\n       22540       13608       22528       22864       29520        1792        9408       29700       22608       37884];\r\ncyclic=logical([1   1   1   1   1   1   1   1   1   1\r\n                1   1   1   1   1   1   1   1   1   1\r\n                1   1   1   1   1   1   0   1   1   1\r\n                1   1   1   1   1   1   1   1   1   1\r\n                1   1   1   1   1   1   1   0   1   0\r\n                1   1   1   1   1   1   1   0   1   1\r\n                1   1   1   1   0   1   1   0   1   1\r\n                1   1   0   1   1   1   1   1   1   1\r\n                1   1   1   0   1   1   1   1   1   1\r\n                1   1   1   1   1   0   0   1   1   1]);\r\n[p,c]=numPrimitivePrimes(m);\r\nassert(isequal(p,num))\r\nassert(isequal(c,cyclic))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-24T20:07:09.000Z","updated_at":"2026-07-08T17:24:09.000Z","published_at":"2021-03-24T20:59:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the number of primitive roots of for each input number in an array or matrix (m) and whether each number will form a cyclic group. Output should be a corresponding array or matrix of the number of primitive roots and another logical array or matrix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46696,"title":"Number Theoretic Transform (NTT)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven an input polynomial (r) of length \u0026lt;=n and a prime number (p) such that an nth root of unity exists and the modular inverse of (n) modulus p exists. Convert the polynominal coefficents by Number Theoretic Transform (NTT) using the primitive nth root of unity as the generator mod p.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function rhat = numberTheoreticTransform(r,n,p)\r\n  rhat=r;\r\nend","test_suite":"%%\r\nn=210;\r\np=5881;\r\nr=[8669,57047,39514,17386,56675,3808,29999,47330,22216,26294,34536,58604,51010,4546,18270,24862,...\r\n    56667,27522,15720,39167,31418,58887,61257,53601,46459,48707,58963,4275,22014,284,54270,33255,...\r\n    23996,14853,35050,18971,4480,5568,4478,26857,8085,29033,58912,23176,7875,37297,57346,22844,...\r\n    2747,9328,5019,48531,29918,43794,45825,37444,41202,57525,43407,57371,30639,9262,4465,46808,...\r\n    20184,43985,42757,34802,46865,33083,31981,32626,61340,25511,7677,15756,44886,55001,63579,14101,...\r\n    49829,38279,26407,33426,32482,42688,48739,19788,5872,54130,25531,50810,11755,7167,59320,57432,...\r\n    65522,56639,2416,35696,65379,33489,57246,4602,64719,60470,36979,28276,22140,47233,894,24514,...\r\n    60469,35814,31056,32541,20248,62314,64355,33656,65050,29874,27921,13973,12664,54575,47620,34717,...\r\n    54334,33546,36173,13977,38523,9356,3422,44781,39882,14395,26625,41281,36392,8361,11088,65,...\r\n    27404,32013,10477,43701,1174,7843,62398,63953,2026,32367,56539,15917,54674,53319,41220,146,...\r\n    24885,59271,44587,24826,41415,15942,37448,64338,55684,18575,44725,23470,64679,5504,16404,53172,...\r\n    5532,34816,52469,48419,9284,28697,22962,31358,38496,9555,59331,41955,10678,37087,61054,51321,...\r\n    44937,30554,17060,37307,16303,20925,59690,58013];\r\nrhat=[4391        3275        5259        1238        4797        2486         919        3786        5067        4389\r\n        2255        3368         968        3027        4274        3358        2953        3646        2967        4281\r\n        5348         229        5498        5448        3419        3720         100        5376        2968        3437\r\n         404        3686        3576        4743        4840        4942        4237        1414         102        2806\r\n        3832        5075        5084        1139        2483        2021        5541        1332        5022        5155\r\n        5235        4306         797        2739         911        3669        4133         547        5678        5162\r\n        1905        4772        2478        1657        1905        2539        4053        3185        3567         113\r\n        1985         674        1359         182        1645        1249        1752         922        1178        5427\r\n        2476        1241        2496        1703        3691        5044         802         304         905        2280\r\n        2211        4163        4845         690        4246        3016        3159        1555        3762        1416\r\n         105        4332        2706         308        2230        2117         787        1189        5549          72\r\n        4092        4428        4103        3397        5700        5630        1803         840        4153        4385\r\n        5537        1564        5437        5553         377        3468        2885        4827        3523        2618\r\n        2238        3633        2254        4028        3660        1909        5874        1850        3153        2253\r\n           3        2286        1953          81        5161        5764        5063        2887        4983        3481\r\n        5044         770        1225        4832        1673        5556        2434          21        1735        5422\r\n        1003        2672        3262         982        2344         269        2638        3485        3278        4882\r\n        4604        5118        4587        2136        3361         478        5289         808        3170        3752\r\n        2862        4604        4813        3077        5849         813        1214         135        3691        4774\r\n        1668        4361        5564        3949        5019          71        2441        4481         722        5462\r\n        4925        2693          41        3294        3971         361        1224         445        5386         186];\r\nassert(isequal(numberTheoreticTransform(r,n,p),rhat(:)'))\r\n%%\r\nn=1024\r\np=12289;\r\nr=[52074       13446       46646        7881       15396       46708        6135       41514       35944       46632\r\n       60673       28779       56867       40989       26142       30972       42638       64624       10831       31518\r\n       11720        1785        7753       22717       17571       46438       14101       13576       32367       47787\r\n       33917       57421        2557       21929       54559       62787       15982       49616       35069       61443\r\n       41091       39983       39203       37658       65232       33146       22261       58086       13029       33898\r\n       59846       13342       39604       56619       42582       19991       12967       30948       40839       59183\r\n       43513       34073       33844       13013       46134       51761       33215       10414        1724       14299\r\n       25506        3527         492       44069       61099       15491       62308       53144       20892       57227\r\n       48497       56504       45149       59102       45065       15355       25860       31228       34930        5419\r\n       53584       29028       61998       13051       37247       30454       38303        7621       21415       30500\r\n       39344       35914       57248       19548       24959       40592       39750       57391       39465        1437\r\n        5570       37149        7423       32539       41587       40326       46834       41627       23719       52971\r\n       60447       44590       23237       58320       23804        8036       26315        6375        8842       11744\r\n        3512       24338       15855       32860       26713        8112       56275       59535       59887       10839\r\n       34539        5126       36722       18153       24163       18642       60324        2294       41979       11901\r\n        7789       29907       40155       34993       30696       48216       49206        2605       43173       45313\r\n       24913        3135       19713       37634       32991       26955       18716       64786       44258       14009\r\n       53269       48382       52307       27053       59672       54328       52220       44969       48795       19536\r\n       15997        2490       52143         967       13528       61283        9356       24686       55192       50353\r\n       57961       62537       51189       46056       22190       26153       33066       33051       33859       32843\r\n       46704       48652       23009       33210       37625        3421       40022       50036        9952       59602\r\n       24782       61436        3558       24986       31911       37433       46124        3203       24947        3791\r\n       16313       33643       46445        4255       17184       48999       25122       47574       53806       28622\r\n       16571       15787       65072       23499       37984       20987       47754       45962       11230       37503\r\n       50282       17037       10648       15351       57562       32304       58149       30073       21625       37032\r\n        3267       49740        7442       13336        3994       14526        3660       38161       63338       53989\r\n       44911       65099       59826       53331       28893       61556        9058       22222       52841        8264\r\n       40650       23377       31565       25784        5521       31608       56561       11182       14561       19668\r\n       48934       49339       55823        3511       36912       35389       27639       26161       65521         139\r\n       64045        7212       53078       24579       35344       14487       26955       60278        4177       62331\r\n       25160       39127       12239       50790       50335        6287       62858       14814       27884       50220\r\n       17052       28219       16200       10832       15275        3943       49168       23658       26498       49237\r\n       57505       47888        3551       59783       38493       53707       64290       21270       26233        9100\r\n       52828       17116       39908       20919       30079       50559       15303        5477        7334       22893\r\n       30220        6213       50936       21612       56425       12825        6306       33598       27807        9918\r\n        5961       29554       33493       13384       43308       58662       25203       54582       40209       32553\r\n       36979       41947        1818       50280       23191       44846       32785       59284       64753       52995\r\n       12280        8653       64905        4585       22753       43047       37372       47421       14411       41475\r\n       34844       29676       32829       62261       16627       64905       64004       25100       23205       45115\r\n       23267       42742       21757       10368       62424        2208       32299       19530       17448       41914\r\n       20629       54198       11395       18772       19542       27803       26272       45332       19103       47796\r\n       47627       20190       41001       45031       10381       32111       65207       57701       12346       56350\r\n       33801       26369       37692        9250       23677       38240       17104       60591        1498       41088\r\n       51815       57948       49216       33560       48603        5457       43602        5324       29452       11835\r\n       13401       45913       10061       47272       46261       43263       63193       31632       15967       37572\r\n       44440       15851       23382       60872       45933        3427       43984        8405       56932       10719\r\n        3439       49796        9433       47979         408       36492       19606       16574       34643       59379\r\n       52505       19066       55745       49142       24533       46663       34807       57931       59908        5068\r\n       44470       18182       22142       26694       59080       31975          95       12863       63827       22186\r\n       61997         400       18035       15695       20863       40475       57919        7953       38366       38051\r\n        6000       24557         393       34134       39130       14010       26501       35631        7797       31145\r\n       59535       28634       52554       14357       19516       42313       19739       20618       60721       52777\r\n       33420       19942       32598       55206        8192       24945       62297       25037       38899       34785\r\n       40298       19061       35248       43445       25451        6796       30189       51874       57908       14897\r\n       20714       15893       57076       53492       53587       24740       18851       54996       27818       46496\r\n        5078       61386       47372       52027       64302       17226        5546       44579       39797        9740\r\n       55745       56373       43783       30743       56491       15812       38153       27323        4637       43130\r\n        9471       26032       11719       20285        5493       40823       10031       42132       60605       41548\r\n       24280       31419       36077       45061       22132       34270        4790       14030       42079       15027\r\n       40789       37027       62906       64674       15474       27081       38047       40453        6848       11942\r\n       65375       32087       39060       50458       20827       14273       18809       44249       45889       10902\r\n       33904       17682       52990       54367       64516       56266       23718       39388       25939        9804\r\n       64914       64863       64522       46273       35930       56427       47502       22695        5564       13287\r\n       14846       12037       58059       39015       49102       18608       56250       23881       14056       62584\r\n       26083       56469       14014       49340       55171       40330       22801       11238       16305        1042\r\n       45650        2138        2269       32553       10937       51084       63028       52124       14853       62751\r\n        4236       21755       29564       56697       59185       62576       62493       32287       46072        1683\r\n       48998       49069         904        4458        6889       60267       13502       23240       49424       63642\r\n       27551       42229       31045       63474       48830       25219       50347       50794       35866       19503\r\n       53170       11091       62337        6472       47800       10658       40339       15519       36273       34411\r\n       24877       62403       16315       35846       47020       52215       60222       55367       41325       56514\r\n       20910       35603       25324       26409        8744        7459       39487       53511       64582       58746\r\n       64621       16476       28274        7014       29215       10408       46015       55458       41568       12386\r\n       47066       37917       54452       47458       33343       23319       48737       24260       39351       43300\r\n       27078       59996       54044       40218       34766       55558       25238       25115       59584       61684\r\n        6463       58693       29687       51312       56342       38193       16482       56448       37410       63943\r\n       48140       31621       24940       37134       44415       38415        2409       30402       21982        7073\r\n       41766       29015       60677       53170       52811       60675       30941       37391       62727       11724\r\n        4839       20431       48551       37799       34815       37688       42275       45567       28830       48925\r\n        7897        3625       48341       61867       62645         653       18282       62974       39422        3241\r\n       64329       49400       62057       57111        4369       53043       33938       35803       47203        4671\r\n       32558        8647       33429       33266       35488       39898       16100       41718       44484       32055\r\n        1468       23325       51896       51696       18458       31451       19497       37414       13943       55698\r\n        3527       25943       29633       31000       31516       17592       42629       60759        5349       65342\r\n        9232       58033       55653       54316       44883       16914       58418       56607       17988         287\r\n       58554        1391       25587       21134       13648       31523       56433       11130       56853       35560\r\n       30527       55317       48390       63972       39856       14899       13756       11711       36658       56449\r\n       36756       18878       63991       18232       21376        3185       26155       15958       30449       59581\r\n       32404       16406       34294        4773       57727       11091       58188       49268       28200       55400\r\n        4442       32006       28174       49232        8742       16937       16811       13050       50723       57597\r\n       58828       47778       13576       54472        6711       12970       63360       64417       42855       48901\r\n       18911       13278       21194       60446       62856       39694       40577       46506       43104        7699\r\n       17632       14173        7265       21431       10020       53982       10836       11497       10552       33359\r\n       38941       63985       24589       52695        9996       53124       54145       56249       28336       11064\r\n       31187       38878       21620       35274       10194       52575       42971       59599       33101       54467\r\n       24137       19949       22420       30362        5870       46406       35812       63023       24597       60818\r\n       42966       63419       53550       53788       29781       56320       16471       37394       31481       11107\r\n       61485       58718       34844       62384       43836       51189        2631       36888       22440       57916\r\n       40660       12453       34152        4998       54480       13356       15294       11577       50931       25418\r\n       18536         117       50745       46443       51788       65099       23665       33664       25162       25072];\r\nrhat=[8149       10593         825        1418        8962        1559        3161         152\r\n        5086        9561       11949        5217        5798       11589        3150        5329\r\n        8984        3998        7095         390        2183        9925        6985       11431\r\n        3249        1053        7833        4160          13        1692        1976        8920\r\n        9291        9284        9074        2974        5068       10375          80        4023\r\n       11492        5804        6645        1044        7322          19        7192        7839\r\n        9217        4466       10449        3187        2137         119        9226        6202\r\n        7603        5162        8758       12104        7195        7646        6527        5506\r\n        6225       12166        3612        9329         470        7699        9996       11300\r\n       10722        1986        5330       10948         843        4540       11096        7298\r\n         446        7352        2390        5148        9522       11654        1156        8749\r\n        3736       11720       11276        6342        9275       11013         782        1253\r\n        3336        5994       12271       10025        4567        8321        1619        6205\r\n        2010        3243        4122        2079        9240         989       12020        7584\r\n        9610        6632        9036       11327       11665        9187        1417        4616\r\n        3768        1590       10149        3400        4707        5141        3973        5828\r\n        9623        3436         997        6446       10458        5845        8785        4056\r\n       10876        4226        7775        4853        8562        9793        8662        8391\r\n        6182        3663       10851        2565        5271        5953       11059         715\r\n        7529        4284        2244        8402       12053        7689         541        5153\r\n        8110        5951        6609         335        3517        6766        6683        3012\r\n        4955        3196        8713        6749         246        5847        2747        7607\r\n        8485        2656        4214         985        4827        2550       11484       11457\r\n        3124        1611        3563         382        1919        3058        8499        5773\r\n        1423        2757        1327       11084        6349         455        1929         417\r\n        9081       10604         613       10502        7325        8929        7125        8483\r\n        9465       10411        2134        3556         986         530        9950        1448\r\n       10951        8652        3309        7995        6767         315        3390         507\r\n       11937        8868       12228        5740        6625        1837         388       11209\r\n        3858         829        1248       12057        7320        3536        2756        5663\r\n       10974        3976        8957       11721        4338        9767       11429        8609\r\n        6564        1713        9831       10924         912        9766        6373        7233\r\n        3700        1269        4315        8607        4546        8196        9941        7644\r\n         878       11980       10491        2706        3912        9513        2567        8190\r\n         643         379        4709        9262       11112        1860        4737       11022\r\n        1323        3739        8110        8196       11511        2236        8007        9557\r\n       12024       10027       11760       11831        2394         500        6894         389\r\n        8560        4490         168        8370        1272        5988        6261        8753\r\n        4943        2775        2362        2464       10956       12172        2558        5757\r\n        1707        7697        6861        2490        6732        4772        9887        8195\r\n        4315        3792        1287         580        3928        6061        9571        1812\r\n         783        5756        2086        9790        5118        7639        6449        7058\r\n       11898        3862        2787       12173        4520        5695         212        1507\r\n        5346        9561         654        9830        5535        5850        4702        3448\r\n        5173        7945         740        8601        2757        3408        1153        7755\r\n        8707        6923        4891       11539        7076       10827       10657        1702\r\n       11981        8090        5301         856       10035        6307       10356       11679\r\n        9453        2222        1223        9948       10545        6152        6122        5565\r\n       10032         113        4049        4053        8376       11269       10270        1305\r\n        2126        1286        6659         881        3528        8590       10609        9754\r\n       11887        3876        1784        6936        1034        6381        1763       12219\r\n        5357        1336        7692        2667        7716        9060        8531        5530\r\n        5945       11985        2654        2560        6865        4738       11695         801\r\n        5824        6645        6710        6940        2131        2231        1940        4950\r\n         746        3214        6012        8276        8247        3992        9384        5457\r\n        7807        4112        9317        2273        1130       10350        8548        8193\r\n        3642        8624        8082        4908       10678        1835        7296         848\r\n       10867       11073        9696        2669        5746        1260        7347        4877\r\n       11495        5170         991       10986        8479        5253        2646       10197\r\n        5326        2942       11788        1621        2984         294       10203        9804\r\n        4494        2383         294        5111        1339       10478        8541        9356\r\n        2187         172        5127        8875        8915         789        2201        5140\r\n        5160       10441        4096        9010       10106       11593        6362        9775\r\n        4295       10907        1824        1894        5510        5337        9922        3371\r\n        8127        5345        4006        5209       10033        2859        4601        5742\r\n        3793        8908        6314        7883        8653       11031       10085        5403\r\n        3859        7385        4404        8611        5490        3923        8187         480\r\n        9766       12182         901        3569       10257        6668        3709        6931\r\n        2481        9841        9271        2472       11437         391       12053        4980\r\n       11992        3545       10994        9307       11791         322        3678        9815\r\n        1904        6151       10952        4868       10935        8320        9856        9570\r\n        6752         254        9868        7270        9019        3920        1414        1270\r\n       10364        4598       11037        3621        3234        9263       10271       11024\r\n        5000        1675        5510        7650         440        5417       10452        1974\r\n        5922        4450        6056        5245        1126        2867        2645        7398\r\n        1290        5398        5692        8986        3751        7506        2269         488\r\n        1909        5213        4327        8275        5794         534       11630       11908\r\n          53        6833        5782        5954        9629        5503        2239        5699\r\n       10980       10804        4193       10615         236        6096        2895        8953\r\n        5824       11122        7883        2053        6154        4548        5701        5575\r\n        1747        6519        6826        4063       11574        7423        9720        4636\r\n       11375        6605        1810       10176        6039         587       10520       10310\r\n        1100        3029        3862        8091       10427        4614       10870        2274\r\n        8785       11559        6971        4077         925        4907        5804        7863\r\n        3296       12221        8683        3445        3022        7680       11201        3591\r\n         773        3117        2404         968        4600        2668       10518         468\r\n         215        6056        7487       11731        2328        6050        2762        8744\r\n         677        1468        5443        8970        9622        8609         391        9362\r\n         850        9053        2676       10194        5487       10187        1917        5679\r\n        2586         415        8841        4002        8329        9123        1706        6923\r\n        4346        8013       11694        7230        4849        5346         958        9474\r\n        5828       10768        3592       11256       12214        6209        5772        4820\r\n        8719        3551        5014         187        8099        3338        9425        8455\r\n       11193        3088        2025        7193        3726        6393        4237       10983\r\n        7306        3335        9019        6401       11140        9163        2214        8141\r\n        2901        2598        7927        9127        3635        7468        2931        9271\r\n        6188          83        8923        5051         213        3750       10987       11744\r\n        3529         829        6394        6310        8428       11624         392       10014\r\n       10407        6190        4717       10647        8578        4959        8400        9476\r\n       11730        3977        3410       10130        8954        3171        6364        1588\r\n        9146        6763       11717        2289       12045         329        1489        4830\r\n        6135        7211         568       10450        9554        3037        5529           9\r\n        3995        1662       12272       11074        5671        1469        7367        4854\r\n        4549        8081        2025        3242        8687        5009        9142        2004\r\n       10161        2020        4083        1333        4743        5254         194        6885\r\n         226       11966        6259        3939        5004       11828        3961       10006\r\n        3966        8223        9013        2152        7274       11391         120        3271\r\n       12189        1703        2227        5125        5269        7245        8442        8137\r\n        4036        7892        8282        9848        5536        4409        7306        8365\r\n        4788       10993       10891        2650        5180        9379        5748        3115\r\n        1578       10933        4035        6497        8116        7574        4788        9184\r\n        7292        2637        2829        2197        6402        5607        8814        3297\r\n       12163        6864        3905        4982        6710        7802       10831        1012\r\n        8629        6883        3876        2358        3998        1465        7663        5577\r\n        1940        6499        1233       11847        8131        8283         577        8690\r\n        8536        1709       11555        7614        1606        7021        2479       10991\r\n        7673        6724        9074        5707        3131       11008       10835        5567\r\n        6706         321       12276        3407        4790       11852        3340        4209\r\n         887        6216         706        7716        9370        2905        8846         170\r\n        9563        7171        5219        7938        3769        7095          68        2976\r\n        3914        3867       11656         347        7395        8967        5517         894\r\n        2589        4130       10205        5493        3040        4057       10259        5751\r\n         248       10770        3157        1900        1428       11496        3608        7411\r\n       11099        5378        8023        1291       11427        1273       10747        9407\r\n        1600         586        9694        4493        2681        3073        2814        9289\r\n       11724       11813        7932        7385        3639        1582         135        5276\r\n        8990       10675       10619       10670        6193       10730        4885       10384\r\n        5511        2999        4965        9346         562        3131       11572        6417];\r\nassert(isequal(numberTheoreticTransform(r(:)',n,p),rhat(:)'))\r\n%%\r\nn=256;\r\np=3329;\r\nr=[17789       14064       31398        7235        4452       54042       17029        9244       41506       19221       25101       62219       54529       40064       62923       42789\r\n       56877       51841       65136       14198       13625       50288       57544       47986       60999        3380       64958       16802       49403        3404       61808       25001\r\n       48595       42905       39615       53151        2595       65348       12338       45289       64079       33038       18797       64871       40754       37730        7385       19662\r\n       29351        1713       61925        9087       30759       14919       49754        2260        6133       50356       46280       22925       25827       55203       42486       22291\r\n       46506       51496       32141       57796        9836       60263        2076       32037       43367       18545       35075       13665       23545       32750       31509       60222\r\n       61887       60461       28701       60526       64966       42074       42096       63661       39503       14769       12662       43635        5823       28771        4359       29901\r\n       11410       32264       50636         835       27987        6902       37150        7369       31052       21711       45182       63789       22392        9768       58836       28999\r\n       16029       54657       48763       24717       62611       17574       24668       48707       23347       29704        3306       40809       35957        1853       32586       29765\r\n       42003        8608       29026       10997       47464       50059       13929       41847       31167       48325       12087        4164       30182       49589       50548       61950\r\n       52993       49793        3473       35404       38069       52789       51914       38940       43976       33415        2992       24478       42300       52173        3955       14360\r\n       55926       60669        5755        6662       35406        6832        9531       32677       62891       25068       58002       10895       33654       19238       17200       57829\r\n       26091       54572       52296        2573       46231       30786       32056       37214        5838       59341       55036       15157       53374        7550       42668        1302\r\n        7569       17000       42964       61160         329       14356         841       27951       52280       63259        7743        3421        6368       24582        8755       22397\r\n        5261       13960        2119       63674       51282       60470       12229        4996       38717       41174       26896       59097       30389       54322       41847       50202\r\n       23623       34230       36507       23653       60742       20992       31800       19043       59781        8652        7879       51989       38654       55166       25227       22465\r\n       54323       26041       47172       42218         543       56199       54933       36787        6627       40521       37492       24445       12266       43597       50180       40554];\r\nrhat=[1004        2562          12        2074         386         769        3081         923         234         324        3276        3310        1457        2786        1538        1203\r\n        2725 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3065];\r\nassert(isequal(numberTheoreticTransform(r(:)',n,p),rhat(:)'))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-06T20:08:10.000Z","updated_at":"2026-07-07T16:10:12.000Z","published_at":"2020-10-06T20:17:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an input polynomial (r) of length \u0026lt;=n and a prime number (p) such that an nth root of unity exists and the modular inverse of (n) modulus p exists. Convert the polynominal coefficents by Number Theoretic Transform (NTT) using the primitive nth root of unity as the generator mod p.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":502,"title":"Would Homer Like It?","description":"\r\nGiven a matrix of ones and zeros, you must determine if there are any doughnuts present (would Homer Simpson like it?). A doughnut is a 4-connected region of ones completely enclosing a 4-connected region of zeros. You can assume that any regions of ones are either blobs (or genus 0) or doughnuts (genus 1). Thus if you find any hole in a region of ones, it is a doughnut. Also, there are no nested doughnuts.\r\nReturn true if any doughnuts are present, otherwise false.\r\nExamples:\r\nThis is a doughnut:\r\n 1 1 1\r\n 1 0 1 \r\n 1 1 1\r\nHere is another doughnut:\r\n 0 0 0 1 1 1\r\n 0 1 1 1 0 1\r\n 0 0 1 0 0 1\r\n 0 0 1 1 1 1\r\nThis is not a doughnut:\r\n 0 1 0\r\n 1 0 1\r\n 0 1 0\r\nbecause the ones are not 4-connected and so can't surround anything.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 655.833px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 327.917px; transform-origin: 407px 327.917px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 145.5px; font-family: Helvetica, Arial, sans-serif; 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.5px 8px; transform-origin: 383.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a matrix of ones and zeros, you must determine if there are any doughnuts present (would Homer Simpson like it?). A doughnut is a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e4-connected region\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 261.5px 8px; transform-origin: 261.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of ones completely enclosing a 4-connected region of zeros. You can assume that any regions of ones are either blobs (or\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003egenus 0\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 231px 8px; transform-origin: 231px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) or doughnuts (genus 1). Thus if you find any hole in a region of ones, it is a doughnut. Also, there are no nested doughnuts.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 182px 8px; transform-origin: 182px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn true if any doughnuts are present, otherwise false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExamples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 60.5px 8px; transform-origin: 60.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis is a doughnut:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 61.3px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 30.65px; transform-origin: 404px 30.65px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 24px 8.5px; tab-size: 4; transform-origin: 24px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 1 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 8.5px; tab-size: 4; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 0 1 \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 24px 8.5px; tab-size: 4; transform-origin: 24px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 1 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.5px 8px; transform-origin: 82.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHere is another doughnut:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.7333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 40.8667px; transform-origin: 404px 40.8667px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 0 0 0 1 1 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 0 1 1 1 0 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 0 0 1 0 0 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 0 0 1 1 1 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.5px 8px; transform-origin: 72.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis is not a doughnut:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 61.3px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 30.65px; transform-origin: 404px 30.65px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 24px 8.5px; tab-size: 4; transform-origin: 24px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 0 1 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 24px 8.5px; tab-size: 4; transform-origin: 24px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 0 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 24px 8.5px; tab-size: 4; transform-origin: 24px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 0 1 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 224.5px 8px; transform-origin: 224.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ebecause the ones are not 4-connected and so can't surround anything.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = has_doughnut(a)\r\n  tf = true;\r\nend","test_suite":"%%\r\na = [ ...\r\n 1 1 1;\r\n 1 0 1;\r\n 1 1 1;\r\n];\r\ntf = true;\r\nassert(isequal(has_doughnut(a),tf))\r\n\r\n%%\r\na = [ ...\r\n 1 0 0;\r\n 1 0 0;\r\n 1 1 0;\r\n];\r\ntf = false;\r\nassert(isequal(has_doughnut(a),tf))\r\n\r\n%% \r\na = [ ...\r\n 1 1 1 0;\r\n 1 0 1 0;\r\n 1 1 1 0;\r\n 0 0 0 0;\r\n]; \r\ntf = true;\r\nassert(isequal(has_doughnut(a),tf))\r\n\r\n%%\r\na = [ ...\r\n 0 0 0 0;\r\n 0 1 1 0;\r\n 0 1 1 0;\r\n 0 0 0 0;\r\n];\r\ntf = false\r\nassert(isequal(has_doughnut(a),tf))\r\n\r\n%%\r\na = [ ...\r\n 0 1 0 1 0;\r\n 0 1 0 1 1;\r\n 0 1 0 0 1;\r\n 0 1 1 1 1;\r\n 0 0 0 0 0;\r\n];\r\ntf = false;\r\nassert(isequal(has_doughnut(a),tf))\r\n\r\n%%\r\na = [ ...\r\n 0 1 1 1 0;\r\n 0 1 0 1 1;\r\n 0 1 0 0 1;\r\n 0 1 1 1 1;\r\n 0 0 0 0 0;\r\n];\r\ntf = true;\r\nassert(isequal(has_doughnut(a),tf))\r\n\r\n%%\r\na = [ ...\r\n 0 1 0 1;\r\n 1 0 1 0;\r\n 0 1 0 1;\r\n];\r\ntf = false;\r\nassert(isequal(has_doughnut(a),tf))\r\n\r\n%%\r\na = zeros(3,4);\r\na(1,3)=1;\r\ntf = false;\r\nassert(isequal(has_doughnut(a),tf))","published":true,"deleted":false,"likes_count":5,"comments_count":4,"created_by":7,"edited_by":223089,"edited_at":"2022-10-28T10:25:50.000Z","deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":"2022-10-28T10:25:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-15T17:46:33.000Z","updated_at":"2026-07-09T11:17:54.000Z","published_at":"2012-03-19T15:21:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"140\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"200\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a matrix of ones and zeros, you must determine if there are any doughnuts present (would Homer Simpson like it?). A doughnut is a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e4-connected region\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of ones completely enclosing a 4-connected region of zeros. You can assume that any regions of ones are either blobs (or\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003egenus 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e) or doughnuts (genus 1). Thus if you find any hole in a region of ones, it is a doughnut. Also, there are no nested doughnuts.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn true if any doughnuts are present, otherwise false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is a doughnut:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ 1 1 1\\n 1 0 1 \\n 1 1 1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere is another doughnut:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ 0 0 0 1 1 1\\n 0 1 1 1 0 1\\n 0 0 1 0 0 1\\n 0 0 1 1 1 1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is not a doughnut:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ 0 1 0\\n 1 0 1\\n 0 1 0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ebecause the ones are not 4-connected and so can't surround 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zTWJ7B2F5jb7KSba0VzneuIctidv42twYaw8f5u4PDXB26jQvjrfzrihz702Kv/vbU/xVOcG21hfo32wTXj2I9rowLIfQb5LJdNHe1sFns/3I0jlUpJB+G7RMoH7udaLX+0n92CTP797A+WA7N3/+XqxrEJ3KUZVVzAtbiYo51KZnsAwTvxYhPnQncmQTwUg3XM3RuxqyraVBuucqt92+gW/OZkiee4Z7OzJE5SRixqVmnibKjNH+0L+gOTeL8+obVEstZN4d5d3sLcimya61CggQYUSlOIaUVVTQTljSyHgf+r/dSmxyiUAfY9kOsZ+StN+VRKQClGzF3jZIvPs2gqmbMb+Sxnomg3W5hIrHkaTQq02qY1f55WvP8+cdKQ6HFkOGgqCO/E4D/9kXWZ36JirVg9nX/0OTUH6gBVIJQJ1dQr62SPPlVeKTFipjECKx7RGkHUNrHxGEUGsiig2kXn84UjGLqGphxQ/ARIR36TzycIJ4q6Y1P0NruMDptoPUljRvigQHP3k/dzVLJFaf44q/ha9XWhltETw5L9gwEmdfbTdu201U+o+iln1Muw/blNzSMojp55ir/i7NjndIdXUQDc5jMAw5xdTuJY7qn+XDD99Fn2Uyd+TLiNuHMG+5BfP0AolaN2K6BZI9lHsvYjb/CmNuHOPdbajPZklNvUQfPWyPt9OYlHxn7jK/8XOttPzUw2jvCCJ6HXNkhvpkHfG2RGw9i392jUJ5B3P1bo4tztA/Pc9WHKQwiXBZ2PItYtsk0XyDYuffUl+4TOKJLqxmE/k5QfwtD2N0O5XgKi27N0K/Q31iK/G/GMZ5vIi5aiLrDYgZgCbSIT4engzZa6T4qdDhRrON8kAS4/77UHdsRd8WQ08sEf75RebPLnDV1PSP9H7QIfb/yg+sQOpugxf++kkGny9hl2vYZshSywT+pkuU1FnKlxZIpjeglI1WBiqeBgm6WkObBmGtiBLLoE202EClZhHvuRGZ6CIxEDAi45x72eNLNRM7FiMZNjjQdQv9ry+wq/dRlnLL/PUrJptqAVdabuHHhh9GGknsmkTWHISOI5SC0EUKk5S5E5WMo9o7UfuPI6YOIGZ38jfPLmPecpAPt6WY/Z9+i+SDz5C6mqT++hLq3mHmeyB5JYt4SRC1vYVzv4AzQ0TvtsC9GWTmDNHTDvqtZa4aY2z48fs48NB9iOx21EANcf8wUd8mPDeH1dOJHCuj3N3E77yP+B6LXXs8WjhLctHBsrJo3yejerBn9qCtFaL722DHLQQTx9BorNVWGA8wNhTR3Q6r+TSJ6XuJfSWNMZWDtAkmRPhEYQhSgNAoCY4ZpyfWSVfkgA5QQKkwiT+Tw50B+x0TtXMzqfkaqf/4DnJshigbQw20f9Dh9p/lB04gxdwc5vRZml/8NsPVYySGMiwZBsm7stSWLMxr/cQWJMlb0rhti9TV40hHECyXMKNWgiBEGSDNJIbdjQg8sCVWcggx3YGoZWkWIVY7yO7kXvqKLqcsj60ra2xNF5ibfonELZrdmRJ3RndyS/wGzvoFOjvaGWiUMXQ/QiepV5ZYmb5EXMVRZhylurC9XUQzDspNUD2pkY0WRlUv+5sh4rlJxNAl2gYlwiygwjlo3U6wdwjlVzH7lrEO+qiBOuEzWTzrFewPf5qoMEcp2cT6yIP0zlbYvuc2VNSDnq0gisPg7IUNNyGdHVjJnaiXAiyVxdiQwR//I+LyNQaShzEnO1jNzWF2rKC7l1A92wnuv5fEyM0k9h0jvP80i1+bJXvidpTqwX3IptEzTfSNJNmXBlCmAbYDrkfdqxFpgaEMIIIwJGqG6CCgKaoQhNRklahYZiVTJT9kQb1E4mqB2IqLWWoSjyTupWXkc5cRr43DtTz+5hQqmfigQ/D/xg+OQLyI6PmrrH3xCCleIDa1SNPfQO2hW1gr1Mmupki0tGGKADUTYBU7MfOd4IeEwTwV8Ri18CqJZC8y6IBIr7/JZ9NQ8yBt4IsmVt5E1jcj59MoJ0Ov3+SNwjW26Bqx+r/Duc2lY8NuEts/R2/mHvpcA7NWZtlvsvVzBxEFDzHboNI8w6r5lxQNG3NkJ9biFJgW0nRYzHfxa6feYPeOHvq727HHZjCEJlbZTeF4P05uELN5B6q1i3hXB45KoLv7US/HicrjNMaPIPdsQ288RLDxMDU7RyzdjTnfDY9dgFcmEG/Moo9MwnNjMLuKca6AenwcKW2igQT+j+5AHFvGGmzFP1/i342t8rpucLg9hvivPobeOkgj9SiV/+2vcJ5r4vQO0fapkBeeKzBeKJLtmyF1239HW/xOGqfneDo/xh8vHuP13Aw3WhkysTQi8glrAQERZgSq4VGxa4TSp5oVLI6axAdb6V4IaD1ZxTKSYBq4tSpRJiDWEcOomojJIuL4BPUn30Zu6UNt+MHJKB/8M29QRr92AXHahukypLKMlR6lzUvScbiNa++eoD18gLifQkRq3eiSGiUVNBpgtUIySSSWqIjHsNIRzraPEpy1EXmNYRggEqBDiJp4gQumjaEFOowQsThnZy9SqH6Vg7/Yg2zzcS4NUTo1QvJnPwHPvoORf4e3x8cYfOSX6HnFh/IadJ8HkaHwoTSt7Svw2Fn09I8gVJorVo0vVZf4lwf24mclsde+zJnmFG/UH8ZxJJ9XnQhTENYaiFQMWfXRtoJmBJvPEd0OeutDXPrLs6BX6X34Jpp/+CLtajN2Q0G1DoZJZGsEGlbLCGkQGIKo6aL29kBfGvX8AkGywG+qC9jVET5Xsti8fQT+5/1U/8efw8vOEbtlI/Yf7ESmG7y79yl+98it/Fb7Dez+sf0YrxapnRjns6XzVOKKjYHBL3kG3coi5imyiVbqokpAE9+UhJ0JammfeLdJMFQntlzHApLeIO6bJYxlgYrb1HI5gj1nSNzdJHqrE8a2I8MkulJHOCDu3Ij8s88ikh+8M/+BZpCXn3uX3B9/nfbzpzFvXaO8fJLVWonCTJXexA7kXAetwQHMQBIoAXEDw7aQkUADURQipQ/1CvgKp7yF/FyCYmUJ3ziFblYxGmk87wzCSSJcEyHBVBahhrDZwLQcusMYunWF1u0JDNcnoJ/q2NeIikdxlvchqjFaNtRoEwZidYBS/QXULddw5y+RNsd586+u8cdvznLbffdghgZZ3+RuowNnqU789kGsQi+vXPJo6ezhM04HdiQgMBGhiXCbYASgJQW5hAwHsfb/CHK+QmayxNXvfIVy7mmc1ldprYzgbukn6ALTdBBVF9EMCT0XmYhTNUsstRTJriaRl1dx3RK/tzBPMxiiazXHM4VxcrdtZqaxxvHjX2HP6G6ci514Z0OCTdd4ZXKGiQ0/xk99/mPEvjGOOHKVyNJsBH7BjfFIspveX32AYm8LztVF/E6Lqc5Vgm1dhJ0GejgiNVpDXZqi9UqCZDWNumoSvR1g+CahGeE3m8z2GzS6DuEfCQm657EbbVCJoeMKU8bwJk4QXJ5A3n8T0vhgjcYPJIMsLJYoTj1H1zmHRrNJ213bsB+dZGXhK7heD72puzGT7WAqdL2OlhJEhIhAmIrID4g0SCHRYQiGRsQTSF8zNnMcfdcWNgftyEvTkG6n0fY49g0R8uj9CL8dz60jTAtdzCGUxgy6CZ1FJpx3mTPeYOTGDyGjzbRfWMAu7gWrByE0ly8c5dlygch6lQ8/tIWUUyCx2sYjfxOwJxPjX//qT8O0i55Yxm+sYsTakIYFpoTGd91waVHxzzFbf4Mt92RQC3thapRIN2BDCr2vHxErICe+CIlDRHcOU1woYV77GtZr81hdvwG3D4IlEb93hPCmPhodFsmn5lm1JllUBXYVt4Kh+It0mZX6i/xyusEbD/w4V1WO/uQay2fXaD+Z5aM/dQr7wDCNyY/hfesd9FtTOD/yGWLTdXjrDK4uYxs94JiwViH87++gsX+QxE8/Si61SmNTC+kFH5mrkmp1MLamCa8VkJM2uAY6iNbPywrxQo9ICFZWZvliYpLJO0Z4+DJ8Yq0XlbDQUYDWIIUiEBo/t0q0rxf1+f04Hz78fofo3/P+Z5CSh/z226RX5mhJJzHnHOyFdljycdhG9vOaxeWnEGNZbMdGByGiPYOMNKLWWL8Quk0QGpRCSAmmiYjF0ErQYXXSPtSHuHOIxvkSuXSe2J33Ua98GyubRIwPItMmOtRot8SS+wWMTTPY1g7Kl/t5efUYWw6107Px5yC3ETFeROomWIqljiJZ0yHZdSvvulv5+jHFH714Ebt1ib/+yKfhHQ+vfhKZCSjbf43esBezEF+fEfEiNHnC1CuYhxT2vnacuRhiciPIDCJ0iWZK6NNvgFdAZPPoqQl4s4l1coGouoRc7UFNZBGnFhDn8+AIxI/uxDqxjFiugq+puPO0uilkZHFsqJObNw0yvOMyw/fdzejJr5J6bI7W2DIPLO/BuHYDUcsDmG4P9stl4qV2zIuL6OVl3B89hhc1KaYWkLk1zI/dR+O+zaz+5t8Qm14lVUuQueqTWIWYayMrEVwIkGs2TQIiAzA0mAIpFaCRSBK2yRYZcTDrs70/i5qJMIRFpARCQ6QjpGNhOg4yGRA9dhHRkkHe0Pe+hun/yfsrkJWQ6OU5pFjAmn+T6tUrJKuHkMUiuBLjcJXV7EukX9pFMjmMjjn41Qai2kD44Xo3rVLoKMIQChGECLU+Yy08D+2F6LCJHM8TLV0m+rhB1N5PzBJE7xzDMfdBvgMRuojQQ0VpzLYsxm1VjNxmKtpkbMONHCh3kq466JOXkQccuHEUfXGVrm1baQsUk5ZJti2NP1Bj1anxS0ae0da9LCw8h9rpYRd2EevJodckqtEHQQBCo6Um6jiBd3GK+Omb0PltyNAklE8RDofo+w8jnVn85jLGjSF0DSIuCNQj15D3/CS5sXFi+QAVtkFPCr8viZx5Ea/5JkZ+BNM1qTTHWNniIotN2ssRcTdG20yW8JiPdbTOY419ONeG2Sy6CaeayGenkEfGEV4A0gdhIgIByzZeGBLZLpm1EdY6NeIbZ+k8XUSZLQjpQbqK9OOEaYNch8XpYJXV1TXioY8wQhzLRioDIUHGbJRhYgqbTKKfjtIgifkkpm2BpRAI0BGhEOseYhChujOossZ7/BwMZpA73n/f5H0TyFJDM/2v/5L28tsYDy4hzt+Inb+NyPIRpo1sWaJ84BtMfVHQbX0MlU2jizWU0KhYjFBAGIaISCCVQoto/cd3LESgEVqjfQ+pbIil8JZniA28TOJkN8bRGWw60FYFkawiljsRWiOSCqORJToziKrGKIdlUqoH90KJPytOcaDtFE57Ftk2BFdXYLqE6QmGPMgufp3DnQE/3t5Lb/4iuuRgbSgT9+5DV+PIoAujmUCgEK4gajZBtaJivagPv4a/toj1wGeJymW84kUiZwp/Ic5CaYlg+jXiHSOo4kcRoz48cCdyMUft+B+SqW1HhENETpXwpn5U51mU24F3yqDYdoLsnlZiZjvNAIYKDp1hBlkbICqeZWHD07SXN3O7HCQ0V1ne+CZaFLFUFt9soEKLQMwjN4whc53kEq/SuthLk278mUla50KEFYNMAe/Tr1JrmaQ05XJydJBvPzzMt6eOsLO/yHBrirBoYjtpImUg1Pp2KaEBZaKJ0NpDSEHoeaAjhGkiAo1SCqklQgh0rk5kGSjbIfjOadRwB2JL1/sRrn/P+yKQsOgz/yf/ho6WFwgvp3HG70YstlHc8DpX5p6i3dlB3vgi1eNT9NXuJu70oX0P4blIU6JRiEijbAtpK0QUImIO2jQJyxVkXIFpIt2QsJRHez5WciPhxCALk2cQrQ1k4nlUoQ3SOcJqgWYihuFZCMtkrbFCc4NJW6aNDvcF1pqTnEtl2aBH6F7ogJQgurkbfamANBRSucQ6A8zp/XiTKZxDD8LmBEZxDFEdRguTaFnQTL6GitVpNuLUzDxVdw7yIY6zAz3kIZttlM+/jmxk0KkyxaBKI1+i95GbCF+TGC9o9PhVrpVf5Gp/gujVAdSlFPG0g956BvXIJ5AJB/FoBSUs7F/oxIq24byqSbktyHgCUqs0zHPUc9NkxA6G9BZqlWX0bZM4VUnc6UL88zLhtEvoLuJ/NMex9nk6xrrIFm+iado0KNNRziBti7DpUx88RzBQwV44gLXSQUvBYN/FGe4tN9glNmH67ThmFoRGyBChI0TAupErQ4i+O2mpI1AKIhBCg2WAhIryWO2PE+/JokoeMuVgoOCZi4iBVtj6/onkfRGI/+Y1jKf/DRhDJMP7oRkQOJOEa9O0pPbilAxopMjqT+IYA0TaRzd80AYiVKAjpBAQQhSG6MBFWia64YHrIzyXytUJJtaep3DzG2Q/XYbJDrzZFUr22ySGNxKr3IoIOqHFor7rO6hKH1FqBZWwiYV9JLcPEHRNsXLlf6HfvIeH0j10xTZAYODPLyDvHiAQoCcqKMNClQZAShr9eb4Rm+cP3l1ho3uNvtI8euvdyK0xxEQMpYfRMQHJeZqlq+iwTvyOw6jcLXCkhJ1qw7IGkM0+KqV3sKIMrepHiA4dwGhRiJKkkd9CY0yjNl6mmjmFzMVJ5EcRm7uJXioilnO4d53jmJ0heNmira7BTsCKR2XnAtG9l2j0NUkv34yYl+R75ok/kKSxvILqaMWsbEa93URvOMOV127lc2/5fMprx26TVN0K7fSjvvIpx28AACAASURBVPuYpIWHXmvFvLgFe7YNQ8RI6pBk1SSj+pFhEjzQfpPI95GGgUCC1ugoQocBoNECQK4/XESaSrEIh0cxP7Of6M7NBLduIpa14fwismmC6QAB0dMX0EMtyK3d3++wBd4HgYRvTTD773+fjju7Sbgfwaim8a0VwmqBlLoLR/QghcCQA5CJEwZ1pGkgTAMhFRGsr7uJ1sso4X93HgOBdn2aXgnXXGC190lSP+8ysO9G5Jkh9GQGpW2MxDW8ssnchRKmOY9TOoTVliXqeQ65cAhRyyK9Jlefe4dyJk7njo+TXN3MdFSinqnj1+bwRw2sWQMztGCl8d1SIUIogzDSVCevcah9A1sye3GSnfg7wUz3oM576OJVomaJ4IaXiIbn8EtvkxzqZ7ltEv/aC8QLN+Dnq4TZc6RGWsigiNZeQA+v8CdLE5CvM7q3F781Sfubkp64RaMSkGhsQqxV0c08om+W4p5dvPKnY4w2LRKeR8V7C/HgJJWu4ySrDYLZOKXyVeKfGmXi/FFSt2aw7woR19YwHh1Ax1YxunPIhQGGibGxVeGHRVoLSbTvEoUhAtbPRhgQSWTMBCHQQhKJ9W5rFIhqE+mFkHQAgdCSyPMRhkJa5vrDihQQrp9pYAs8K2B2bQ3vbI7My1dJHZ1HnsgR9uTwswuUo3OYuhdDxJDPXCAczLwvIvm+CiR6fRG+/lWUqGPuOYCxsgHqFQydxgzbCGQTKSUEAjdyMWwbZYKwFNoPiLRGOjYikSDwQ4SliUSAFBLheQjLoVGrsFh/ilRfma7GR5HPjiLHBhG2BekUMbkPVU1j9cZwPp1EbF8jeuMA05c8xId2kSi3UJ1e5I/aVjgjTA4c3k8yNDBHOnFKERTqJMtd6IsFmM6vXzgtExFqtB9g6jRDRgtGu43XK5iZmWIh/3dEY5OUvD6Op55j0903E5u9ncTFAVIffgC/fzdm81HM2AgysR1VqGNs7MFI3oi8EIeP3oCMX+LPv3SBjpVNtNbrfOHyRR6vLLDJa2ck34lIOTC9grhWgUstxDffRn//ErH8oyzUq8gP5YgttJEZ6YeTIzhHRnE+lKRZepdUsYW21zYSFqrIs33Imo2USaLCIEkVZ7ttEcoaiZyDMhVKKUAipAYlQUi01mgJyjCRShF5PjR9REsCHtqL3jeAFD7B9ArCNggtge/66/1rlgJDESlNFEG11mS1VuRry5f43WqVvw2q9EaKEZHE72oi+yKCoovlplhrRLyoPIaPzqOUgME2iH//Jhi/fz7Im/M03zqNMk2CyUnMxHa8oXMUT0zSVr8DpzVO2KwTqgsElovXsoLfvEp2+yeR6Xa8C69jFGo05jLIzbtwEmn0qgGNFrQtEYGLcJsIKYmkSSWYQuoyZktIWDMIUq1krG2AWp/f7kxAu4HfUiBYOUXseAK2ZmG+nbm1N0j/3iMkRIq5U89ReVWytTuPkbPB305YLyEBcUMveBX05cr6mp7OFEHpKpVmwNXsGOO1s5RXl7G1gaMiXKsbw+rnwzs/Tnz7EN4z03g3d+Bk36J6/EtYXR/HvmiiTrVRzZ7E3yDoLu7DDePYUY3fP3GePbE+7t+7HdwKU1taiC4+y6bFLgj70Ftz0LGAd3UCsbaV6sc2UTM86hNxeubXSJysobw2SCpCWSLIL2AnOuDjFfR/DGhsncRaHUHVWxGWRHsaocCrVLAw8NtDooKPKeO4jRJ2PIU0THQUse64CqJmgDQkui9DaU8Xrbs34oYe8sg4l8/P8eeTJxks5fmVDXejlMSUcv2VKvruHcQwQaj1+Xrf5bJf5XIiTXI5z+FMC1KZ1HuPoxJJzFOtHDt0ij8d7+NL9YPYa2tEB7oI/+IzmO2p70sYf18Eok/niP7DU4i7D8Ccz9rpJ7Dpw2qdwnH3Q5TEFwGCkIY4hmg3cdpt8kfHuWSOkMt0srnYoC2IsKs5jMGI9n0t+BNHqeksutGDHe4hJlpBQxRFKCMBnofbcZJC/Bix0n2k65vAtCARRwQl1vhfMW7ciNXxcey6j1y8iHvqLFFvDWfX7yEurvLG/Ku8aMbZ39bNR9Ya6HIHqt2BWsRpYwUz9NhhbwYJVzJHmSg+ycqyR0iAQqEMc93lB9AephY0PZ/2xCCdffvpqTVRiavYI2mSU3XycwtY4zHio2nY1UF8cTucSaMtE+3VkUi0H4IBYncbTC9TsWaJrQ6gvBCEC4UK+tYy8obzvPiNG6l8pp8fmTlB461lrJYU1tm9+ENzFLKv0H72k0TdM4hrEtnro5e7EIEBhgAk9XAVXW0iW0LcrU2Sp/qJTI/ajjVazgyhIxCmSUCIUGBigw/BTRnoTMELcwjX5z/l5/ndVoNHCmV+KtNNv9W5ft9QCpKw7gqa6+tVgyqRDlHKJFwsIW4fQN57M9HROcR4jlCXCHKz2LqXSts5GJij8pqkLbsfY8nBO9CF/Zf/DKMj816H8ntfYul3luALRyFRQ04k0aV3YV+VQHewNj/KyyvjdPg1ksksIhI4YgvWSjdT8608tudunu7r4VU0c5uHeT6V5N2DB7notVM6Jykvp0hV5rAPJqh7lzAbBRQdSGlD6BNpjWiksZoeSW//+mFKvX5ZlMC+84hkivD4EMbgJrTdz/L0DKfdfjrPXcHy4nzrrWME0ufjG27DcsusbHoJp2ly/FqN75Rz7LW7yRoWJ4Jvc3zmSapNsV6GSBMh/6+2CAEIodBCoQyDelRmMX+WhcI0C3WfQnqEXruf9rVW4p13YP7iz9MIOll98gpRqU7MSiAAr1Kkti0iWqsT9sZwB1ppmi7GQoDp29DQiCiGjjURiytMrw3wWPMKd8YmSbQlid5JUQ5WiQ1aeJNFbL8Po9yH7DURc60IV6xPGDYiGrJBvvNdRNqF9iyJs1lMOwmBJu62IT1FJDXCkEhhYEiLMFYhTBYRahr3nUmssI2a3yCfTvIbQ1v4SF8fiVKNcK9FOFwkvMPA//EC4l4L+eF2/IPTrG5+hejDPuJByVjlFOHNYxi3W1QK44hdh/B3jBBu2IRdB3shjbnagpFexFASKz2KMZ5j7dirxO7fj4jH3stwfm8Foo8twTffRTwcIGaHcQ8FXHj99+lov4MvXBzjW5fH2JFMM9rah+lFiChASM10cZknll7lfPk83V6eUX+VrsnXqbz+FOEaLHa08axf5NTICC3sZcu1PtL1bWhfIM04IpGESCD8Cm58mcDfiB3ZkFkPWlnzCcoVVG8bcuYKIqYZP3YF54H9WO1NXj6do6M1TVtbO7LFJr1Zs+3GTdTdFZJ3HsSMDeIvwT2pflqDMq82v8x4cA5DWRjyuybX90QghcKQNtqS+DqgODvOYm0BHbnYd84SqbP4J3xq87OEO7uIKiZycY1ws8BwNbnlr6H6jpE+Y2GL3Zh2HJGrr7fZWApRsCDoJb2hzolv1bk5t43kwDDio/fiHu4l0bVI/PVNyCADO4s0fvpJvrXgkbBGmGmc4ny9yEC6lfgDhwnGBIlzEiOZJmjWkJgI1yTSESruIKJgfdNKGKPefZIwVaRq5MgUBpBGFvvmEUY+uwd5T57c0FMY2/OYj+wkvPUysvMIQeka5bEjuPW3aa5NYKUj0i0S79IYyf4UqWsm8tkC4oUqT5yY55lSiTNZh+1r8zhrEiEzoDoxkmlEzUQk0siJeYKONxFbb0Ba71259d4J5NQy4j+cReyp4q0I1J6dRLlnkOEyzlwHfdEeHundxrZkFtNqQfggghAduSSUoHfwONu2n+OWnjq3dxcYjZ/iQ5siPr5nA23+HP3BRbYXS3RH/fQ1wXIcZBRD+ALtNVgrLBNpm3h8lrycJKX30siOk2+OI+LTqDvO08gt4MQG0IfXcJ8WmIkuWrp9Di7Nkc7txfAa9O9vIdM4hykkdn4Y+4gFM1WyG21sp4VyY4l3whcwMJD/P/5eRSAQQqCUQcP1mZcFJq4VWHziNEtvPUlPeZqu/htZy/rYBYNao4xoj5FMesTzG5G5Pnx/kYJ4AwMXQ/UDPrppQEkhuzZyqHOFxsQYqZqBFDXM/ps59bU8yTkXW0EUL7PkSl4ZfZgb7jEIG6s8lh2iX8zR/UIFu64wkg46CgnDcH0WBI2yLISSrOqIy41FEjsukMhvwlhtJahL5LZDTO3poZbJMHP0OZwzb9Bt3EDgj9Gcm6X+hZM4Yyl0MUKrCF2IMEMbZy2DN7aEeipLtLyJvHeOtJ/BcW8lNT/D6L1HGLnyJjX9Dl7bKMkwS92bofahZWJGLyw2MK04J2QfMlcm3TcAqffm4v6eCKR29QTWv70M9QC9ZROVRJql+W9SmH8TI5ciITbT0R6jUriC1YhTUZcob1rDEYuIoqIqzpEYSNMd9ZKqShbeeYpEvp9k2zaKtSmytVPsa1vhQCbBximB5VkQGhBohDLAkDRdj2ejOmevNRlQLpnhLDqQhJU1YmE/gT9OraOH2mtncM7Das1l5dkn6dApVCUgiFV4a36Jq5dqnI33sn/NwpiQ4Fj4/gRV+xLOtls5M/VtVt0ZlPyHr9+UUiC1QRQpqu0tNLJZLK+NlqE5Oh98COuKhVprYPtpnOoOgrkEwghRGy5gDpjIX/h5miNthMcnUOk8whewPY6643nsQzmMy4OQt5BvTDGfatIYLRAVn+batltpPdXBbbsnyL45TuOsixE1uXGLxL6QWX/KtQyiIEKacr2jVpkIywAfrgqLN4dX2LdnGuf0NmQzg7PjII8PFHjq2hi1vndxv3GcG2buRecqRL0ODXOexpkc2rZxB2P4cwZiQhLNJfGWfYJ4ksTBndhbW7EyyxhbDuCW5yD/Nr3/qkbX2jDplw5g7WxDPLIN+3kXp2DRsK8S7L4KiTJeM8Pi8jStT57Cf2gHlvUPL7f+4QI5vcL0b/97jpUU8YdHyOyfIrYq+dbRy7Sf2MzoyM+h6jOU9zcxUgqVrVLd+QQrw2dQ7Q2cvR04u7vWlyMbScJEC+fPzvDaEU1n3y46h3oQqVYcS+LW6+T1MsmBfvKdr9LcUIcZHzPIYqd9hoIGM6WQ0LpEb2YREWsQKx9EHhxGbL6ZxjMnsdqbpLYO0mYMULc1etol3mNw/qDBn2V3oktFEvJldo+2we13IbrjyEkPu9pOVPI5775Mzc+jxHu3EEYIkJEGU7HYppmPaki3G2c2IB61IRuCurVE/ZYU8Y/cBG/nMaIsOnEZ/+wk4qSP9ZM3ImoaUXwb5ceJjscR9S6kHyLyEX2BwLKP0ChDa3MPaXEa80yehmmTv3WC3SWf1PHNhEKvdy8Ycr2tx1JEUqJMc71xNF2jnXe4pZ7AmN6B8JPQ3UbDuIJtHOXTixl23zLL4M8skls6jzXfit21Eykj9A6BaK+S6LkDczxO47Ua2dUHieYh8vPEN2xH9nyIYGAHfqWJcyqOJZJYHxtChBLvwhyq0URtDxGbN8HJS3g9s+hDXTQuKf4P8t47yLLrvu/8nHNuePl1ztPT05N6MgYYDIAZ5MAAEhQohlVZRStQtqTyaiWrtnZVu5bLqnV5S7JlS9otW5IVLEqiSTGAJAiARCRAhAEwOefpnukcX37vhnPO/nF7BqBEIVFyyd5f1Zu+fe97r9+cd773l7+/oZk06btfpH6hgR4ZJjuy9kf+bn4kgCycO47+18/RL/dQztbpvG8ab6bEU9qn/3XBhsEx/t2b3+RMrcnayTnmRy/h3jMIzgjX/ssMzecK9Nd3I4Ju2LgX07sZ276B1NZ76dm1k/V79qO6duB03Y7bvo/UeJH88DpafWWm7Dkya6axdxmEWCaYWcbfpdlRGGbItnH+wgHmW0fp+8cfxZ5J45w/i1eMyX76LoTYjziVpzO7Hc/vxxaf5t997wydzg5+5WP72DlxDbWSx57OIkoBsiUROsv0/AFOmpdxZOpHXvgfKhYUglYsmZw8wrh7iZpXpmqXKLZ1QKlO89vfJX3revjIw8jnv02UP4SrG3z1lObl0hluKuRwuBenbxj5hkS00iAkOmhR2b5Ae6OTtktFwqUWqaWNRBkQy8ukzwwiG21Yx6CkxEYRYJNy/SjGkhDiUahhRYRc2w7lLkQsif/3W4h6L9B3IEU1s4BzJIP383tJ3TpKfOY44lyIbRuC9B0Upn3UoQoOErZ3Eq0vITY4KCeDvjiBPLGMPdXAG9mMyseYyqssmxThjjsQAtTey0THD+CNTCPP78BjPS09jb6rSebVXtLRIPHN/aw89yLhriHy7f0/0lfygQFidMzBL/1H+sZTxM2Ixk6fdaUO5lKjPP57/4lPeT282DPL6+MNPjYySOdYL/PVduIvB/Re3cSA3k5PZgOSDAQuYi5AXq7jXKrRccXQX88jp2qIqzX8qSbyaohcziPOeqhjLqm5DahLPZypSHKj4NkKV+Z6eeLUFKPeAMXsZnSqzGTtJL2jd6NrU7gb+zD1Ovb4ImIlg5UGaTKYxZjhQhdbxnqpHrzGADcj6u3IKIDAENSmcVyHgyt/TimXhHP/PkUKgXRcIidi1p9iOjPNpLnCBXOCK+5VGNxCbXoc54V28pUUalsbue9bzi+Wybf1UE8vM7uuQHXqPPPFOU53XeaNdSeYFwq51I734XHyKgfZDazkDtK5bEnNb0ZkQAmf6cYpmvEK+XQfU0EFTyo8x8MiYMXHDDiEPcuY8yFqzQZKY0/jLB/Cxgrvn8+htnyOcGIP9i9PEjln8EqbSc1vIDVeJ+w/RNzbouldg7YJ/NEaYWqCZnwFk5tHKY233IZzwMC5JsgMrWtnyBxuxxt5GH9/O41Thzj25jSzl/sYXG4nVeknigWNnit4JY142aE+XeNK2zWGb74nydx/QPnAADn6zT/l9FNfZrTzJo4VHfq3DKOKsxSarzOSPUjU6mKbn+YzuRHWtLm0bt5LezPLSDmN0AZPuDiOg/A9RC1EzCyhr80hVlrIZoSuNFHlELVYQ8ysYOfKmCCkFVWQhQxpmcOPu4hPVTDFm1DFzTQvTbOw4PKMnaW/q52uy2t4fCZk570j0FnAtjdwXpaIqSLGS1hE652zNGkxVJnn+bnjFLvuZHBZY3AwViOlw1L0HeJmnXOd84Sm+YGc8w8iAoFjk7KawAmJXYgLHtdKR7hcOsRMxyyzUnBluUp9aJHBoYBz6eOcsyeYmjzERNc01wpzlNIVtIBWFHG1uMRUbZlJ26A0YlnXMujJElZkETYFsaSx5hrHu9o5ftOd1OYOMWwzmJaktWke758uoVIN5q4skA0GcRqWqYWIl3pctqxPUTuxgdLxGm1fmUX11zEzXfi1MchZDDGe144JulCmm1ToIkrtOHNbsM0Kvu3EVV1InUPaDsAjcC7j7i+QvlgkfnGC6WlD1/5/xtKOXp5J1egsHGNlpotc1EHDTmHqgsLMKF7vCpPTV3Bv30qx/YOXpHwggNSX53nlC79FV6ONbWOPcE7XuKmtn2htEem8SMeQJH35NnyxlfKm80z0G4LnF1gzbbEZH9GIEHeOcs2r4E6VcFsx2sTIfBbhejRNxHJlJekJ8DxE2kOkHKwylJslZloreA/cgowNnTaFP1VC3L8DE51nXxCztXMYt3SZ9lwOddcSr8g8I+6reH19yDcyCN/FKgeWK/g/u5vsbTsI3jzKzm19DPjrkLUYrasIAoTKY5t5qo1JpvOLBLqVjDL4bygCgUQiSZqK1GoOouUFLKeXKKVKLPllFvwKSImLh5IOyiqUTcrHJSKpeUMQ4FHyA2br42Qa3fTdO0gzKuFeLiDXtpFfu5nCtdfZkbaMbKjgXm0nGJig1V8h/WMDNI5Pkh/fyZlqN2b/Czxx5zBDKz/GsN2F/OolMqcXcbNtiFoaLxxE+GmE4yT5qmonzmwR1xYgCrHLEr8yTGp5J15lK6oyhIg7wEqEdLGhoRHN4kVdiChDmD9I/rikv2s/E14H18bOEy+HhOkNrD+nCOQpUu09+JV+xMIcE/lphvfehxAfjKnuAwHk7LNf49yBJ9ipHkSOn2Nt5g3U5lPMP25xTnSxeOIlokqdXOFWdL2Ic8VjoOEgMxlM0CB6dDsX1viogxfILlbRG7sxn91N+Wf2UL9lkKnukENTRzjvL+L/1N2Iz95B9Mkt8OkdmPNzmDOHURuPovcM4+p+nPkS3pkFckEHOvLJxVXClYNEt51n/d467pvHcfN7yJcbzPoOs6eW6Ernka7Dcu0ah8ZbdDZ9qtdOkMtsxaZWiNYdJepZh7eYx3cKnM4f55q+lJRd/wOhBZRW3gDB9ce752SS2d+OTZJ9k50l7NqI9iuj+HNpzIMbae3zcUbepPTQNi7M9NB3rEmqTaFUidZMH+rFEVbqPicyl8lvnOFCaS3p5+rMnR5nbb9DuqcTmmlm64alRoNKVKUcNfCwuL5H6FkUGWRlAGXXJVOzrELgIWKJkAqhLWBRbgfp8nZkK4+KJUcutXisGXD7gRJ/8epLtHKWz+1r4VxbwXYt0Jb3Wa5eIWxYum5p42D4Ch1r95Lv+mAl8u87FNOqljj73Ndx03l09Sqe6sSm17H05Cxtsw7aOUB473Z6y1sQx5fJOpBTKawXQyuELX2EYwW8L/4a7RsWWZ5YQ6dYg9jaQ2q4iDNcJHdLPwM/cT/NS/Okuwr4XYlTLA9PUphtkUoPwqVL2Lm/RLMVkdqC8V1EWePILsr1kzQfyJHNziC+9lF6p88j96yHkQECsUK1dRgaK9Q6L5Fbugs50MB4V8kGe5CT0CpX4Eo72Y42ZqIzHDMvMCsv4+LyDwUcfxcihUA0LIcOzDC+zmdPc5j+LV0433wVKW5n8do0aSYQO2/DtC3RDM6Qe24UNZjBS7/BJ27fyRGnSP93ezH3vMLNeU36oz/Hge8scvXlWcabp5HZNKqaI8oU6FnXSVG3aNRClLbMT0+wvDTLjw/dQrajQMMG+MrDtQIXH9GM8ebmSKVaOLUp/DUdbHXX8ye9Lf4wVOya7CXX24b7yB66jl3GnD1Ga1iSumsr4snjnKutp1heS2nhEv1jOz/QGr3vWqzT3/0rXvmT30L4Ke64dQujqZ+k9sx5wvQKvfVhovzjqJ0P4E0Mw+QiJk7Y96yQKGHBTxPG43D7MYJ5TfVojt54J7KzgLlrHTbrI+vJa/RrF5G5FHbnAGahinrtKiCQjkMcaHTvFRy/hVrejmgrYmKNabSQVqLRyDGJupqjWl+mnh6nb98slw+4XLtSYX//fSgvhcj2Qf0Ki0tfJDf8K8ymcow0ABSX7Su8ap8iFAGe+LstYfiHJYJYB1gPtuT2cvPTHTQKl/G8HJnBQcw5B5Gt0Rx5FaVi3OU9BGE/rxfOUC2PcW+6HX33VRy/jYW5ItmZRcI90+jUK7QPb6D54i7qxzx6ah4yJZGxwmqPmdYSh6J5UqMb8fNFCGOaOmSxusRUUePXDeGi4cjyJP94i8MjPzGMujzJ5PRhnj5zE2F5lH+0+RkKd/aiX1+HOjJKc83z2EcDMn+6lYVqFWtWOH53xP2/+fsfyHN8XxokDlssT1xAOA4FEVLK7uQAOdo6c+yaKiAyChs9gPtiEasqCFeBWe0RCHUSY1cBKkwhgocQzgQioxGiDVsJ4MvH0NYgHImQDsoRiNk6+sQMkY5R+RxIS9hqIoTCnV2PdF2Mb5ClKlEY4nophDbUy9PUp0/SLz9EFg/ZGOXECx45d4L9+zZgroY4cpDF0kmWt8PiRBde+hSLhRwyCGmFDd50nkVbg8f/yOAAsDjKwxjDuZVDtDldyIExis0e0idr6IfOIo/sQLe6if06fmmY87UqdnIND9+8FnXLMOXXWngbc3S2V3HSU5huQ+7Wf0WzUUauT5OrV8gebGKXGsSqjLumjdGmYnRuAKaqMOzDuh7ql09j277NytAcrXOKdNdHeHRpmPaP7yP2q8zlvkkhHuCnVob54twVvr1rOz3Pptm+4tKXhnTHBpbk9/FuuUbwfBY/7mXtxQqlhat0dA+/75V5Xz5I1Kjx6p/8JkopdLZAFLfIvlljOOqjoJO4uQgKNEZPcWX6NfLBAI6fSorughbKdUHIZMjlHIjxLL7sSZhKrMa6AlIeoTYYLMoRBHGMSiWU/bENcX0HlIPRID2LFjE2jFHWRWmFUBqjLOlMkXQthxNlESpN6JcopZc4G7lM3bSDdfr7zOiY573vcLH8JiuixXx4mkblOBc5xVV5HolC/nc+AOb9iEAQ+Jo19SFGzzapVpbxbprFXd6AyAhYazDje5honWK02MWItsimRPT2ItYfJ7jyIt4t+3CHPoJ4bBox9BJXv/afEa+eJpufo9F/hoWeWcRtvYgH1xHkq5QvHmdpbh6nowNv7Vr0h/tIfXwjbXeOkuubJNVxmu5mJ23DezChpDmXI5++D7eRZ1fL4YTfxYvDG9kwEdInHexVBxHM4H9smcL3tiEf2YCqxJxvHmPopjved8j3fQHk8mvPcPXwyxgp6PCL7Ai6UVwmc61KrtibzPA2Are3xZXgG8SLa+jI92OjFsp1sNqATjoCEQ5xFCAwRFGEcJMZfMJEaJ2cd5SH6/sox0cagWt9hHTQSoAw6DAkboUoY7hUe4lm7wwF1kEYJyOTTZ658jFkKkLoMn0dLvZMmbIzyfzSK5zKjhPEBk/4q1GepFtOkTzei8P7P5pYbejq7aLrcpqjG7N0bxtGTZdxO6dxFvoQ2/IsTVxD5jrJ6wLyFx9gausl/DN/hTfbizg/i9sxRmnXACv/73nWZB8ku7QR2dyCUj04nb2Q7iSzYT2qv8hidJLSlWN0cJqw+hqLz3yTzPYA2bYfa3fgX0tjxkOi+hFSM73kJ/uQ92yGtSnEiXl2tAQfnqyTDWYJVI2U6MMd0nA6gNOduEMLKLuWC6efo/vjD+C774+t8X0B5Pi3/4LFy6cRGZeby/sYurqewi2SyJyhUZolp7Yh8g6i2kV3uIVi2xAiEsYsJAAAIABJREFUijDGYA0gQEcRxsToVoREYIVBCUlUqxJaA0aQcnwcfKSbQpuQenOChpyjURgnNBX8SCYkAELgOU7ScOOkyKe78GyeqN5M+jGERaGQuy7ht0nk+TF6B7axIcpzJqix6Fbw/vuaIfT3LrG09C4qhsubWfurnyXDAJVTBzjbPkafGMGZCejefA+5JYnQDuxpx+mdJnN5AHXiFqL0Jp7ZnyF/dprONxTpaATptyO0j4racSdTqDMt1LkYezamEHYzsPZmnMYgVXuOsOc8naNraT1+kcbVjWQ+/rOoD92JXjhF5dAhvIUO1OE5uDCPiCOQCuoB06OLZNp78JccqisXOXvqJXIdvSwfPYe/Y5D0jEtjV5G2vvdXfvKed0cctDBRiFQOVmuKt28ldbxI6nAfWbuOUDUIayVEJHHSKTz6k0Z96gihMMRJcZ4jsWGML7JoERMGDZASpRzioIX0PKy2xE6ZFe8YlYFxlstXSUmH7HAHzOWRQTfywhApZxTrKayrybXa8Ws5rAjAFVijkQJy6T44MkiQHSe0i2SaPs2UYr59Hs/8/8d8eq9ipSFT7oBWhvp3vka0vgRehtTGeZjqxnjt6GyEayTLH99MdXOJ7JVxfrfezXau8WFvA/5/OEBb5JJfvxaUxgiDUC5ojXRDvEwOqhpVE9g4h7Ua6XTQVV2Ld/kQ8ZrdZPq34Z+/yuS/+Wf0bBqj8eJJantGye3ai/xPr2NaMYuDFSpzM9Tqk7jdfay54oAypOLNyMICca+CO1cQp77HwNR6zj3/Jtx01/taj/esQWbPHuHwV/4AL5PBYPELBQbn+iGqIWKFI3LgC6STQq80sNlFZpbO48U5lAIhk2SVDiO032Ku+zmqrUWyjV4iHeP6Hp7r4CoHKyrUR1+m0XURf3mQYvtN9FR3UTvURLQa5O/8MO7de1mwbxCVz+EFnUihaNYr6DACbTCxRhiL9iLiKMCt5mi2XeVSa5lu20/FWWTJWfx7Lxt5N7GAtTbReNd/hw+c2PpRRUvN0PIgPe0a2ivUTkoKTh+50QJ+sRN9TeNeCIk2LDApr/LM3DLnTjrcefgMt2Y3kPbTrMu3k85kwVVJVDyyCCtBuRg/TCYcORLUKv+V1lgd06zNE+/bgP/rP4Ec60A+PUlm0RBWT+P0naDj4V2w5z6YaSCv1RGNCCfj4abTtFeapPYYmqKb1JygeM8W1Oc+Qj2eQzzRSfreiygriHbsJJXNvef1eM8aRDku1yPCUiounXqZrcEwWZHFSIOJWjjpDFa1KN3zFHJohfJj3bRXhtE+OMZgrcRGEuu3yHRo5OIgJuPi4iSsGcZglcDiUZzeT7q9xEy8CNk54raQYL5MEJcQp79HOnWKxSPzDLGRIGihUhbluMTaYKIYISXaOJTlBfKDI3g9VdIXivToHK6UdBTaudDQuOJHL1t/J0nWTKCtSdqDf0hQ3WKxNqnqhdVuxIS3/QdEiOShhATs3wuILCCkga11xK4F+q/civXWIianWRofJz06hr21THRlhoHTgq78GtwFnz3pO6E9jWklDJfSSSE04PkI1wHdgkaAVHl0HCCUQqZ8qIXIXIa4Wee16iyNnjEeOTgLjx2Hq3UcuZX49QzRR6ZRWzahOjowrgHTIptqIxt1gbsRPTuB3Gr5bhsUHn+WBz9/O//2/CX+7AtNvjyQp+1ShXBDlfnTB8jf9YmELOQ9yHsGyLnvfXP1TQXKKuqpOuPRBbZFeyEOQWsIQLRP0dbVhfPqPXQGGUxBorUh1jGRCXBdBxl20HHhU4S6QRC1Eoc7DlFCIa3FtZKwoKjcFxEtdaC+Pk/aCNbWHyKT6iA6GmJsjBevQ7keKEsYhihPEAcaTymkgJauka4OoqpZmlERu1CmO50iqMzTVsyRt1kCJ0Lav9vSEW0tdhUJsbG8PdVkVlWFscn5BD6r/6w+7fqzrwNAiuuNVglAIgxCCByZXBdSoP6uwNKMCT82DCf6cf7gErbPRdzZpJk+zMx6zcgdu1F7Olk5n6b5/xzmM5PtUGyDtME268itc0R9SzRefY2M3oJU69ENB0cOQipK/j9GQgym2kCm0lgJTkcHa8wYf/LyFC+fqPJTkWCsdpmJzSlSN3tIWaB50aG7VEG+MoXNp2itLBOub6MQ+KhCL3w/ze0favGFBwybHc39tXG2Lc8z3JOHT+xg4LkOZr57BHvPo+95Od6TiWWt4cjX/jNBrYJ0EkxZYRGuor++BsfahH3Cv0Zleons2T1Q9tBeTBRolEr6m7AJ8ZtyHVrNKp6jcJQgiEJsGCeRJEcR65h4JUSddUi9KvDqI/hqAJlWhMRJojCOiU1MyneRUiYbzggczyeOY6RMNJ2QErtcQ5eaGDdhgw+rLdKTiqnOeRpe40cGiLEWYyHWllgbtLaE2hBpizFvHcfaYqxFW4s2qw9ria5fX/3d2usAuv7eq6/Rlkgnr2P1710/1sb+gHb6oNpFS0PfSjf9FwYQfRbz44awq0kYdzC4DVKTF2ilC1S+toC38xncWxqoLXVsfQY7n0V2r0EO7ybevgnn3g7Cwato/3moV1FREeM5YDykNQjPxQYh1k1olDpJc99Ig2vpo/xFkOVQ9Cb3fHqBrh//ODJ/O377ZvTvvIqrPUQmRavVQj+6ncrFg+CM453tI7fhGt2ffoS+/BbWFr7F6KyB/n04O0eIXrjClVwZd1Mvhc73xvP7ngBy4aUnuPDi47h+6oYdoFCUxSJ91Q7aRDdCuVSjy8TlZVKiG7IkfEqKZOANCqMNjkhK76IoQscBjnSQQhBqkzDwYdAGdABptw2LQimLVBYTGXQYIZWLlQLlSMLIJKFZIzFhE60qSKVwPI8wCMHEOKkUwlO4lmSAjnRxtEJah6ud13DMB4tkGWNvbOxImxtgSIAA0duOtbHE5i2gXAeDvg4AY2+YWtfPX39efP01NgEciBuvv3F8HTQm0V7X/Zj3gxMtNflWlv0nt+FsGCTck0F6EcQlsh2XUVtd4uI0yxcG6V4apK37IZxyEXPKIJo9SNWNmA6xRxZx6x3o6V6Uswf/vofQe/JE+ZM0J/8MQYDjbQNfYk2MMBbhudSujvPbi0eoZTrZXXuDpZ338soZya61hvZ9j6C+eB738BIi50O9hqe9ZDrwriLe6LM46xuYqRV6rnioLyzRCs+zImq0Hd+COF3Dbp3m9OVLyE3d9G+46T2tyXsCyPzFk4y/8Rxu6gdjyLEwuBYyK4v4qkjWG+XrcppG+hsMBWMImyI2EgS0Gg3cVNIn7IoMniOIjSZoJaUhUiXl5Y4VICRxFOKkUmhtMBissSghsGI1qksKLzDEcRmRqaHGqizteJPM3ZvIdfUhL18nolPJ3VS6OMqlrmep1ydpL45QqDlUvBpLuRLO+4hoGZsAI9KGKDZobdDGEml9QyPE2qCtJdSa2CTH5joojCHS+q3nmbc0SmQ08er52Bi0McSrpljizK9qKWuwgF597xvHq5rkuua57tu8F41i4piujlE2ZW+h0bWMymdwz6xBbhum8VWgPEg8cIW2/i6i8BTl00/ibiqhbu8iXldF27PIvIWedsScwS60UHNl7OEqjl6PrnQhK914jRzEeYwrUY6H0IJmbYU/nDvM+Ucepac8w+d+7ibuO6h56sRpNmwfoe+sj/jqKURaQjPC6pDGvna8QgfpcUGwkiW6qR33jIFzENRO4+d7SFc3opoOzdpVWvUs89kyc3qS9XseQHn+u67JuwIkatY5+dR/pTo/g3L+mkMrBJEIKWzJkfG7UMspvhVd4ibVTa8eQfoOVfka5aUabZkeIh3hOw7T4gDVUolCZgAdRsTGgDF4qyaRFMmASN1qJaUeXpp6tbrqoDq4rkOTQ7R2lZjiMIcnn6IwuIFCdhTvNaiXLoOMSDldCE8iEKiUj1YClzS5XAFtYoR1Ga6uoexVWMos4dh31iTJnR7C2BDHb5lFYZxszFDbG5s0fNsmD+O3jo1JNI1eNY+SY0OoE6BZm2imtz+SaVpmFVjJT+AG8CDROvGqjaXNdUAJ7Cpg3gtQItdw66Im3bWJqFIjWxAsFBROYRha88ybL5Oa6sdvbEcsXcLvKWGas6jhNPW0gvRL+A+2oUcuIvpLmFQdtZBDloFrSzizNeLZBm6mAyEKyIYLXgocQ215ienBATbX4HPVkKzswjmV5rahaboXKngve5DOgtY0KCN/dT/enkHEs9dYmp1Cfmof2Qc/gWj1IE41cO9tIA93oBZ7oW2Oy/dX+P0XVxgdqjPXusaWex5Nws3vIu8KkLBR5Y0//x2Ecv7G4koEdSekfSVFl1b41Xa26Tzrum8larSw2ctEna+hZ4oU0iOIWNNIlZjdfZJoska+0YfrewRhgGNF4sgnTHBYEm0hrUEIiVCClJcmUOO0PtNieV8T3deJOphmo38HueEmM+og9Z6zlKLTZFqjZGw71tqE8lInUS6jQ6r5C2TT3aAyKOkxWOqj4ldZSi/e6Lx4u1i4cVcPY0sUmxt3/8i8pT2MtQRxojFi85Z2sKuOevw2X+S6GaVXQRevmljmbSbWD5haq2C0q5v9ull13TyLtcG+zb9JQGFv+Ed29bz8IQ69xaJFRC7MsL46jNvRy8InBdPDC7jNLNmnqqTCDCk9QsbdDRUPsdyHWtqOM38T9s0c4vWQ6LUOFg68Sn7XEHJLk2hrQEtcxO/PYWtpaGYx0Tnij34btX0eE9Zozkzh6W6UoxiKWgyrCL+tgmIFu9DAdu4m+79+HnHPWspPvo6JPbxHb0NZi/i9g4i6xokF8s0pSF0iulhFXKkhusuIpY6EnK4SU2isRaoys92XiFpNlHIZ2LH3XQHyrsZ3q1JCOg4min7odYllTgfcsjxKPZ4kFaeIgwbGRETTafLln6TYnaNRWcax0Nij6O77LG3xEqFjkcLgKZfYGqwVOEJhhMXEUbJRlYMBcpksphnQyszhnsqyrvNeSm98F71mifLak1TsPN61Iu2tW8kGgxTZgBUtsAalHIyNUJHCz+ZRwe7VYIFAo3FUhrtL93OpfoHzbWdYcSsIm0SJrm/GIDI3tEO0auLEcQIQWL1r2+v+xuq5Vcf6RsWK/ZtRLeAHK+j/ttpqAUoI5PXIFeBImYylIzmvk/IBlBQYZdBGopTEsXb1WGCsJe0p1GqYM7YhLhYbdtNevx2/vci1Td9BHf1pnMk0+fAFav0N5k9n2dT7CDQcrLUItxNjDVoHyI5B/JYh5UbY6XbMV88jHvBwb72b5dbX0PoJ2j49QvTdYfxL+7Fne2C0DPe+jrg/Q3Rhgvnl/Xgb9yJWqjifvItq7RDeC8+y1KrhF/YQNWKOzXybLfdH+MuK8NVd+PWboajwHBdaAfzXC7hmiChqoQ8KvFQaMNj9Y3gn5tieVkw4MaIF5Zmr6DB4VzPrXQFy+jtfolkt4WcLP/S6tJJKqsLM4gy5ikcYNzHRLF4+j0y1g3Jp1KtYEp+jcNjDOa2JXQcdR4goSnIfsUW6ijiOcRA4ShHpGBlbhIqJVufddejbyFxOY85VyPXmKasVGB9gQ3kfBb0V8BJTwovRVlErV1EKpOtjEUhj8YQibkZJpl80cFMZRFBgq9jL6ORGLq9/nfPFc6ysOIkZE71lJl33MfTbNMR1W1+bxEe47k9cP347DiwQxeaHruU7SWJ2CqxefS8Brkz+rqsSoGAT0GgB2giUtChjiKXEkRbHCPQqwDxXg9B0+8NItYddfRWGGptgXYP2zHb4/gx468F7lLi2Qn7AQ6Z9CMIkginBGoNEIUQINsBmFW1r96AvtdFceJ7c0HkGb7mX+BvPY1fquJ+6BN/ziVs7cLaPIf9gGxlVgp+tY7s24x1/kraFYcLfkshPrMU8/PPoM0vI7CBXX/sqkfcKtb0PsPTVI3TYJdzcBLKao9j2ILZlQfQg0honnUdQgNCA0ZjtQ8jFA4ShBi1w0zmuHn2VhUun6duy+x3X/d3DN6tM3n/rF4ek5taZTk+xa2kb0omwAuJmE5VJExmDbYW4QhELB12PiKrzSReZ5yCkTEZ+WYFuBTi+A0ZgjCGVyqCtQUmImgGxiUlnc4RWowlJr9xMztmLjjRC+aA0OmyglYVQETdDlHTxXB/PVZgoxDRCnMFO3LvXYS4uMvfqs/jrNemRfvLOzXjhAFuX72J94zauOJMc5gkmGjFWO5gkyLZqPlkiY5LwbnzdYU5AkWidVV/jr2UGr5tr71ekECj9lqoRAmL1Vq5FiMTkjWVyzrMSRyRUuFIatFS0iHEdQVMLsnjc73+MTWI/gRNSqvwhj100hEd6GMtuY9fWYYgjaBgcusD3sPUgCZK4CeG0FAH4ClsLQQmEEiBj1PAG7KkJaq8eJffgh5CDN7FwfILs5ArOgwfRL1+kpLrJ3afwT88hvjxM+08+y1L8ZxQfvBnv6x+D73wPz7+Vddt/gdLvPM75X/88e7/+a+SdRzhX/ecsPHwHa4aqzDz3dcqvu3jbWrTfN4v/5jY4vge8COIAWwuJnSUonkNc6IE+CWYV3Ordt/87PmPl2mWmTryBl3rnCkjXOEwWptggRxCoZBe0IozVmNjiu8lMiLDZRAkQno9QBgR4nk9oWygJSIWbThNHEdIooijES/mEOsAqgSOTMc5hMyKVy4KAUEcYadGmhi8VxrPoyOAYB+U4eCkfqQ1B2EQMtBNtHSD9s3cguz2iAHrP7Kf0pSfQ04epZuvUP7OX/i+F+NMtxvxNDHsZzvQKXms+TW2mzIKtEwmN0A7avGXbAzec7utm1g8DyPWw7t+457wtUfjXRYjksrrOjL76fEfJt0wtkRDRqVUNERuBkhKlLXHUxPEUPaluiulebtt5B51n06xN3wk2xIk0afs/48kLTIXn+avzTzLcvJNLFhZn5/nl4TH2f+JmhoaGsK/MIErNpGJaOWA0woAONSLlIJUALRH9PeBcBFPFXOghdalJ7f4BUkfLuPsOIcxT+D+5C331daJnnyHnbsJ23ovoKsH/dpDWb09QeqJK9089QGtumV2/8e/p2bQP8X8eY/dHR4h//kM4rRRL9gKvLB7hM4O7cK5+iPmD1+i6fZrGmQXSqpuV+VnSW8bIXB7k7IVpJPYGu2WzvPSO+xreBSDN8jLV+Sn83A83r66LMorlVIkrXVNsnl5HSwZJnqIR4mfTmDgpaY91C4lDHERketqIdZwwhyhBFEa4KZ+g2cQnjZNxCEyYDG0xEuO7pBwP40h8Ba7rEcctrI6T5iqpkI6DdAVSWIQRKE8htcXcNEjjjkHi/euZX5infPB1/EZIc6bELW0b6JvpgcqDlOfm8L9xDFuXWCdCpjNkltaxbXcPhV5onprmWOkyuZl2XgoPU9d1Qi0IdZSYGkbd0B5JPsPcAMh1v9heBw9vc01WnejrQZC3+9DJaOTV9lhhfuCao+UN4MjVnEdkNdpoMtYhlyrQnipyz977WRif59beh1jjDpEpnSDuehmbroDJYYPtoLJ8bMNmUFv52Zsfot5q8e2z3+cVUeN/Of408dUjfOv/+Dz7P7oR+9QFKAXJKDVXYdDo5UVk5CJzfWBisj1jiOUu7CtXWMr9MXqDIR9+BOXvxH0pT1fKoXH2i3ipIq4YIf7ibvKqTNjxGHI+S6mzQs/+BzHnWpSjS2zecge89gfQfz9nvj7N8EMHmIvn+NOXt/ORvQJzaCN/6qbpbbvEw/EybqdDdNs63EMK8ZWDcCZDub25WrWQrNWJJ7/I2lvvfce9/Y4tt/PnT/DE//ULP5Ag/NvECIsVlpsmtrJhaRSJomkCMoUsOoywUiKsIa63MFLgZ7JEcYi1mnQuT2wNshUTO03OVw+zxttFIdeJtRqBTfIlroeTT+PrkKBRw4o0jnIxcYxI+SjPIw5DXNfFanB8D92mCH/9AeRoF6GFc88dYPk3v8Rgo4O09hkp9CALaawOEUZA7GAGs8ihdjg7T9h1lvjWeYwaxpvJo4Um/foQk5kDEDU50UzzrcsvgNCMm2tJyNoKrBXEWiOsixUWYyMEEkc4iaK4kdtYzZq/DTDXN3vCEC9uXAt1lBC4CQchNEomTCWuUrhCokPDbV1DeHnFzt13s1U3CVQ/5+xujpWfI8pt4qMrGbY3j4AyZFKDyEKDyjxk3O3YTA43X0AYC0EEsQGrmZg8yy+fO8zLIsdjt97NXR1t2GqQfHjXwdikaS2uP0+re4ZM8xO4chBb18h4kVhNYLL9CAz1zCR+c4R0+3r05DnU5jVMzF+hezmHjq9SvnOG/nO7CIbHSbc2wr696Ob3cL73JNbpZLFnC9mNd9H4yn/k0splIvUod/yrT/LHr5whe3KKT+7fQvrELEFT4y4LtD2KmomZF508P/odtDJIK4mDJp3rtvDIb/zRO+7rd9Ug71WkFRgsR0ZOUc7W2D23Exk6RGGIEAIjLHGYeJJ+LosxBoIYoyRBs0XaS6M3KmbTJygvHaP3yjCKHoyrMHFMqlBEuj6OMVRGv8fRoy9zs/gF/OwgmDBJnAUBSJVMoHJcbDNCOgH+tSrxaBeRgNFMH7u791GdXcYv5pLpSFYjAgO9BcIf34bpLZKanaPe+ySyWIPTLiI4jxgfIs06KjnNUGsvxDDU0cV+cTcNZ4VJxomFy1euPMFEYx7X8QjkFCLOIOMBarbExcq1JD9BMrNP4GGtQtNKGOqFRQoL1gUDytUgFcJqRvOD5HM54ngJj26kkEjXIVgsMbotxZ7bRrljaJB8Y5i2NQ9B40UW60/wlecmuGt3in3iL+hf3E88UsG5pY/4NYXbuI9CsYaJGghHJE6tAOOKZIya0awdHuML+SKfe/nbfPSVp/m19j7+xS37sPVm4pdJiZPvohX3UWs9TircQCOs4nQ4XL1Qo+vTd9Nus3BghuJSEfPb9xC+fgU5t43lbVnSwxuZf/wgnZseIhNJ1JUSmZkBLs+eoOf+FrmXN2L6R4nbz6Kzd5B5McCr7+M27oJPjvH8Y0/T29vLj822Eb45Q3WbwjtwElUuYLNzKLGJhf4ZGm6LtH6LFdO+hyqDdwTIySf/MlEc77FeQVqJMJaLPVfwSHHL5E5qYTWZShTH2CAm31ag2WwirUj8DmOwWhO06pCGHr2Vrum1uNkC1rEIKXFchfVTOIUsdqVMNDXEaP5+MrqIMTEKgXJ8tIkSomUtCTvOstw6Rdfch4l+7wXiTOL08/uvIUsBbZ3FhEwCi6kGiHWdBL9wO3K2wty//UPG/e+x+6Y7kAdbrEQvkvnUZrL37uWZx2s8vWMt2w5P8Ggrh5SvYjeO0+f107d8DyDYm99GbDUqnaUsXqJuL9Jd+DBzExGPzb6E67iYQCOcLFVxklhP02buQmRDwIfAwaYvYntT2Ml12OYcUTrDZ277HGukSzM4jRdtgUaEyClWqmVeKU1Q797D/70wQ/Ts8ww+MMUd+z/D1is+v2SOE5/byIzfwhtcYWBhPxyc5mrrzxiYD8kO7kf5aUyjjglCZFsHAotMeZighdaaQnENf3Tzfax79o95bN2P8y98F2vNakhZYXWNjDtGVv57bBwT7PlTFu7r5V/+7jA/79TZ8+H1eLlzsPIE6ukUy08eJf+PFmle3E3X7kdp+ycP431/CR4/i10oEaUt3R+7jewrVaKFZ1CyC2d0LX1PzWMuuTjr1lILx0m9cZJtC4qslwFVx8wsU574S7p3dcHSfTiDtxE/HLH0wgxK/+B2N/rd+UreESDG6PcEjLeLsAJXO5zrPE+xlWP90joCGa3O8nCJV9tylecRxC18P4UJDUIK3FMuxkTEoohfyCV5B22SfES9Thi0kNKhI9iBTLmYqI6UyV3UCnCEC01o+SeYafs++aVNBOtPM179Fvpnnmbn1s+i6wEm5aCMBR0n/fFj3US/eBuLzx2la/YY5paDrP/+buxLCyxveZ7C7vVkpnO88tgpvtw5RKa7m+/eYtl0eI7i8RcQv5glN3MrYjrAeMnn9aQD2tAR7sMxKZrpOj1a8ivrfwykhlhArh8yITRWINMOew/CpSLs+wz0C1hcxn7jJZYbZzHBMN2mG6Imufhm7GAGESmChYN4N1/lk+ssjfmvsuH8QQ7ev4/T4yHzp3+XN1qn+NXyA5Qbs8xv28Ll029Smvo2e/f8GrnqOOXNr+LXx3DsAMRVTGmOyux5Mm0bIJdH+h7GaEwQ0r1hJ/9l9i4+Pz/Fn3XP8lOd/eBIhNaYlsLYk+gHTuC98VGiyggrOcHQJx6m/4GteN+8hFIHCB46i/nS71D4zAreyhgDl7oJ//UrOJEDdQOBRjgWJRSZp1cQpQZLfTXa7VbMgdeQoxFybBelnQPc+9P/ko/Ytfyb/Z/COVSilQvxSgEr0WmKx/4n/FqRqKuf1lyJKT2F+9e2e9Bq/WgAER+QQVDYxFR4Y+gwWhjWz64lchyII+JWgPBdAh0n9rUVeI5LK2yhMXiuiw0lUV3jpJ3Vz+FglUUImwyedw1Gx8hMGiHANFurPQcWrMZzOumdegSnf45w5HkGyw9Rq48y3t3ABEuMxn2rgx8lJmjB1k78UyXWXLzCyk+epf8v95G6I2bcPEn/Jz6PfT3Hn//xIb4Qz1LcvhO9vMTu8RLby4Lm1hTF5THUpQHivIdyLVSbWKGSCE9Kko13Q0Mg+12MBuvZBJhhAxmksKIXG8TI799JUFvhavAs0XLAunpAfP9RnJN7KDpjhOVpRCqLIy3Ca8OGAY7ahBqfoNJ6jNSDa1hz5Rpu9F0uYCjv2MhnRl6mef4i4UsumZbGaR9msX6CBfsN+r1PM9f75ywPHcQ9NUAhXI/T1s30kS+yZuwO/OY+otpqZEq5EMPmdDuNk08zsftODBIZg1UqycN0Z1H7mtjFKzROlRBTGRoxhO1pPOvCdC8cf4CUXILLn8AeHwER4QUtjBBQ6ARjMYokuRt8KQn5AAAgAElEQVRD/e4eMnf8EtOvPY4udzN05y/hTAIX/5w7bo/46qkBfsNobL1Gc0yRCgXbCz+DuDpEfX2Md2acoPY09AnQb0VKrIUdH/rUu+7ldyw1OfbUXxHVSsi/XoP1XkCCwGKYyc+SidL0NnswjsQIjZACx3FxREKM4CpJJAXSTeOrkOXCY6w0p8maEfxcijgMEypNP5XMI0w7KA0mjJIBLyZxZKWrklCjbMMzXYiVDEo9AD/xczifvRPXgcK8xg8F1hEQRch0CjlehTfPoT91gvqbFYKJCrXuN0mvHSU/+EkO/+FlHvvQR+j96MM4Xe3sPjfDL18Gr/dlnJ4GqYv3QK4tmYAbWmy8+j0YC66P8F0kGrRBCg8Zh8mx42BIwt3CcxCuwHF9clNNMtMl0r1jhMUDyDDCq25DpA2iFQMCUy1DsEzo+2T0Nuy5CVLDRSbmF+ioT7Fw9CXObfklynGWQufjbCrtpbu8nlRHjtpwB0viJIXRiOzZtcgxzUr5KB21HZQnJ4mz36LvIzEsDCF0H1KR9H+bmGKhnb9anOOJ8gq/2DVAJjQIE2FVxNSpcZbtMbrkDrLXHkQf7qBQixlbDslMBDAzhDu+jmcOVTg0W2Sj6+BIgXAzSG25Wv866aEGojGIFBItZzHDLrkzZU6++EfkU7fTM96ideY/kL5H8GHvZn66cTOFdOb/a+/N4+wq6zz/9/Oc9a61b6mkUpU9kA1CgLCJKCCI4touqL1p26292t1j98tx/M20M+PMr5221dbuHhcUu/VHI26AoggohCUhCwlJSGWr1L5X3Vt3Pcvz/P4491ZVQggEYiCazx+pk7PdqnOfz/nu3y9j04eYMA+SshZgTS5D5cqUa8p4XpaHzMcpuxayanQICDyPDW/9PZL1zadcx6eUILUdy5kZPHLa5KjC0AZKKLZ17KRoFlk20YUlbMqeh2FqzFgMUwhyZR/DdUnEk/gzGeId+5EDDZgzb4jq2BFIpSAMcBNxyr5HqKJmEGgDOxYDaaKlwPfLkf9fewgjhZGxcb+zC7ccIgankIYNVhQJJp0gnJlheGI38tppmte1UfedDqZyR6jZdivmviITvzzGjhUr6OpqRw9P4u0/yvXHSqjGQcrvXoD5o3pEzRJUWiGm85APwJbgh1FQ0PeRfohpmZFHyy8Teh6mY6Pw8ZC4wkSXQgJdQKoAx03iLEhDshmjbxphNiPsqKujNCTCNAmCPDKmiRkOoRdATYKw/xhtmzvo/fYg126MEwt/wDOZ93DR3iP85fa7+O3Ot9LZm6bfzCLdRbjNP2fN1ZuZvivNfTtm2LxxglVyO01XBoTHbIzphUhDoAOFcEy0Ajdez191rGeXymAUcjx94J9YsHoG54qLSKk02paQaUPYSRYk0ywYysLPRhkd2UGy3mLLwDT/XKP5/YY4ZuhCWVPwjmK+vpvapjzmFgtR0GCFhK17Gd79ffyRMk3uShrNEcJFE4i112E6b8F6ciduwoBymYZEE4YnCFem4dE8os5iunGCvZntZIWBPS/IKqUkWyiSzWZ5oYakp5QgibpGDjz0Q0zrpY+zqgZlBmuGySQytBXacbVDoKNuJlJrfKHwwyASr6EgnOqixt6ADJNRQE1U0uGVQqgQEYA0bQQKx3ERrksY+PilIrrsYxomuFE/Lulr9MAkshBEJZ6mAeUAimXQioNTu+huHmHRn7RhDgyTGdyPHktQa1+OVE2owKaxHLLu0CQbj83wmvAYsZq7GW7bB9ZqartXo00LHTPRk9NRq6CK/1YlHaQV5atpaYBlgvCjIBsSYZuYmJHoNwykJprbaJjowEcJkyD2OH5g4fgXoY0wUl8DjUjFwUwR5IpI7SLrbAaNR2hZ3oCZ1FgjMVx7mkx6Mx1PC35cs4jDa9u5/j0X4RUf4L5+m/snL2HxFVM0dfazu7eNz4xMs96+l6Uru1D9b6cUe5Yx/TDx2DokbqQy+h4XL+zk5vYVuFbIlHcP8ZYW6utvIeY1EV+YIH94AX2jGWQdcH0H/qFpgtoBtopH+McxyR82XcTNZhPCk4wZD2C97RAmq4j/8mr0dB26sQSexJpopqZrAaXkIG3uhSQ7Q+SjGzAHlyD6MuhAIAwN4xkMM0Z+dJJYycHUaQqxDL+IP8RkeQz7hLJqr1ik7cJNrL/pXZV8rZdIkNHeI+z+2fdJJhMvmSBVkhjaYCqWZSwxTtNYA27golBR0qBBpEKZJqbrYMk2tJdEeQXM0EbYNiImIAwISj7aL1JiEstOIaSBtiJ9X3shphvVgBCoaAiMGUWZcUxUvgB+QJY8M1ctJGvNMGPm8VuHqF2gEKMWqctvxj2UQoo6RExia0FDUVOvBDW42HXD+Bc/gzVWR0P3GxEqhpIhRskDz0eYFsKyELZFWPYwAS0kgR85IrAEoWuDIaNEOUNGzQ0sA5AIw0AbkOvtxrbjlJdnGZUjxAbbsK04ylSochi5pwNF0GpjJeOE3VPINe2I3BIS9XkS01eydbtgV6yB3dueYaBrOatfczWvXb6Ezqkx2rwH2TEpuPvoRTw90MfrzGa2Nq7H9hq5ytuMTF9BvsXBq2+mplSHKIagouRRoUN06KOFTXPrG4iFVyJyzZBPw7GV/LB7H99aoNmYbKDhLWvIL43RMNpM68RKbqpdyoZYDZgSf+ZZ3JW9xAbWYDy5HD2m0bethNcvhy3b0RePIsc7qZm4FJkaYLrg4FtN+OO7MLIBBAZqdAzWLkQJSJVczJxNJjHJg+mfkAkmseTxL3choJjPUbt0HWuufeMLrt1TqlixmjrchjZCvzhbavty4AQ2E7FJHlu1lVUjK+kabUfFTfzQQwQBvgpRlotwAFNhBpJyaohyziCuWsCUWDKGt3wP+c3bse5+J4bXTOjPIF0HAwsRCELlR8QRGhkEkb9baobWxzGv2YAjwHVtyg/nEAXFgstCUo6LuH85ViwF5Rq0qyHQkHAoZDK49TWIRAIllqN7HRJqPaZOI6wo6zicyUfN8UwDFQbocgHTcsBJQr6EHXPBUoRlH8OwkUCYLyJrUqhyCZlKogp5DNdleqif3tgE69deAbl6pN2HEbMQwsUozBCg0F6IEZQRyYXoUoh0k6SeWoIWccy6evRMwOULr+crz2zhcavMTauXc01nLfZQAe7pZO3CGv585d0cUZP8077L2BckaHJ6CVouha5VqIMHSY261BpLo1WifMJiltz0GIlUE5adRgc+tLYi/QKaIJq4qyRaGlzXtIiufgf+/SB1N3YQimESTpKECqK8Oz+HtalAMO3Sl/khbbfVYw5uxmiyYGcbSidhzIUghQ5mCA2H4qJOGmuKlLcPonqbGck8hbtxOU5HH0Z3hrjdxTPJx9lbt5eClcdSz9V8tNZIy6ZmQeeLWrOnlCCpukYGuvcyfugZYonT60j3vB+oDUp2id76Pkwlacu0RF+AKRAKSjM5DA22G8PSUNg0xN7DP6ap1IltpzG0hb65m0nVi/N4F1a6GbOuFhlqBtQDZEcy1KU6wY68cBqJdOKIWIzUkjYC/RDqgQeovVfg2JqJuikaR3K4YymMZ5rwyll0qRSVC3shKI1dU4/QCmULZGgTz63B9lajLI0II+NbSA2WhcoHeLXPMFb3QwzVyJ7Rh0nrUQqj/YhMCIGD5boEhAgUIgiQgYhURyQ6CCEZkPzEm4jZaZyHCzgliRVfyNDR+xHKwU02QhCgLRM1lkMjMerrIauQvkCVG5BuO0eeeZgfHdlOx01v4ron9nFNRy1TR54iO/U9nNelEM2addMX8vvJzVwW72CsWOJL2RHeoj3MGxdjYiMnitDQRFjMkh26HZbuZkaXyKxcgXtJGtN7iqmBu4l5F6BjCbQMabcsLsgZWMkEjBZQTw0iyzqqDC37CKnRoUZmV5APpymtHKHuwiZUzocnPcSTApFohkkDykUwQE83oDoGKYifEDRuYPDYAK3pTlJGAWU/ib/uKvZNPsS29JNoQz9v8ZtWCmHHuOGjn4oyRF5ovb5QwVQ+n6N/z1Ycy3zRAcMXgtQSqSWDtcMorWjINWCUBcoPMF0TLXxUvsShZoeHnEa2ZiboKJg01aRRSuEteZrwaA2J8csRloEMfLQ0cVdMMbl4B1M9Pg3JLrRQKBmidBmtJLKnQDB6EL8gSJhdhDKgWPC58zFoPVJDw1tbyF82jdpbwjGaEKaBsCy+v/M+jhXHWVa/COH5iCAWFXOl0uBF8/uUBG0amKFJIdlHvnmYeKho+Z1x7BtnmGrvx+wco2TuZcuDD9Bct5KYW4culcE2UV4ZchOE0+M4f/wa3BCCf92C3+ESr9tEMPFL/JvuR9BFrLwKbUfZjaIcRANAiyXQYWT7iBBDwYMDu+hbvpxLj+3m2o4+nPgvKYz+hNjaDEWVwmi9iLplfwnbC2grQ9KpYZEX0Hp5Iy3XXYT52CgEktGjWxnO7KGpcTNSdsE7FpHe0EswcDsjA4PEZTPT0yBtF8MwSZgxLOkw2PcMRquDqS2k5yGRKKGjRoFOgmJhnNLMEG35Gxl7rJ7EqrdAagV+y7Pkd/0YaS1AN8QwSi6SIvH8ozjX30amz6R+zCeVGMQ3HqPPMXly/DDHvL2VNrLPH54QWlMMBatfdyvumagorGlq5Ykffpu4JV/WrLcTUZ2aNJoeZzQ9hlU2SRbjWESpH04yhmFatMs6FqulNLqK2NpDFKYniPVuID11IaaMoYMgytCUAmuknbolNdgNcZypRiCk2PwY4S0zTAw+RuFoSKy8kpr0GkKdxyw7fGdwko9ND/Jmq5b2uCY13oGjFyAMA6TBjCt4Y89OsjMF3rZwJcKyUNpEmg4U82ghUIGqdKNPoO0hhJunfuISnMQ1WM8uINyzmNqORbjr08ilNrJ+mprBZdhGM8IxEdomX96OvPZ2wgu6katvYuJYFnlxPeLaJkYO3ENs+f3ULHs9sZ6rCAIwmmoQhRCNAiGQZhJVKiIqpbmGaZGyR6kLn+YNyRzrPrAUp9lDxKZZuOxi5N0bcJe9B/uyTvztO/Haj6BHHuaKFp/k5Utxf5qHiWgxy857ca7dz8yRCcLWh3A4SPyXLv/5W4N87P4MN1z4XtrfeTHWlYuxpi10Xx5du53pmrvxalMkS62IwIrSgDAJMhMMDG5jaOopHLMefyZA3LiAOD4s/T4jw3cR1qwl/parCOUTBAd3EJYyaGlhbfp9UmsE8cIv6Kl5ll8czNDj5ynlJ7Gk84L9lIu5Gdbe8j66Nl79onpjvSBBtIbJkSHGD+0hFjuz010FAqEFeTtPX8Mgk7VZpDZJlWuIOWkSjkHteIk2ESdVuxBjqA7LaIJyGqFsRCqGUDpSS3wPZADH6nBLC0FqRFCg3LKLiWafunFJX+xuSrFJ4sdasFIu/Y0/5d+f2kbBaeadNa10WssJJkLCIEdZjaKVz9/np/DzWT7pdNHWtJBQQn7qMfKT+zDNRqQdi2pbyIAxCslBvGu6mTk2hhxxMIOF6GIaDrcht3RgPt1GfbgOK4hRLB1ElcuYhsILCpjxTlw2UPjFGPEGcINWyg/8CGv0G8Stt8POSxDDJsLUUChHgVEvxCMDshvTakCINIYjYMYjXjvKuk+uZWLyKHrgIGZ+Cq2X4Y7Xonq3EjRlsZOrMLs15mgb6a5m/KZRnCcyDPZbTPQfJdP/KOL6bdQHdaSWShJrXcqPtPDpXzbypF/iM5dcwdXNK7COCNTeIdTgTmQygbRzpNbtwRhrwJ7eiDBNSvkxRiZ2MSWH8cJplP0MzeummWp9krqaS8kPehD8hLDzWpzGtdhHf07J+wV+7TZSxZtRXRuYrLsDw/0JTx4aYv8hn4IlkdLAkC/cdEMKQT6bof3ia1h04akLpap4QYKYpklmbITuxx8knU69qJueDgQiyuHSgqybpa92gKn0NIZ0qCs1kk/3cCy5D3o94k4TXhBECX1aRW7dIECqqIhHWHG08Cod4yEsTWN2LIGeCeyGAyizSDoVkl+UIRmL402XuDm+lptrl7A4WUcsHQchCMrD9OvPkDQdOoMO1q0ZYPkaCzdsRuRtwov3UrxmAnuwCaNci4w5iMQkeuUUxugSrMk1zCxM4xdHiLmdBC5YtQnQUddBUUyTzxxmf/k/4dUdo6ZxJQO1Y/i9gvKBJnq2fodk+B1ihy5FF3cTtpuoQ2/EDmrBCKIad8tE+j7CtPGNHrYe+Bii5TB4HpZaiEw4mMkWMrsHebh3BpGYpm+giFu/Ed9LEIgSxkCA8VQSihJMgZqswxzpZHDQ41PDT/NYrMC2YJr9Uwspla/ne7vTPPjoEr510KC7K+BvLjN5XcJFiVYYy1GQdxMsfBY36EKXlqFHVmMVV6BadqJjk2T7iwRJSToxQMP1NsbaA1itcVqXvBPr+ls4MriTYNcPaV4zQnwgwPCuxZ2E2Mi1hKksowvvZHBkF7sfmuFor0IYGkO++B78KgwxkrWsveU2aptf3HjoFzVhKj+T4Y6/ej9mYYJYLPbcYp8zDF/6CC1oLy6mbmaG5rhDXWItciZFPF9TGcwDCgiVj2laEEJZTWEaNZi2S+jl0cLC8F0wy4imMjrvI1IuXHWAoZqduH0LcHd3EMuvBisBjgH5AkGpQN7eRmhO407UEd+8iYnWnQQP5kkZS4g1r0O0OjCkoWxALoOWdtRyti4BBQ1Sg23i+UUMoZGOG0XMpYQgoKwCcmxBLIwT71mKU99Gweghe+gwiUVbSLdsorA/jdG1ByN5HcbhFWALEBqRL0eDBkMFTpwJ9Rjh+lFibSGyR5DY+yaQAd3DR/haKUtWfpvff087dU0fIjbeSN2VyxD3D+I8lUWXi2gTRKUlU7kuR2ZtI1P3HuIZESIWLiU/4yNqLP7Pz+9kaHqYy9s0f7Qx5KLmS2jYdwW6tB/au5GL0sijl6EzDsgQXTbQTKMvOIQ40oLBEpgqka39Fna7wB67gnCyFllbh/HuRrDuA8NhoH+KILsAeruxxmrY2z9Avv0AvlRkBmwsR2O8hJbKfqmI07KY9/79v7/oa16U7zaRqsGoaaI8PULsLAxbspSFRtMf62HQtZgsNtDWMYDzTB8rCm8mqIkjLYkUBiKa2wMYTKV/wWDPFBeY7ybWVosKPQQFsGxyfSV8pXC9JOEPbDIX5wkv2odzxVGyjw6ReORCnuoLuYMZ6o0yt75+B6vWFsh+u5YZ7wj6p2OUW5eSukIQ3jMIU+2IuoBed5rUujpqd4eYykFpH2krCAFfR4VdxTyy1kEVPJSnMBMx7PIMteZm/IMmIraDgvwBztG3U998OYa9hKA7ib/mc5jtKYa+dZDYNX3UlzcghttQcQFBCZmKo6eL1M8sQ2zbABWjs7/YzzeGDzF16QZuWbSKzX1dBMUpElddA/8yBHtsPNelPH2A8kVxkjVLUTv6MJwYbl0H9rDmx89up7slwc3J5aj8U8Q7hrj9Q4uxB0os6yshpvrRY/ciB2oRS7+Lsj3k/k+ASCNEDkwfvTKJ3u9j7L0EQZmC9xBh2iUduw3SjXDxcsKHt5Bd72H3PM6BA08wE1+NUVND/+77yE0OY7gxRErBlInUBm78pb+dldasehGxj/l40TMKD2x7hHv+x5/R0lh/qurQXwl8GSJ8TX2YYk3hIpYEq8FOokVUdyyEAAVlNUZm+dOUMg61+1aTbmtFFfNo02R3zyOMLJpgQUcnqi+Hu7iB0sR+LlyTxtvXyjf7Aw5dtYo112zgqiWLaNr2NeKHjuAPX4P+UDsiG+J8dxLTWEA4MYmIJcjW3I312jfgsIzis/cRPghW3UpiiRRSAnEXVBmUAaFNWBjDK04RShc7mca67QKmjSJuditm+1149wQkxj6GMurRxSzy6ocJlv2S6a8sRzU14YZjlMcE6cQt2FZtlPna5lJo8nAPhhhmPQiPp48dZE+TxcZYK7ltjzBcCLjsi3+KJE/Nl7cQqkeRqfXIW68kKGWxdngYY0RSKV8iCHxKQpCoV6jw54RjPdix10NsKWgZNRheXkOhpszB3c9y5Mm/56ZrpjD7LkPoDyC8BPKaTtT7lhB8+jHMQY8xbz/Byh6SK28gHVvJaKyPwYP7CXbs5ZDTDUJQLnoorwBaYTqxSs34mVlpGpiemOCtf/cVFl648UVf96LHH9Q0tTJ4cD/T/YdxzrCx/kIwtERKSc4s0xvvZdQYxMUmbbQgPKL2ppbANBtItK7Au2EbsjDF+IEYn0oM8WisyCWlFAtbStS0dJNML8O+YiO1y29EDy7A++3XkP6tjfxWZwuXTB0i0fsD7PBSzNf9IfnpSVKvvQbzoMQ46KNLZaRrI9a3kisnKNw/Qs1QiIw/hb96nNHRPdTVuUyMHWFysJ90vJ0gmyVoPEz5ikeJ3bAT5GGmhh4h1rMTwkW4F1+K0XYRdm4aPbgQmaoBC2TBwfcexZhYR33hRjLWMAVnggaxEmk3RiknrTXwoQ1kC3mCgz9lMP41ZKaXS5NPs6Cg2Oq2smt5P8fKNrm7dtNuPYnvPotIXoJV347Z6hD2jsNU1P4zahyvsbVAlAsoy0TELkWK1eSzwwzofVir2/lBfJz/9YvHebZzIcmRWtbXd6LTCQynhdFjj6JFH25qIcbeMsPBAP/WMMjBmSRT3Q9w8Jl7OfD0/Rwd2MKYNQ5BNK7CMASGZWFY9hn1mGqgWCxjJGu54LVvIlnf9KKvPa0pt/d++TMc+OmdNNTXzTYHONvQaAIRINAsDDq5oLyONm8xQsQgDigBbZOEDTmGtin2L25ldOQZ6g/tZIO7jMaFHajXjjORu5vU6o/gbXgToz/+ER12Bve+AxhvugKVP4y3t47c4k6KJUEbtZg9MQhMwqAAlkJsXMj0NQvI7O1m+sH7WRHvxVpQRi0uwWiJXNEit6MWlM3C32ogcCYRkwbBZC+xxoAyS5Cdb6Q8Vo84eghj1TDiEY0ztgnpJiFpo5tKqMsEDIPxZBlEHAJJTk8x0N+D4dgs8CXxt27iUHELE1s+QedVt+E90Ua91YQbpCnbfXgX91K7ez3MtEOtg/IlUoVRmssfLMUzFMa/dCOVQZAvIIVExy1k0UcqM0q+DDzKKkP+Yp+pcp6H/30bmzsuYeWfvhZ1OIc1XiCoNSgMHWUq/wRGfYnRLTkyaRPPzDMc9kYeRyRa6rM2/1Fr8IKQ6alJVl93Kzf/2X87retPawRbQ3sHu376vUoDs6hRwNmGQERj1TCYNMY54hxk0hrFkAZxEWekOExypBk1GmO6uZe6+DhLS4LxVIoHyyXWmhtJHKnD0XFsOYS4d4Caw4uItV/MQL9LIjuNcf3TmO+Mk/UacS+4jHgfZPr2E6zYhog5WKoZP/Mz5NZf0nzh1aTam7DHJLI3w1R2lOldB2myLRrkTXjtklLnHmLTBuaCpxl7pAP38B+gGy+kcFhQeyCFnAkQ6RmchZsQsb2UZrZQOlbCaWxDJtvhyRlEPqQ4M0w+nGRP/25ueeJHfG16mH3eDKPbemnsasJMbmZZ73WkVDtW3mLQn4b3Xsb4Vpv6mTZwNKqUI/Az5L0Rhsf2U1uoRV69CFkMCPdPYFom+D54PkbMBccgLJWQtoXpW8TGHNKxOJcsWkXTO64grHPpnTlKX/II/ZPP8Ni2b9NfHqU3l2PIGGJCDJPTM5jYCGEiRfTdiZc0lPn0oInI4YeKfKFI3aIlrL7y9ad1j9NKsHISKRLN7RSGe9EijmsZr5gkAbC1g9aaY8YRBsw+UrKGvCm4RG1iVbiWzsw6xmofYNIcZGdmBVtecysXXtDAVbu7sRo7yO4dpH54VSR5dIqWj70B078b1l/LTM9KWtffCN/ZQfD4APrSXZivy6F+4aDGfYyaNejJJ/B/eTvxxkXQbCGzaWqZoW6hS3BgNdaCtdQOjZB79BEyiy+laf0tNNe2k8scI3csj7Eji9e8jMLbVpO49ga83jGs6V6sDb2IRIn8PoGxbS/uuoUU4qOouINz25VsNF/LQ+oPKWZ8slvuYXzH3XRtvJy68o0EdzwJrSm4qpXk6pXUHIRGtZCM+SxmayMincCMpzH8OHZPieDgBPJ/7kQIiXQqfcosE0wDHYYEmVxUxixNSDsQCHJHjlB0svQ/8ij9U0fJjQ1R9CYxTRMrHvUyI+chpYnzCsyAFESDiqrkKJZ9tOWy6db3nf69TkfFAtjxk7v58Rf+H2rSNViWgWsbZ254y8uARhMSIkXUTrRdd5IoJWl1TWJGlidjF3LvqMlHP/IOFu58hpqnHkU3WahsjqnB3Xx3oIP72ySXdnXyu4svJzc5gRmaLDviIWrqYGkOsgoaGwhGB5DTdYjXNTOz7ftMHjzIgg98FMtpBTuHyH6D8MAhxo+mSC5tQA72U7z4Mia3FqltWo6iQLJ+Bc7mTkRSUixCbGMX/s+OYf9sP/l8N+MqS5jagTc6SePyt5NqXovAxulYBrk8hFmmcj3cvmcrzc0OVxyup9HrwCqP4l1zgMTSzRjPrkQdnUQ5ElMG6KJGOQ6G50cdCywTr1zELISIegfhxiBXREsDYVYkibIoTB0jV+7j6OheSqsSDIWHyKsshh+1XjFMCyFeRfMeNfhKUfZDyr5iplDETtfxkS/eSbK27rRuddoECX2fL3z4VkqToyTiMWxD4lgGhiFfdMDmbMCnjBYCt+zi1sapj4fI7ZIVzc2krRrib2mm/OBW+rqncNa9gdyKi/jm4X6m793NH9Qug8s3cP+u+3FdlyW+wZs7rwCt0PkcwomhTR8SJnlvFwE9JGM3YsRb0KFElEqI5H78YJzS+DiW38lUe4C/q4cFnXWIq6/CcFKQbEJLjb+qgfLUHtyHf4rsHOZQTvHOvz3G62ua+OvbFmCOrqZpZiX4AdoQqJk8Pdln2Z3bxQHXIHbx6xkamyaG4P1lRWPLIZyxlTjO5SA9glIJI2lB4KEkSFOAL8C0EIeJvj8AABm9SURBVOUSbKohWN2I+PeDSG0g4gkoQ1lNclg/zUD2KQYZRAUBygbLiJ0y3+mVRLVzpReElLyQYhAyOjzMDb/3F9z4u39y2oOFTlv+GZZFU+dKugf7sGynEjQU2EQ9Yl8tsHCiyUtOSC6fJTujMbtgRA4RN+q5cKadZOcIC3IO1kwCa7iG/1lbBzd3QWKMoOdh1jSv52gqQXlskDAoYLhxlCuQLpBKwVSOhLoYoTaBlOjMdJQwaJqozBIs6wKsmINyNGb/Fg6FTxH01bFkw3vxHtuH+upTGEsuwtvzP3BKj6D6mjGOvInOlMXSphQDRZ+2Je8nXG3CwxOQkfjeFD8f387fPLOTKRnj02u6eGNcEKQX4YtGSgNPEDcuwFyZIowfAWmgx0bQI00oUYdpuZGbNizjT42zLTtEsXUZawYKtAQGuCly/jhHvG10h0+R8UcwbAsDO6pfOZv+/dPEHDkURT+kFIQUSmWU6dDcteIlTd06bQkCsH/rI/zzn7+fltZWLNPAkoKYbWKbcrYN5qsVoRZoQpRXJG420SYXs8BrYbG3GlslIWkRXJin8OwWUlMXIpoWgiUhVyDUYKTqISgQ6sgLJKVEBwoZiKiNkKkRZRVVBNoGxG2EtPHyk5TtDMF4iRrDQak8glasWoWfvRfDqkE2Xg9OLWQKHJueIAxD2o0Ysi3J0MgzuF31NC9bzp6eb3D4iWcpLL2WSzcto+3m12FtL2J/p5uR2ifJ3XCI0b48nVYzRjFF2q/F7lsHYQMHhg7w0+wUdQs7Ua7BUG83l9WuYKOZIBYX7FWPcqi0nWw4gomN8SsecnqmIIh6FJf8MCKHH1DyAqYzWdrXbOSv/+nFR8+Pu+9LIchI71H+6WO/QykzTk0qmhprmwauZWKZAts0XlXq1skhUIT4lJHCpE40sNhbRmvQQVuwDAwbZBnq42DYlCeOwAWCsYNP4Ay10dh6SZQQKYnmgJshQtqEvk9w6QL09AzWtnGULID0MN1GRKINpCAXfI2sfoi6cD0z7kF0+4XEVn8I1dWOpw7if+Ze2sXNjEwP0GvtZ8VF6zDsBn702CPYy69jdft9XLBaw9YVTLb5lL02Gt/xRsRXd2GKBP4FScqeR9x0kTJJ+dgI8ql+LCtGbzBNjyqwZtFSRNGnLpDQotk//CgHCk8ypUcQmFELpXMISmuKXkSMoh9S8iKCjExM8sef/Sobrzk971UVL8nF0NLRxaab3sF9X/k/OI6LtgyUrk4vitQs2zSIhhW/WqGRSBxioDUZPcVT1qMkrBRJnWKJfwFdYi2JUSDMYFkxZD6G406i2xzKUmAbEhWA0kOUk7tIXvZbiOwoLFIYv70Z474j+D/+Onmjm3juSmK5Fkj2YLoe6elr2aHauOMIpOtv4PEHD5ErPMPNa1oYeHqIho09rHr/lazqraN3X4kdaB600tygvkfzwTYYu4pwwiMx5FGv4zDRjcoJdKGA0ZMlEUp8b5r85B7qVi1DX7yA0HfoOCrp0DWQ84E4SmR5YOa7HCluI6YdLHEWconOMEKtKXshRT+IJIgXUPZDhsfG6Fx/OWsvveol3/slSRCA6Ykx/uv734QqZkknYhhS4tomMcvENiSWKXGtV5Fn40UimogYEIqQRlqpK7XSUT9Bw+hSUlwfTSwyymArtNTomIUOc/zcG+P74xNcMaN54+LLSF/djLppAcEXHiM2YIEoUK59nKnuSerjlzFiPEb/1R3UL/4tgnyBH2zfgbMvx/IPvpZcUhIMHuNaT7CPFL/oPszGxh4ubH6I1eY62LeZwYk4zW9ej4wlGenuZuqBJ1nR1IUQNWAIDGUxPf40w5NfYeUNn0KvXY++ejGlBw+ReCiLV57mmNzLgfwTjIa92Ma5RwxBRI4TJUfRD8kVS5S0yUc+/Tk2Xn3dS/+Ml0oQrTV3fumz3Pn5/07n4sW4poFtShzbJGYZWIbEMQ1s61xQt06OkIBABBhmwIKwg4X+GvywyIKggwajA2lKMGNweT0zm1t5+K6nmGk4Qmf/ATYevgyzsQnlawydRy59jHLD05SO5bEvbcSsbWDXAxYjM69nJmExY/vEDx7DnthJqs3gda/5MCLexMzRaZzeJ0isPADJRagdVyI8G9/MYKRSqGX10GDj6yKxnjIczoOpQYVgGAhLQjGM8sEubKBoeQzuf5ID+V8yrHoQWmKJFx5m+WpDNLdRU/aPlxwRURTdh4/wnr/4JB/40//0sj7nJRMEYHpynM99/I85vPNxGupqiZkGjmUQs03cSlMw1zIwDfmKBhRfLrQWhCIgxCMUITW6nrhKYRRdGlqXsWr1WmqGf0B5/1OEdoL4ze0EbhrjidcgJpYzobcSe4uJNXYEmSojRzdS2pnmSAnKt63G6mrH3zpM3f5JnPEJ2hIKMg4iVgOOAC+AnEYbBjoWoIo5TMONur7bVpRegxUVjZkKtAI/ANcG7UKhgDJ8nij9iFE5SMYaRwkdefrOMVSJUR25XfYDyoGi6PmU/JCCF9DTP0TXxVfyyS98hfqGxpf1eS+LIAB7tj3Bx997C61N9aTiLjErMtZjtoltGFimIGaZ5zxJ5iBQBFFHRDShUCTLCTrSWS5oXoBZWEdiqh5SLugkDKZAhfjJAsKsxQzSEJPkukLkpibiQxJ27YGpHCQXg0hCsYgKSlEprWWjVYgwBNoPENJAlT1Epf2W1BJsmJnaTrY4TXvbTVGATzjo8gAzbT9nPN3F/r27GYn1IZFR95dzUK5XR9sFSqFmJwyHFPyAQtmn4IUcGxiife2lfPpf7qC27vSCgifDyyaIUorvfv2f+fr/+hStjXWk4zFcS0YkqRDDtQws08AUYJqvTA7XrxKhVmjTwDZsyEuWq1XEVBNjORvd1UF+eIoNXj2LahsADyyNTtoIT8F4EVU7inyrwuuZQj/UiBPrAKEpBzPIuMQwTELPw7ITUYDPcQi9AqKskZYL9hST6qfkMltobL2S+NQbGRcZntWPcMzcTmgnCEohNi+9AeAriepQorAy9i4MdTRENYymChc9n1w5oG9wmM4Nl/Ofv/A1ausbzshnv2yCVHHnV77EVz/zSRY0N5CuSJKYbeJYJqaUuGaUt2XIaBjl/KlIvy5QWoPQBMJHBR45z8Vo62JlfjWdhTSLWjphxCNmpqNkIVOBEc1nLMhDyCXTTO4YoC22GXHLYVT9BME9SdS6dqxsDcbeWrDroBS1wqGkQMqo91a5jwl5Oz3qKGPhKqaMLHmRxdEJ0OolBcleaWggDNXsCOxQKYLKyOvqmO1yEJIv+/QNjtCxbhOf+vK3SNXUnLHf4YwRBODfvvw5bv/7/0Z7cyM1CZeYZc7aIK5pYhlRFrApoxHLskIUQ3JOivxTQgikUOD7CMA3JPWLVqJ7slwQbKIteQHxwAZPgjTwVQ/WMgu0Szg8iLjhEPLoGti/mmjWswk6ILTylCmCHUNnCkzqAY7a3UgEGTXBaDiAEGFl2vuZKzg6m9BE47MjYqhZ1cqvTBUOdDQWww8UeS+gb2iYxWs38Ykv3n7GJEcVZ5QgAHf80z/wjc/+HQtbGknHXeK2gWVExrttRHO7DRERxDAiKVLdNn7NJEoV1RFqgV9CWwJDW1jYLNVrSOl6MEDqGHUzNdS7dQjHIpMbYcSeRNk+MtRRG1VX0i8PMaFGENJEK02gSniUAIEhrKjX7zmKaK6jjqRGRVLMtzuqUsMPowGpJT+kb2iYRWsu4RNfvJ26l2mQnwxnnCAA3/jiZ/nmZ/+OlvpaGmrTJCwD2zQwjWj+uSkjg11KgSkitcswojSVqE/vqyvx8Uwjmkio8PGjvlYASpAgTcJMgoaiX2RGTqGlrgyejLxpJmZUaKR11AQCec5L32iEtiIMq7aGwq94qkIVbQdBWCFJZQ69VvQOjLBw9Qb+yz9/i5ozLDmq+JUQBOBr//j/cs83/xVblWmsq8G1DJxKrtZxhJCRmmXO+ylENDPEkJyTuvNLhSKseMeI5g/qcy/QejrQaEIV2RmhilSqUKvZOfSzZKkeV3O2yNDoKO2rNvCJL36D+qZTz/h4OfiVEQRgoLeH//2Xf0TvMztoa20mVlGzhKAiLaoSpWqLiNntqupVNeh/g3jyGwGlKypURWpUbY05MqiKihURJKge0zAxPk77qvX87Rdup6H5hSZ8vDz8SgkCMDk+yn/5g9vo3/807a0t2JVxBJaUmIZEVrYN04hGGkuBaUhElSCzEkfMjj0+j3MP1U44ETGOj2XMkqFCmuq2Hyj8yrEqQXK5HItWruXjn/86dY0vvvnCS/69f9UEAZgYHeE/f+g99B/YQ1tLM4aUWDJSo0wpMWVkdxhGVc2qql88R7KcJ8q5B6X0bAS8qj7NGd5V962aM8pDRaigFISVuEdkh5TKHoPDI/z327/LFdfdcFZ+97NCEICRwQE++eH3MXRwL82NjRgSzApBLEPMI0XFo1WNmczbbxoRMar7DSMiiRDnupn66wWlNeioPkNrXYln6KgjTcUYjwJ9VckQRsG/ed4qL1B4YdVrpSl7PuMTE7zzo3/Nhz72N9F4irOAs0YQgLHhIf7299/FYPc+GhsbIkliyMi7Vd2uqFhSVNQqIbCMuSDjnEEvZs+pShMpIs8YOprUcLYb3P2mQUDVB4fW0QIHKt4nPRsBh7lqv/kqVhCGFXWK49SochDOEsMPQ0qez8TkJB/4s4/zwb/8xNn9G88mQSCSJB//vXfR172XhvoGbNOYJYllyFnbpKpiRRWKAtOs2iPP9XgJiIZ9iogSsnJcEBHlvDp2ZlFVlyCSFmEYbYcVkggqblsdnR2Eep79oebsDKUIFMdJDT9U+GGIH2jKYUipVGZ0YpLf+fOP89G/+dRZ/1vPOkEABvt6+ZsPvpee/Xuora0h5tizEsQy5axtYlWkw5w7uOL1MuYIAlUSRfeuqmDArKGPAImYVcmq553Hi0M0k7RCglBHKhRzKpTSESGAue2qikUkSUJVkR7VnKpKuohfkSZ+pZa82qrHDxWZmRyZfIEPfPQv+YtPnl7DtzOFV4QgANNTk/zsB9/l8//148Rdh0QsNic9jONVr/l2StWjZRnGLAGkqMxJr7iPn28bIoky321sVKQQ8CqvgDw7qKql1Td+VVIEoZrt6h+ouW2/QgY1T8UKVUQihSYIFELMqV1VUswniB+Es9LDC0PyhSJDo2OsumgTn/zf/8iGTZed9edQxStGkCru/tbtfPqv/hjblDQ21EfViLNEqdofJ6hg1VyuiioFzNvWFSlS2V8hxOy2kJFEqaheVRXtOFvmNGZO/DqhusC1nlOLqrZFlAaiUFWShOo5JAorsQyYI5E+gTilIIxsDaUI5hGjHIQUiiUmMxlSjW3c+t7f5h3v+wCLOjrP8lM4Hq84QQB+cOe3+e4dX2P7lodprK+vlPAKLCmxDAPLnCOIWSVLRSWL7IwT1CpDzm2fqG6dZFsKgZyVKBIZceikAcrq550rUM/z9VYXr6p4mar7gjCSH7qiIoE+TjrMeqbmGeChUvNIMqeCzUqSWcM8MrqDMCp28sOILNPZHNl8nnRjK29+9/t59+99mJbW1l/lY3nReFUQBKBUKvHxP/4wjz7wE7ITo7Q01JNMxnEtK4qZVIz541SveYFGoNIzuLLwqRjuUgBirmfXvPOpBCarmB9fmb8tBcfNs3s+flSJc0rHQPVpC07aem3+l3HiHVT1hBMOqMqCZd5in71fZYdS1Tf+8ZdXPLJzNgRR6gfM2RPV43pWlaocr3qrKttVsvlhlTiVfVrP2hqRxIjsjJIfMDE5RbqxlRve+k7e9TsfoqOz6+TP7RXCq4YgVWzf+iRHup/lrm9+lQO7d+KYksb62nmGu6yQJZIUVsXLBVS2owVQlSJVVWp2sRvzSSBnPV+GjLKJNRE5jJMQZe5B6dkEwflkOJEU87hQSSxklsDPd371XPRzuTD/zVw9zrxzqgZxlTC6coe548erPHre3zFfSlRJoBGzxjUVV2z1eDX4FyUOVmIcYZR6GTyHIFFwMIpthJTDkPGJaUpBSPvSVXzpju/QuWQZr0a86ghSRblc4od3fps77/g6+3duJek61NXWRGW8xpynyzYNqi/3qjdrvifLntft0Zqneh2nVhnyBNKcXMUSzKXjvxg7ZT5xXkgrq9pCQghkZUZN1UN0MtfBLBGY8zCdiGghV4lywvXMvfXn3/NkalNVrYI56RDMLv65awKlUOq5BJnzUoVMTGeYKZRYffGlvON9v8tb3vVeHOfVWxv/qiVIFfl8jvvv+SH/9n+/xLM7n6I2FSeViGNbVmTQV4gCVHK4jieINStJ5vZVPV9CCAwxpxpJEZFFa2aDkjBHlqoUOBHVN30kveYkzslIcfy5Udbu851bPT/yElVUHE6ies07fqLUmX+9Osk3XbVDjrMb5gf8KiSsGt3VRR+eQJBZV66q/l9XbBgoBQEz+TyZbJ4V6zfyng9+hBvf9GYSiReeU/5K41VPkCp83+fe7/0HX//S5zm6fw8xy6S+tmY20AgV22IeQQQCy4xcvbNBRaErhKrGWOZUqapaFQUd5yRGVZKc7EHNkoeTqUx63nkRI4x5UuX4c6v/inkZAJr5cuo4r9I8BWu+ijXfFpj/O8LxQb0ToZgX8KsSQ1fcuECgQrQWswu/2lmkKiGUnrNHIpdwdI9sNkvJD+lctYb3ffhPuPlt78Qyz52irnOGIFWUiiXu+vY3ueuOr/Hs0zuJOxa1qQTxWGzOdYuYJUT15yxp5Mm9WWbFI2bMkzRyHmnguYu6Kq1myfM8DJrvdj4VqlJNiqpU0C+gPp3keIVd4TxxcSpPVlU9qp5XfetHaSHz1SeNVvo5EqRavKTmE0drMtks5bLPyvUX8Zbbfoe3vvv9uO7ZHd13JnDOEaSKTCbDfd//Lt//zreYGOpnpO8Y9fV1uLZdeevPkUJW9HvTMCpv/DkVyzSOJ8ic9GF2pIPk5C7fEyGqcZaT7D/l/4nsjpO5j09mJ8xuz/7DcWrSiaimgJwMzzXOq8mFFYJU4h1VNcoPQ2DOBlFqfi6Vouz5FAoFlq1ey3s/+Ifc8Ka3kj6DTRTONs5ZgszH/md28x93fJ0f3/X/MT05Rl1dHbZlzSU4CnFcftZxBJm1X6LiVSnnCGIakXpmzYu2P9/DMk6QNifD/M8+GearVSd6qKqYv4ife72uGNTHfyZEQb5QPfcaAfizsY1KswRVsVd0FNCbVZsqP6t5VmElFd0LQiYmJyl5IYlUijfc+lY+84V/OSclxon4tSBIFYe6D/DNf/0SP/qPb5PPZrBMSTpdE8VNhJxd/PMlizFrg8w1jTCrRKpIENMQJ327V/FiRj7MqX2nTmeRQsy6m6sxiBOhTiER5qeBHIdKLOJkmFOX1GzsI5yXYxUZ63OR8pLnMzOTw1chGomdSPL2d9+G5wXc+s53sfmqq0/9MM4h/FoRpIoD+/fyz5//B452H2D7k4+jwxDHNkjEE1GHFdvEqahiJ9ookrkYilnt3TVv38lgGfLk7q15mE/G58N8mwgi1UidJhHm50zNx/ORqmp0R/XhVYLMtdtRWpMvllBKky8WmcmVSNXVsPGyzRTKPh/8yJ/QtWQpqy9cc+oHcI7i15Ig8/G9u+7EK5UIvDL/8oXP4ZdLTE+MMZOdIRGLYisSsCqN7WRFkhjzpA2cenqWEFF3lucXI3P5YaeiSFXCVb+QqspzIiKPUxTIO+5TdGQwPx9BlJrtoXK8Z2u+wa00XhAQKs3UdIay79Pe0Umu6PHGt76Ntes30Ny2gOuuv/EUf8mvD37tCTIf+VwOpRT3/ej77Ni6lezUJPd+/y5ijoMOAwyhicVixGMxDMlsqr2Uz9+KaL7naX7E+jnnUHHxnkIXq6p3VVTf6Cei6kKdb5RXXcMnCw5qQKtIZarur8ZMoviJIJcvkC8WIwvIMCmUy9x4y1voWLKUD37kT3DcGLW1tad4ur+e+I0iyMmwc/s2TMPki//wWcaG+hkeHKB7/yFScYHruMRdF9MQOI5zXMrKies8cjFH2cQn2itzAcTnT3SsuoznG/DVQN18VGMhSh8fQdea50iPubSTasQdENF9Pd8nDBVl32NyKs/yVStoWdBOU1s7f/TnHyMIQi7aeMnpPs5fO/zGE+REPLt/H09seYxk3OHRXzzEg/ffT8wxGezrxZSCdDqNbdvMBvEqwT8xTzoY80hUXe/zc7cEzEuqnCNENcJerW+ZbzNoKqSoeLCqeVazDREqRKgmJVYzbgEKxSKFQqFi00AYQvvCVhSSFWvWccutb+eyq65ixcpVv6rHes7iPEFeAFNTU2Smp/jql7+IIeCn993D0cNHcF17Xo6VQAU+SunjpMT8REZDChKJBFJGzQbkCSSq5mFFd4swt/DnqURKkc/nZtM65qeISEMiK80M/ECBgELR59LLNnHJ5VfMXl8slnnvB36bpctXEE8msa1zax7h2cR5gpwmjvX0MDY6gnXcotL83y9/iUMHuom5NkLOLf5qgRYatj62hUymgGUymyiJgKoTTAhBMhHHkJJSuUzZ8ypeJSrRcZAGbL76GmynMua64s3KFspc85qrufVt74h+o8rX6vkBS5cupaHxzPet/U3AeYKcRdx3z48YGxnBtq3jVK+q5FBa8eXPf46BoRFuvvkmrrrmWqCiLqEJwxDTcnjnu99zXH3KefzqcJ4grzLk83lKnkfDGZiOdB4vH+cJch7ncQqcl9PncR6nwHmCnMd5nALnCXIe53EKnCfIeZzHKfD/A+2yBpWqMFMoAAAAAElFTkSuQmCC\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44961,"title":"RSA decryption","description":"Decrypt a large integer string using RSA decryption given the public key (n) and private key (d). Convert the large integer decryption into an output message string with UTF-8 representation.\r\n\r\nExample:\r\n\r\n encrypted_message = '158037161019988039882393476857386648994978438821991287680442802412825849535544067751541256843540494019';%input\r\nn='418336393847020647250825879743341651032293545176800777981294580200903315345456262337972725306797613061';%input\r\nd='8444986024072025211908427894173383040354675378319105204646840203847580180874615752845913488969020869';%input\r\ndecrypted_message = 'I like to swim!';%output\r\n\r\n\r\n","description_html":"\u003cp\u003eDecrypt a large integer string using RSA decryption given the public key (n) and private key (d). Convert the large integer decryption into an output message string with UTF-8 representation.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e encrypted_message = '158037161019988039882393476857386648994978438821991287680442802412825849535544067751541256843540494019';%input\r\nn='418336393847020647250825879743341651032293545176800777981294580200903315345456262337972725306797613061';%input\r\nd='8444986024072025211908427894173383040354675378319105204646840203847580180874615752845913488969020869';%input\r\ndecrypted_message = 'I like to swim!';%output\u003c/pre\u003e","function_template":"function decrypted_message = RSA_Decrypt(encrypted_message,d,n)\r\n  decrypted_message = 'I like to swim!';\r\nend","test_suite":"%%\r\nm='158037161019988039882393476857386648994978438821991287680442802412825849535544067751541256843540494019';\r\nn='418336393847020647250825879743341651032293545176800777981294580200903315345456262337972725306797613061';\r\nd='8444986024072025211908427894173383040354675378319105204646840203847580180874615752845913488969020869';\r\nmessage = 'I like to swim!';\r\nassert(isequal(RSA_Decrypt(m,d,n),message))\r\n%%\r\nm='99761240327251194937668282784881225946299704960682605372368300120848092908591455333889649815054891832920433772438140697229743047905660648016064750862552787515723449901585029566883857331537912668878918706229773460108043130645834201085405226084010413433457258525704626839479467337463012332940952234541291286602023412313079939518264986360860440514106228995186076871512459300140814669747884371890194124';\r\nn='2044371069952561243871813747701535503388267616657953475148898181142012590397809234167373308955772082860082985954286137615597515257087506574051530104475374974920093127841789408014496870693507622812332673504654584870100580476794800708440785082437228308551107726064054828640053321250498545183042994878498928173976370185712833904492317580152665428272199317847097773542066059565512439224992672101163367819';\r\nd='131358569595346680469722564224349085322306406056832660693226883146757023027681686453130430199929142940992255578581548217026735077095312421736286269892515739496597527524021166625708322359741224036234988705082882699895245449017415856831226734459122764117157172961113990706104659539690141481103935528273973382371183154438463086325519326121228923730136467766036183357672350586091588640276470994058874793';\r\nmessage = 'First, have a definite, clear practical ideal; a goal, an objective. Second, have the necessary means to achieve your ends; wisdom, money, materials, and methods.';\r\nout=RSA_Decrypt(m,n,d);\r\nassert(isequal(RSA_Decrypt(m,d,n),message))\r\n%%\r\nm='23055330962704323769878549529115024711681463755869375992447358448257597289666397997393945478297323372847937346015110864832142828615195632399869833059964395947034849804307978652470092440225822549097020437344501330227622390881049097656181781980124142659454562923055085607225529541369345564097544873012395850084756321027482195140106724706102857159831541577386517426252851135917933602432485339455137853480425755360413522537180403768732770990453717801905433194599201771294559164174484366213507079896512750859909040228686293902666244968559905065091421969981123917913807285202549025830873320919273470513619143052127674709353494599047667391749001044180280253098309127910967801244777547067797257847396027373615105278074126621948502699483945442597921239032762535839481741386676784123570880434889025648597593711911259097408384527597630246903648267481820555872340696607290773027177673329986283293168575528258578575033034179306629426942699054620008867304832513427178319015491321861291086200676826846740503213061372327825278234127270730394825241275398344604061667061892125034848354745243512927194104643800196788262228848172689053393410972717679060779374106225778531311917434399927265718394014531619654762559111657295163989321031700962115070401533540746801357628868609255941469541707984326602981168016264720519340003693219403163278843126513912057794102645161814569893320900148891952732032827189210372803453777673309727629845360314416264926243414888253428149538146304399700653423118791724424837155323935319171814705469113037576054893140065594406360362408167462563925199225169055130480445976569760198217276692195730775524801021060293503580957364539210146595506177369243830063105693396808209631409860229448190041996912370291877581261016834769083953407597967437841733812344230896457097759403613339974363380556576775192238298546579676296359906794868505900966056565863994904406875527092603782089107591766239203672780399852597928423220774857864301715176837587724591257928112610743311445186658958007825888475800717425136849205837547536117562642680';\r\nn='44842008376687803367401704855862174057751658874412319214254366772513580664834338103711248053800336314605433363839051280089244765499067546768593375603554906634041005882836398715141891796137918851678901692978242458027064144613729242304549721699241688731628849316717564354846304644497408201649639245333007226999680183209765262168096747256549932760714835163829498814356014506466022681051474161134416048209239076204778228261950266231966892099194904195589855692846886804440024833800891898474520523721428667143505915995217245366095168045283186412220277535584022415882288464175935131208288146822299727657938865855853054174274144036081729604573534323903573564345990066095029031133576597298513883268061041004553754062342541175017746399640362184228727837219293246060058323563065371426108553463224921179093569734439828568435658070810483844709529476015493154462587917722806971578721201741643550136095893915598053953011321347017522943202801820158823344592288227452688958887872572522782675644714289349442555731461112275849176682816627205790162163242534462778708459909915826953853537650009043468930450287584181263070727575137424307931682948818963610116434419852585517456098152109913486868606969385133300794635427715727859479612757775192862801547635779921771426233897718528292667112148507798722127322607462037572360649156150337532940752245966765201596748120586383127825681873289878451591957019880886587602576426267683951317718936847177641679183717321862429721190212389237395890951104472937261743929446841800523276218816808066432194473964294708564511969507018959711475230849760902049071415838600456901108854663197095849833602808088094456341330276320302662577163562657750920481798540333412112880539002713127873625438212479154166226846436038698572615482646490520911334607730484144343834476612603467400722323562384577281087071440008144012534847478593412147312743274523095010025887231371129897419306984829625295595332434377173711414555784685658774002600022998291909172576630780759729269867715816511099791566815282862210319017784751883446582453959';\r\nd='6565816445407878925089441991498747612160839198603241148969054176252198301108538816900577327681584864655900309129187116952811278662878254707896639032786256375181309679291058212467790617143590175026484896254317631677185521639888090836542092702228103896557828982761215001435908561096741216458335569193212038242350596427680660630865867932219252556141104387324837429582683296520255026128293117631961432452139374326884841820676484348718346835892309697741432400454075190738155214690226263908349465883864526754491093121291860880617807231984031261908018115438062149668224668541927056762969514272957080528641551440449912383177971011340773567381595669197227397095749281691989236351340479846140946699426488082757798251098448588056674770754671643802109836061405587518383808732642252532232749119323532411226969424472963287039513173436339822906642733903667734412972727748722945805719038892729473535651253460092450459024621811281873600606895132005494130257832946742084673535377347237875132451694131873556170785954511701761479583203082125987308962572083138475191433479413530168163642321800669575367485309537509082240852273955663933547032858727060003363699057579114677450927657082252183166216411898446363400905797006665507108575986344278988745322935954278566001664060256959781130851422164231215979527541890717097899466088129536122753240075629363188908753526503257284825826946057815889269456925910606842810401392503996936381736547569711529540423604489529836981870198914784848089842823822656591932437295439032050213520000125621624734133380868707883468507784350355251698659006842220673722867592264770652693364873913361956132623339827358272992906883218249723187904101702943978747751691915678242891407493339828656260188711974558580485287404900248093520605466868886511014909072710668999090169680693653605673085931199903788603401848851956524927526592113342563256817891019122155938256416456381627581783190684277329685396205824988569434587069719626936811661218907123975873968219302538615272967013401476757929690613750478379916399826582503908605565505';\r\nmessage = 'People who succeed have momentum. The more they succeed, the more they want to succeed and the more they find a way to succeed. Similarly, when someone is failing, the tendency is to get on a downward spiral that can even become a self-fulfilling prophecy.';\r\nout=RSA_Decrypt(m,n,d);\r\nassert(isequal(RSA_Decrypt(m,d,n),message))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2019-09-08T23:48:25.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-08-29T18:26:28.000Z","updated_at":"2026-07-16T15:42:37.000Z","published_at":"2019-09-05T14:41:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDecrypt a large integer string using RSA decryption given the public key (n) and private key (d). Convert the large integer decryption into an output message string with UTF-8 representation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ encrypted_message = '158037161019988039882393476857386648994978438821991287680442802412825849535544067751541256843540494019';%input\\nn='418336393847020647250825879743341651032293545176800777981294580200903315345456262337972725306797613061';%input\\nd='8444986024072025211908427894173383040354675378319105204646840203847580180874615752845913488969020869';%input\\ndecrypted_message = 'I like to swim!';%output]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":57517,"title":"Easy Sequences 90: Triple Summation of a Combinatorial Function","description":"Given a positive integer , we are asked to evaluate the following triple summation:\r\n                \r\nThe symbol  is the combination function, nchoosek in Matlab. Therefore, we can write the function in Matlab as follows:\r\n    \u003e\u003e S = @(x) sum(arrayfun(@(y) sum(arrayfun(@(n) sum(arrayfun(@(k) ((-4)^k*nchoosek(n,k)/nchoosek(2*k,k)),0:n)),0:y)),0:x));\r\nHence, for , we have:\r\n    \u003e\u003e S(5)\r\n    \u003e\u003e ans =\r\n       -1.3302\r\nPlease round-off the output to the nearest 4 decimal places.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 313px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 563.71875px 156.5px; transform-origin: 563.71875px 156.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a positive integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, we are asked to evaluate the following triple summation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 57px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 28.5px; text-align: left; transform-origin: 384px 28.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-25px\"\u003e\u003cimg 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\" width=\"169\" height=\"57\" style=\"width: 169px; height: 57px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 55px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 27.5px; text-align: left; transform-origin: 384px 27.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe symbol \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-14px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"28.5\" height=\"34\" style=\"width: 28.5px; height: 34px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is the combination function, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003enchoosek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e in Matlab. Therefore, we can write the function in Matlab as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 560.71875px 10px; transform-origin: 560.71875px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; S = @(x) sum(arrayfun(@(y) sum(arrayfun(@(n) sum(arrayfun(@(k) ((-4)^k*nchoosek(n,k)/nchoosek(2*k,k)),0:n)),0:y)),0:x));\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHence, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 60px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 560.71875px 30px; transform-origin: 560.71875px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 560.71875px 10px; transform-origin: 560.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; S(5)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 560.71875px 10px; transform-origin: 560.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; ans =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 560.71875px 10px; transform-origin: 560.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e       -1.3302\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ePlease round-off the output to the nearest 4 decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = S(x)\r\n    s = sum(arrayfun(@(y) sum(arrayfun(@(n) sum(arrayfun(@(k) ((-4)^k*nchoosek(n,k)/nchoosek(2*k,k)),0:n)),0:y)),0:x));\r\nend","test_suite":"%%\r\nx = 1:20;\r\ns_correct = [1.0000 0.6667 0.1333 -0.5429 -1.3302 -2.2084 -3.1635 -4.1853 -5.2659 -6.3992 -7.5801 -8.8044 -10.0688 -11.3702 -12.706 -14.0742 -15.4726 -16.8996 -18.3536 -19.8333];\r\nassert(isequal(arrayfun(@S,x),s_correct))\r\n%%\r\nx = 25;\r\ns_correct = -27.5763;\r\nassert(isequal(S(x),s_correct))\r\n%%\r\nx = 50;\r\ns_correct = -72.3576;\r\nassert(isequal(S(x),s_correct))\r\n%%\r\nx = 100;\r\ns_correct = -179.0764;\r\nassert(isequal(S(x),s_correct))\r\n%%\r\nx = 1000;\r\ns_correct = -2936.8505;\r\nassert(isequal(S(x),s_correct))\r\n%%\r\nx = 10000;\r\ns_correct = -40871.0455;\r\nassert(isequal(S(x),s_correct))\r\n%%\r\nx = 100000;\r\ns_correct = -523824.1437;\r\nassert(isequal(S(x),s_correct))\r\n%%\r\nx = 1000000;\r\ns_correct = -6389513.2367;\r\nassert(isequal(S(x),s_correct))\r\n%%\r\nxs = 1000001:2000000;\r\ns = arrayfun(@(x) S(x),xs);\r\nss_correct = [-9902420 -9888371 -13472171 2045750];\r\nassert(isequal(floor([mean(s) median(s) mode(s) std(s)]),ss_correct))\r\n%%\r\nfiletext = fileread('S.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'java') || contains(filetext, 'py') || contains(filetext, 'regexp') || contains(filetext, 'eval') || contains(filetext, 'assignin');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-01-07T10:58:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-07T09:14:32.000Z","updated_at":"2026-08-01T15:00:25.000Z","published_at":"2023-01-07T10:58:56.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a positive integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, we are asked to evaluate the following triple summation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS(x) = \\\\sum_{y=0}^{x} \\\\sum_{n=0}^{y} \\\\sum_{k=0}^n \\\\frac_{(-4)^{k} {n \\\\choose k}}^{2k \\\\choose k}.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe symbol \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \\\\choose k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the combination function, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enchoosek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e in Matlab. Therefore, we can write the function in Matlab as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    \u003e\u003e S = @(x) sum(arrayfun(@(y) sum(arrayfun(@(n) sum(arrayfun(@(k) ((-4)^k*nchoosek(n,k)/nchoosek(2*k,k)),0:n)),0:y)),0:x));]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHence, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex=5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    \u003e\u003e S(5)\\n    \u003e\u003e ans =\\n       -1.3302]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePlease round-off the output to the nearest 4 decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45355,"title":"Connect Four - 03","description":"Previous Problem \u003chttps://www.mathworks.com/matlabcentral/cody/problems/45354-connect-four-01\u003e\r\n       \u003chttps://www.mathworks.com/matlabcentral/cody/problems/45356-connect-four-02\u003e\r\n\r\nIn addition to previous problem\r\n\r\n In this case, there can be empty places on the board represented by 0.\r\n \r\n Also no of consecutive elements can be more than 4.\r\n\r\n\r\n","description_html":"\u003cp\u003ePrevious Problem \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/45354-connect-four-01\"\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/45354-connect-four-01\u003c/a\u003e\r\n       \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/45356-connect-four-02\"\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/45356-connect-four-02\u003c/a\u003e\u003c/p\u003e\u003cp\u003eIn addition to previous problem\u003c/p\u003e\u003cpre\u003e In this case, there can be empty places on the board represented by 0.\u003c/pre\u003e\u003cpre\u003e Also no of consecutive elements can be more than 4.\u003c/pre\u003e","function_template":"function y = connect_four_2(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx =  [ 1 1 1 1 1 1 1 1;\r\n       2 2 2 2 2 2 2 2;\r\n       2 1 2 1 2 1 2 1;\r\n       1 2 1 2 1 2 1 2;\r\n       2 1 2 1 2 1 2 1;\r\n       1 2 1 2 1 2 1 1];\r\nassert(isequal(connect_four_2(x),2))\r\n%%\r\nx =  [ 1 1 1 1 1 1 1 1;\r\n       2 2 2 2 2 2 2 2;\r\n       2 1 2 1 0 1 2 1;\r\n       1 2 1 2 1 2 1 2;\r\n       2 1 2 1 2 1 2 1;\r\n       1 2 1 2 1 2 1 1];\r\nassert(isequal(connect_four_2(x),'invalid'))\r\n%%\r\nx =  [ 1 1 1 1 1 1 1 1 2;\r\n       2 2 2 2 2 2 2 2 1;\r\n       2 1 2 1 2 1 2 1 2;\r\n       1 2 1 2 1 2 1 2 2;\r\n       2 1 2 1 2 1 2 1 2;\r\n       1 2 1 2 1 2 1 1 2];\r\nassert(isequal(connect_four_2(x),2))\r\n%%\r\nx =  [1     1     1     1     1     1     1     1     2\r\n     2     2     2     2     2     2     2     2     1\r\n     2     1     2     1     2     1     2     1     2\r\n     1     2     1     2     1     2     1     2     2\r\n     2     1     2     1     2     1     2     1     2\r\n     1     2     1     1     1     2     1     1     2\r\n     1     1     1     1     1     1     1     1     1];\r\nassert(isequal(connect_four_2(x),0))\r\n%%\r\nx = [2     2     1     1     2     1     2     1\r\n     1     2     2     1     1     1     1     2\r\n     1     2     1     1     1     2     2     2\r\n     2     1     2     2     2     1     1     2\r\n     1     1     2     1     2     1     2     2\r\n     2     1     1     2     2     2     2     1\r\n     1     1     2     1     2     1     2     1\r\n     1     2     1     1     1     1     2     1];\r\nassert(isequal(connect_four_2(x),0))\r\n\r\n%%\r\nx = [2     2     1     1     2     1     2     1\r\n     1     2     2     1     1     1     1     2\r\n     1     2     1     1     1     2     2     2\r\n     2     1     2     2     2     1     1     2\r\n     1     1     2     1     2     1     2     2\r\n     2     1     1     2     2     2     2     1\r\n     1     1     2     1     2     1     2     1\r\n     1     2     1     1     1     1     2     1\r\n     1     1     1     1     1     1     1     1];\r\nassert(isequal(connect_four_2(x),1))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-02-22T21:18:15.000Z","updated_at":"2026-07-29T13:51:35.000Z","published_at":"2020-02-23T06:10:14.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrevious Problem\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45354-connect-four-01\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/45354-connect-four-01\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt; \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45356-connect-four-02\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/45356-connect-four-02\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn addition to previous problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ In this case, there can be empty places on the board represented by 0.\\n\\n Also no of consecutive elements can be more than 4.]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45366,"title":"Connect Four - 04","description":"Previous Problem\r\n\r\n\u003chttps://www.mathworks.com/matlabcentral/cody/problems/45355-connect-four-03\u003e\r\n\r\n\r\nIn addition to the previous problem, in this case\r\n\r\n a 2 by 2 block will also be considered as a winning move.\r\n\r\nFor example,\r\n\r\n  x=[ 1 1 2 1 2\r\n      1 1 2 2 1\r\n      2 1 2 2 1\r\n      2 2 1 1 2]\r\n\r\nhere, there is a 2-by-2 block of 1 and 2. \r\n  ","description_html":"\u003cp\u003ePrevious Problem\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/45355-connect-four-03\"\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/45355-connect-four-03\u003c/a\u003e\u003c/p\u003e\u003cp\u003eIn addition to the previous problem, in this case\u003c/p\u003e\u003cpre\u003e a 2 by 2 block will also be considered as a winning move.\u003c/pre\u003e\u003cp\u003eFor example,\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ex=[ 1 1 2 1 2\r\n    1 1 2 2 1\r\n    2 1 2 2 1\r\n    2 2 1 1 2]\r\n\u003c/pre\u003e\u003cp\u003ehere, there is a 2-by-2 block of 1 and 2.\u003c/p\u003e","function_template":"function win=connect_four_4(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx=  [1     1     2     1     2\r\n     1     1     2     2     1\r\n     2     1     2     2     1\r\n     2     2     1     1     2]\r\nassert(isequal(connect_four_4(x),2))\r\n%%\r\nx =  [ 1 1 1 1 1 1 1 1;\r\n       2 2 2 2 2 2 2 2;\r\n       2 1 2 1 0 1 2 1;\r\n       1 2 1 2 1 2 1 2;\r\n       2 1 2 1 2 1 2 1;\r\n       1 2 1 2 1 2 1 1];\r\nassert(isequal(connect_four_4(x),'invalid'))\r\n%%\r\nx =  [ 1 1 1 1 1 1 1 1;\r\n       2 2 2 2 2 2 2 2;\r\n       2 1 2 1 2 1 2 1;\r\n       1 2 1 2 1 2 1 2;\r\n       2 1 2 1 2 1 2 1;\r\n       1 2 1 2 1 2 1 1];\r\nassert(isequal(connect_four_4(x),2))\r\n %%\r\n x =  [1     1     1     1     1     1     1     1     2\r\n     2     2     2     2     2     2     2     2     1\r\n     2     1     2     1     2     1     2     1     2\r\n     1     2     1     2     1     2     1     2     2\r\n     2     1     2     1     2     1     2     1     2\r\n     1     2     1     1     1     2     1     1     2\r\n     1     1     1     1     1     1     1     1     1];\r\n assert(isequal(connect_four_4(x),1))\r\n %%\r\n x = [2     2     1     1     2     1     2     1\r\n     1     2     2     1     1     1     1     2\r\n     1     2     1     1     1     2     2     2\r\n     2     1     2     2     2     1     1     2\r\n     1     1     2     1     2     1     2     2\r\n     2     1     1     2     2     2     2     1\r\n     1     1     2     1     2     1     2     1\r\n     1     2     1     1     1     1     2     1]\r\n assert(isequal(connect_four_4(x),1))\r\n %%\r\n x = [2     2     1     1     2     1     2     1\r\n     1     2     2     2     1     1     1     2\r\n     1     2     1     1     1     2     2     2\r\n     2     1     2     2     2     1     1     2\r\n     1     1     2     1     2     1     2     2\r\n     2     1     1     2     2     2     2     1\r\n     1     1     2     1     2     1     2     1\r\n     1     2     1     1     1     1     2     1]\r\nassert(isequal(connect_four_4(x),2))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2020-03-16T18:43:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-03-16T18:31:40.000Z","updated_at":"2026-07-29T14:01:01.000Z","published_at":"2020-03-16T18:43:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrevious Problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45355-connect-four-03\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/45355-connect-four-03\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn addition to the previous problem, in this case\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ a 2 by 2 block will also be considered as a winning move.]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x=[ 1 1 2 1 2\\n    1 1 2 2 1\\n    2 1 2 2 1\\n    2 2 1 1 2]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ehere, there is a 2-by-2 block of 1 and 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1907,"title":"Capture the flag(s)","description":"Flags are distributed randomly on a large board. Starting from the corner position your goal is to capture as many flags as possible in at most N moves.\r\nDescription:\r\nThe board is described by a matrix B with 1's at the flag positions, and 0's otherwise.\r\nE.g.\r\n B = [0 0 1 1; \r\n      0 0 1 1;\r\n      0 0 1 0];\r\n\r\n N = 6;\r\nYou are starting at the top-left corner (row=1, col=1) and are allowed N steps (steps are up/down/left/right movements, no diagonal movements allowed).\r\nReturn a trajectory attempting to maximize the number of flags captured. The output of your function should be a Nx2 matrix of the form [row, col] (not including the initial [1,1] position) visiting as many flags as possible.\r\nE.g.\r\n path = [1 2;\r\n         1 3;\r\n         1 4;\r\n         2 4;\r\n         2 3;\r\n         3 3];\r\nThis solution captures all 5 flags on the board.\r\nScoring:\r\nYour function will receive a score equal to the number of non-visited flags across all 50 of the testsuite problems. You need to leave at most 10,000 flags univisited (among 50,000 total flags) to pass this problem.\r\nNote:\r\nThe boards and number of movements allowed will be large. Optimizing over all possible trajectories is very likely to time out.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 676px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 338px; transform-origin: 401px 338px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 21px; text-align: left; transform-origin: 377px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFlags are distributed randomly on a large board. Starting from the corner position your goal is to capture as many flags as possible in at most N moves.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDescription\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe board is described by a matrix\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eB\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with 1's at the flag positions, and 0's otherwise.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eE.g.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 90px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 397px 45px; transform-origin: 397px 45px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); 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text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e B = [0 0 1 1; \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e      0 0 1 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e      0 0 1 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e N = 6;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 21px; text-align: left; transform-origin: 377px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are starting at the top-left corner (row=1, col=1) and are allowed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e steps (steps are up/down/left/right movements, no diagonal movements allowed).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 21px; text-align: left; transform-origin: 377px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn a trajectory attempting to maximize the number of flags captured. The output of your function should be a\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eNx2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix of the form\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[row, col]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (not including the initial [1,1] position) visiting as many flags as possible.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eE.g.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 108px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 397px 54px; transform-origin: 397px 54px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e path = [1 2;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e         1 3;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e         1 4;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e         2 4;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e         2 3;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e         3 3];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis solution captures all 5 flags on the board.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eScoring\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 21px; text-align: left; transform-origin: 377px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour function will receive a score equal to the number of non-visited flags across all 50 of the testsuite problems. You need to leave at most 10,000 flags univisited (among 50,000 total flags) to pass this problem.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNote\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 21px; text-align: left; transform-origin: 377px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe boards and number of movements allowed will be large. Optimizing over all possible trajectories is very likely to time out.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function path = capture_the_flag(B,N)\r\npath=[1 2];\r\n","test_suite":"%%\r\n% test cases\r\n\r\nrandn('seed',0);\r\nrand('seed',0);\r\nN=randi([1000 4000],50,1);\r\nS=randi([1,50],50,1);\r\nBoards=arrayfun(@(s)convn(randn(100),ones(s)/s^2,'same'),S,'uni',0); \r\n\r\nFLAGSLEFT=0;\r\nDOPLOT=false;\r\ntic;\r\nfor board=1:50\r\n B=Boards{board};\r\n sB=sort(B(:));\r\n B=double(B\u003esB(round(numel(sB)*.9)));\r\n n=N(board);\r\n path=capture_the_flag(B,n);\r\n assert(size(path,1)\u003c=n,'too many steps');\r\n assert(all(sum(abs(diff([1,1;path])),2)\u003c=1),'no jumping allowed');\r\n if DOPLOT\r\n    imagesc(B);\r\n    hold on;\r\n    plot(path(:,2),path(:,1),'y-');\r\n    hold off;\r\n    axis equal;\r\n    axis off;\r\n    set(gcf,'color',0*[1 1 1]);\r\n    colormap(.5*gray);\r\n    drawnow;\r\n end\r\n B(1)=0;\r\n B((path-1)*[1;size(B,1)]+1)=0;\r\n fprintf('test %d; left %d flags\\n',board,nnz(B));\r\n FLAGSLEFT=FLAGSLEFT+nnz(B);\r\nend\r\ntoc;","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":43,"edited_by":1,"edited_at":"2026-02-11T16:03:17.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2026-02-11T16:03:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-10-01T05:38:22.000Z","updated_at":"2026-07-28T14:22:02.000Z","published_at":"2013-10-01T06:27:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFlags are distributed randomly on a large board. Starting from the corner position your goal is to capture as many flags as possible in at most N moves.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDescription\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe board is described by a matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with 1's at the flag positions, and 0's otherwise.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eE.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ B = [0 0 1 1; \\n      0 0 1 1;\\n      0 0 1 0];\\n\\n N = 6;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are starting at the top-left corner (row=1, col=1) and are allowed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e steps (steps are up/down/left/right movements, no diagonal movements allowed).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn a trajectory attempting to maximize the number of flags captured. The output of your function should be a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNx2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix of the form\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[row, col]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (not including the initial [1,1] position) visiting as many flags as possible.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eE.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ path = [1 2;\\n         1 3;\\n         1 4;\\n         2 4;\\n         2 3;\\n         3 3];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis solution captures all 5 flags on the board.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour function will receive a score equal to the number of non-visited flags across all 50 of the testsuite problems. You need to leave at most 10,000 flags univisited (among 50,000 total flags) to pass this problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNote\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe boards and number of movements allowed will be large. Optimizing over all possible trajectories is very likely to time out.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42829,"title":"Number construction III","description":"Given a positive integer, n, return a, b and c, such that\r\n\r\n1. n = a^1.5+b^2.5+c^3.5\r\n\r\n2. a, b and c are all positive integers greater than 1\r\n\r\nIf a solution does not exist, set all three output variables to zero.\r\n\r\nExample 1:\r\n\r\nn = 168\r\n\r\na = 4\r\n\r\nb = 4\r\n\r\nc = 4\r\n\r\nExample 2:\r\n\r\nn = 100\r\n\r\na = 0\r\n\r\nb = 0\r\n\r\nc = 0","description_html":"\u003cp\u003eGiven a positive integer, n, return a, b and c, such that\u003c/p\u003e\u003cp\u003e1. n = a^1.5+b^2.5+c^3.5\u003c/p\u003e\u003cp\u003e2. a, b and c are all positive integers greater than 1\u003c/p\u003e\u003cp\u003eIf a solution does not exist, set all three output variables to zero.\u003c/p\u003e\u003cp\u003eExample 1:\u003c/p\u003e\u003cp\u003en = 168\u003c/p\u003e\u003cp\u003ea = 4\u003c/p\u003e\u003cp\u003eb = 4\u003c/p\u003e\u003cp\u003ec = 4\u003c/p\u003e\u003cp\u003eExample 2:\u003c/p\u003e\u003cp\u003en = 100\u003c/p\u003e\u003cp\u003ea = 0\u003c/p\u003e\u003cp\u003eb = 0\u003c/p\u003e\u003cp\u003ec = 0\u003c/p\u003e","function_template":"function [a b c] = numcons(n)\r\n  a = n;\r\n  b = n;\r\n  c = n;\r\nend","test_suite":"%%\r\nn = 100;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 888;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 19666;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 314159;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 1100;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 116600;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 16999;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 10000040;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 94940;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 9990;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":"2016-04-28T18:19:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-04-25T11:29:04.000Z","updated_at":"2026-08-04T19:45:23.000Z","published_at":"2016-04-25T11:29:04.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a positive integer, n, return a, b and c, such that\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1. n = a^1.5+b^2.5+c^3.5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2. a, b and c are all positive integers greater than 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf a solution does not exist, set all three output variables to zero.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 168\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eb = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eb = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1533,"title":"Criss-Cross Verification: NHL","description":"This Challenge is to verify a Criss-Cross matrix has no invalid words,contains all of the word set, and all are simply connected (Up/Down/Left/Right). Separation, UDLR, must exist between non-intersecting words. Diagonal is considered separate.\r\n\r\nThe word set is a cell array. The matrix is an array of Char with spaces being represented by '`', char(96), which is under the tilde on my keyboard.\r\n\r\n*Example:*\r\n\r\n*Input:*\r\n\r\n  dict={'abcd' 'cag'}\r\n  \r\n  Achar=['abcd'\r\n         '``a`'\r\n         '``g`'];\r\n\r\n*Output:* Validity (1 for Valid, 0 for Invalid)\r\n\r\n\r\n*Related Challenges:*\r\n\r\nThis Challenge is derived from GAMES August 2013 Contest \"On the Ice\" to fit all NHL Team names into a minimum area grid using the Criss-Cross rules.\r\nCurrent Best solution is 19x19, 6/3/2013. Contest ends 8/31/2013.\r\n\r\n1) Create an NHL Criss-Cross  (Score by Area)\r\n\r\n2) Complete a Criss-Cross\r\n\r\n3) Create a Criss-Cross dictionary from a matrix","description_html":"\u003cp\u003eThis Challenge is to verify a Criss-Cross matrix has no invalid words,contains all of the word set, and all are simply connected (Up/Down/Left/Right). Separation, UDLR, must exist between non-intersecting words. Diagonal is considered separate.\u003c/p\u003e\u003cp\u003eThe word set is a cell array. The matrix is an array of Char with spaces being represented by '`', char(96), which is under the tilde on my keyboard.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003edict={'abcd' 'cag'}\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eAchar=['abcd'\r\n       '``a`'\r\n       '``g`'];\r\n\u003c/pre\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e Validity (1 for Valid, 0 for Invalid)\u003c/p\u003e\u003cp\u003e\u003cb\u003eRelated Challenges:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eThis Challenge is derived from GAMES August 2013 Contest \"On the Ice\" to fit all NHL Team names into a minimum area grid using the Criss-Cross rules.\r\nCurrent Best solution is 19x19, 6/3/2013. Contest ends 8/31/2013.\u003c/p\u003e\u003cp\u003e1) Create an NHL Criss-Cross  (Score by Area)\u003c/p\u003e\u003cp\u003e2) Complete a Criss-Cross\u003c/p\u003e\u003cp\u003e3) Create a Criss-Cross dictionary from a matrix\u003c/p\u003e","function_template":"function valid=check_crisscross(Achar,dict_cell)\r\n valid=1;\r\nend","test_suite":"%%\r\ndict_cell={'abcd'\r\n'cat'\r\n'dot'};\r\n\r\nAchar=['abcd'\r\n'``a`'\r\n'dot`'];\r\n\r\nvalid=check_crisscross(Achar,dict_cell);\r\nassert(valid==1)\r\n%%\r\ndict_cell={'abcd'\r\n'cat'\r\n'dot'\r\n'bcd'};\r\n\r\nAchar=['abcd'\r\n'``a`'\r\n'dot`'];\r\n% Need a unique bcd word\r\nvalid=check_crisscross(Achar,dict_cell);\r\nassert(valid==0)\r\n%%\r\ndict_cell={'abcd'\r\n'cat'\r\n'dot'\r\n'acd'};\r\n\r\nAchar=['abcd'\r\n'c`a`'\r\n'dot`'];\r\n% valid matrix\r\nvalid=check_crisscross(Achar,dict_cell);\r\nassert(valid==1)\r\n%%\r\ndict_cell={'avalanche'\r\n'bluejackets'\r\n'blackhawks'\r\n'blues'\r\n'bruins'\r\n'canadiens'\r\n'canucks'\r\n'capitals'\r\n'coyotes'\r\n'devils'\r\n'ducks'\r\n'flames'\r\n'flyers'\r\n'hurricanes'\r\n'islanders'\r\n'jets'\r\n'kings'\r\n'lightning'\r\n'mapleleafs'\r\n'oilers'\r\n'panthers'\r\n'penguins'\r\n'predators'\r\n'rangers'\r\n'redwings'\r\n'sabres'\r\n'senators'\r\n'sharks'\r\n'stars'\r\n'wild'};\r\n\r\nAchar=['```````hurricanes``s'\r\n'rangers`````o````m`e'\r\n'e`````t```flyers`a`n'\r\n'd`````a`````o````p`a'\r\n'w`````r`capitals`l`t'\r\n'i`ducks`````e````e`o'\r\n'n```a``sabres````l`r'\r\n'g`kings``l````oilers'\r\n's```u``bruins````a``'\r\n'````c````e`````p`f``'\r\n'blackhawks``sharks``'\r\n'``v`s``````````e````'\r\n'``a````````i```d``p`'\r\n'`bluejackets```a``e`'\r\n'``a````````lightning'\r\n'canadiens``a```o``g`'\r\n'``c``````panthers`u`'\r\n'``h`w``````d```s``i`'\r\n'`devils```jets````n`'\r\n'````l``````r``````s`'\r\n'````d`flames````````'];\r\n\r\nvalid=check_crisscross(Achar,dict_cell);\r\nassert(valid==1)\r\n%%\r\ndict_cell={'avalanche'\r\n'bluejackets'\r\n'blackhawks'\r\n'blues'\r\n'bruins'\r\n'canadiens'\r\n'canucks'\r\n'capitals'\r\n'coyotes'\r\n'devils'\r\n'ducks'\r\n'flames'\r\n'flyers'\r\n'hurricanes'\r\n'islanders'\r\n'jets'\r\n'kings'\r\n'lightning'\r\n'mapleleafs'\r\n'oilers'\r\n'panthers'\r\n'penguins'\r\n'predators'\r\n'rangers'\r\n'redwings'\r\n'sabres'\r\n'senators'\r\n'sharks'\r\n'stars'\r\n'wild'};\r\n\r\nAchar=['```````hurricanes``s'\r\n'rangers`````o````m`e'\r\n'e`````t```flyers`a`n'\r\n'd`````a`````o````p`a'\r\n'w`````r`capitals`l`t'\r\n'i`ducks`````e````e`o'\r\n'n```a``sabres````l`r'\r\n'g`kings``l````oilers'\r\n's```u``bruins````a``'\r\n'````c````e`````p`f``'\r\n'blackhawks``sharks``'\r\n'``v`s``````````e````'\r\n'``a````````i```d``p`'\r\n'`bluejackets```a``e`'\r\n'``a````````lightning'\r\n'canadiens``a```o``g`'\r\n'``c``````panthers`u`'\r\n'``h`w``````d```s``i`'\r\n'`devils```jets````n`'\r\n'````l``````r```jets`'\r\n'````d`flames````````'];\r\n\r\n% jets is duplicated\r\n\r\nvalid=check_crisscross(Achar,dict_cell);\r\nassert(valid==0)\r\n%%\r\ndict_cell={'avalanche'\r\n'bluejackets'\r\n'blackhawks'\r\n'blues'\r\n'bruins'\r\n'canadiens'\r\n'canucks'\r\n'capitals'\r\n'coyotes'\r\n'devils'\r\n'ducks'\r\n'flames'\r\n'flyers'\r\n'hurricanes'\r\n'islanders'\r\n'jets'\r\n'kings'\r\n'lightning'\r\n'mapleleafs'\r\n'oilers'\r\n'panthers'\r\n'penguins'\r\n'predators'\r\n'rangers'\r\n'redwings'\r\n'sabres'\r\n'senators'\r\n'sharks'\r\n'stars'\r\n'wild'};\r\n\r\nAchar=['```````hurricanes``s'\r\n'rangers`````o````m`e'\r\n'e`````t```flyers`a`n'\r\n'd`````a`````o````p`a'\r\n'w`````r`capitals`l`t'\r\n'i`ducks`````e````e`o'\r\n'n```a``sabres````l`r'\r\n'g`kings``l````oilers'\r\n's```u``bruins````a``'\r\n'````c````e`````p`f``'\r\n'blackhawks``sharks``'\r\n'``v`s``````````e````'\r\n'``a````````i```d``p`'\r\n'`bluejackets```a``e`'\r\n'``a````````lightning'\r\n'canadiens``a```o``g`'\r\n'``c``````panthers`u`'\r\n'``h`w``````d```s``i`'\r\n'`devils````e``````n`'\r\n'````l``````r``````s`'\r\n'````d`flames``jets``'];\r\n\r\n% Non-Connected jets\r\n\r\nvalid=check_crisscross(Achar,dict_cell);\r\nassert(valid==0)\r\n%%\r\ndict_cell={'avalanche'\r\n'bluejackets'\r\n'blackhawks'\r\n'blues'\r\n'bruins'\r\n'canadiens'\r\n'canucks'\r\n'capitals'\r\n'coyotes'\r\n'devils'\r\n'ducks'\r\n'flames'\r\n'flyers'\r\n'hurricanes'\r\n'islanders'\r\n'jets'\r\n'kings'\r\n'lightning'\r\n'mapleleafs'\r\n'oilers'\r\n'panthers'\r\n'penguins'\r\n'predators'\r\n'rangers'\r\n'redwings'\r\n'sabres'\r\n'senators'\r\n'sharks'\r\n'stars'\r\n'wild'};\r\n\r\nAchar=['```````hurricanes``s'\r\n'rangers`````o````m`e'\r\n'e`````t```flyers`a`n'\r\n'd`````a`````o````p`a'\r\n'w`````r`capitals`l`t'\r\n'i`ducks`````e````e`o'\r\n'n```a``sabres````l`r'\r\n'g`kings``l````oilers'\r\n's```u``bruins````a``'\r\n'````c````e`````p`f``'\r\n'blackhawks``sharks``'\r\n'``v`s``````````e````'\r\n'``a````````i```d````'\r\n'`bluejackets```a````'\r\n'``a````````lightning'\r\n'canadiens``a```o````'\r\n'``c``````panthers```'\r\n'``h`w``````d```s````'\r\n'`devils```jets``````'\r\n'````l``````r````````'\r\n'````d`flames````````'];\r\n% Missing penguins\r\nvalid=check_crisscross(Achar,dict_cell);\r\nassert(valid==0)\r\n%%\r\ndict_cell={'avalanche'\r\n'bluejackets'\r\n'blackhawks'\r\n'blues'\r\n'bruins'\r\n'canadiens'\r\n'canucks'\r\n'capitals'\r\n'coyotes'\r\n'devils'\r\n'ducks'\r\n'flames'\r\n'flyers'\r\n'hurricanes'\r\n'islanders'\r\n'jets'\r\n'kings'\r\n'lightning'\r\n'mapleleafs'\r\n'oilers'\r\n'panthers'\r\n'penguins'\r\n'predators'\r\n'rangers'\r\n'redwings'\r\n'sabres'\r\n'senators'\r\n'sharks'\r\n'stars'\r\n'wild'};\r\n\r\nAchar=['```````hurricanes``s'\r\n'rangers`````o````m`e'\r\n'e```jets``flyers`a`n'\r\n'd`````a`````o````p`a'\r\n'w`````r`capitals`l`t'\r\n'i`ducks`````e````e`o'\r\n'n```a``sabres````l`r'\r\n'g`kings``l````oilers'\r\n's```u``bruins````a``'\r\n'````c````e`````p`f``'\r\n'blackhawks``sharks``'\r\n'``v`s``````````e````'\r\n'``a````````i```d``p`'\r\n'`bluejackets```a``e`'\r\n'``a````````lightning'\r\n'canadiens``a```o``g`'\r\n'``c``````panthers`u`'\r\n'``h`w``````d```s``i`'\r\n'`devils````e``````n`'\r\n'````l``````r``````s`'\r\n'````d`flames````````'];\r\n% invalid jets on row 3\r\nvalid=check_crisscross(Achar,dict_cell);\r\nassert(valid==0)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-06-02T16:57:18.000Z","updated_at":"2026-07-23T08:49:46.000Z","published_at":"2013-06-02T17:33:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to verify a Criss-Cross matrix has no invalid words,contains all of the word set, and all are simply connected (Up/Down/Left/Right). Separation, UDLR, must exist between non-intersecting words. Diagonal is considered separate.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe word set is a cell array. The matrix is an array of Char with spaces being represented by '`', char(96), which is under the tilde on my keyboard.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[dict={'abcd' 'cag'}\\n\\nAchar=['abcd'\\n       '``a`'\\n       '``g`'];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Validity (1 for Valid, 0 for Invalid)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRelated Challenges:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is derived from GAMES August 2013 Contest \\\"On the Ice\\\" to fit all NHL Team names into a minimum area grid using the Criss-Cross rules. Current Best solution is 19x19, 6/3/2013. Contest ends 8/31/2013.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1) Create an NHL Criss-Cross (Score by Area)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2) Complete a Criss-Cross\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3) Create a Criss-Cross dictionary from a matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":58468,"title":"ICFP 2022 - Create Command Script from Color-Region-Fill","description":"The ICFP2023 Challenge is Jul 7-10, registraion opens late June. Updates at TwitICFP2023. These contests are insanely complicated and competitive. The challenge evolves every 12 hours with new files and rule updates.\r\nThe ICFP2022 HomePage has details of the RoboPaint contest. Twit2022, WriteUps, PriorEvents, Spec, ImageSubmissions, Puzzles, SawickiSolutions are useful links. Posted 6/27/23.\r\nThe of Command Scripting is detailed in the function template. The commands have been matrixed and simplified but are based onthe Spec. Commands are Horiz split, Vertical split, Quad split, Color, and Reset.\r\nGiven a sequence of regions and colors writes that produce the Lower Right image, Img 13999, create commands to fill the image. The Goal 21.png.  Base costs  Cmds:1525, Img 13999, Submission combined score must be less than 17000.\r\nVisualizations of Image creation: [21 FBS Draw], adjust speed in settings.\r\nInput: Color regions  [M,7] of [r1 r2 c1 c2 r g b] where r1,c1 is TopLeft of a square and r2,c2 is BotRight\r\nOutput: cmds  [N,5] matrix of integer cmd, index, and parameters that vary based on cmd\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 659.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 329.75px; transform-origin: 407px 329.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://icfpcontest2023.github.io/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eICFP2023\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 197.5px 8px; transform-origin: 197.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Challenge is Jul 7-10, registraion opens late June. Updates at \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://twitter.com/icfpcontest2023\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eTwitICFP2023\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 95px 8px; transform-origin: 95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. These contests are insanely complicated and competitive. The challenge evolves every 12 hours with new files and rule updates.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://icfpcontest2022.github.io/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eICFP2022 HomePage\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 120px 8px; transform-origin: 120px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has details of the RoboPaint contest. \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://twitter.com/icfpcontest2022\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eTwit2022\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://icfpcontest2022.github.io/writeups/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWriteUps\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.icfpconference.org/contest.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePriorEvents\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://icfpcontest2022.github.io/Specifications/spec_v2_4.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSpec\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://gist.github.com/RafaelBocquet/e464c2d199f2d7a725cafdc22b30df7f\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eImageSubmissions\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://github.com/icfpc-unagi/icfpc2022/tree/main/problems\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePuzzles\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSawickiSolutions\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.5px 8px; transform-origin: 103.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are useful links. Posted 6/27/23.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.5px 8px; transform-origin: 381.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe of Command Scripting is detailed in the function template. The commands have been matrixed and simplified but are based onthe Spec. Commands are Horiz split, Vertical split, Quad split, Color, and Reset.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376px 8px; transform-origin: 376px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a sequence of regions and colors writes that produce the Lower Right image, Img 13999, create commands to fill the image. The Goal 21.png.  Base costs  Cmds:1525, Img 13999, Submission combined score must be less than 17000.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 105px 8px; transform-origin: 105px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eVisualizations of Image creation: [\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://drive.google.com/file/d/19MSfeGmn223KCGujl8Le6tQPqbW4EFXT/view?usp=drive_link\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e21 FBS Draw\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.5px 8px; transform-origin: 82.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e], adjust speed in settings.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 323.5px 8px; transform-origin: 323.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInput: Color regions  [M,7] of [r1 r2 c1 c2 r g b] where r1,c1 is TopLeft of a square and r2,c2 is BotRight\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 278.5px 8px; transform-origin: 278.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOutput: cmds  [N,5] matrix of integer cmd, index, and parameters that vary based on cmd\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 365.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 182.75px; text-align: left; transform-origin: 384px 182.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 360px;height: 360px\" 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\" 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data-image-state=\"image-loaded\" width=\"360\" height=\"360\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function cmds = create_cmds(regions,G)\r\n% regions is r1 r2 c1 c2 r g bof color regions to create\r\n% G is goal image [400,400,3]\r\n%The FSB set of paint commands balances Img and Cmd costs\r\n% Initial Commands could be\r\n% 4     1   254   254   254\r\n% 1     1   397     0     0\r\n% 4     1   209    88    58\r\n% 0     0     0     0     0\r\n% 3     1   392   381     0\r\n% 4     1    39    12    10\r\n% ...\r\n% 1     1   381     0     0\r\n% 2     1   380     0     0\r\n% 2     1   103     0     0\r\n% 4     4    10     2     4\r\n%\r\n%Painting small regions is very expensive thus overwrites are used\r\n%Creating small regions is expensive. Goal is to cut on largest region possible\r\n\r\n%Create Image script\r\n%  Image Delta Cost ranges around 10K\r\n%  Efficient cmds can be \u003c5K while direct coloring is \u003e100K\r\n%\r\n%Score it for commands\r\n%score it for image deviation \r\n%cost(move,block,canvas)=round(base_cost(move)*size(canvas)/size(block)\r\n%Point Cut 10  Done on abs of canvas, creates 4 sub-indices\r\n%Line Cut   7  Done on abs of canvas, creates 2 sub-indices\r\n%Color      5  Index filled by r,g,b\r\n%Swap       3  Index to Index swaps r,g,b contents\r\n%Merge      1  Index with Index creates new Level0 index\r\n%Reset      1\r\n% size(rect)=width*height\r\n%Similarity Checker\r\n%alpha=.005\r\n% for each pixel\r\n% rdist=(p1.r-p2.r)^2\r\n% gdist=(p1.g-p2.g)^2\r\n% bdist=(p1.b-p2.b)^2\r\n% dist=(rdist+gdist+bdist)^.5\r\n%scr_diff=round(alpha*sum(dist(:))\r\n%\r\n%Command costs\r\n%Reset/H/V/XY/C/M/S 1/7/7/10/5/1/3  [0:6] cmd ids\r\n%cmds have various numbers of parameters\r\n% cmd: cmdId region p1 p2 p3    Note: no region for reset\r\n% Reset cost is based on 1*(160000/(sum of min+max regions) \r\n% Reset is a matlab variant to simplify cmds\r\n% [1] is the starting regions andafter reset, ones(400)\r\n% H: 1 1 100 0 0 creates [1;2] where 1 is [1:100,1:400] 2 is [101:400 1:400]\r\n%  the cost is based on orig ones(400) thus 7, 1\u003c=p1\u003c400\r\n% V: 2 1 100 0 0 creates [1 2] where 1 is [1:400,1:100] 2 is [1:400 101:400]\r\n%  the cost is based on orig ones(400) thus 7, 1\u003c=p1\u003c400\r\n% XY: 3 1 100 150 0 creates [1 2;4 3] cost uses orig ones(400) thus 10, p1\u003c400, p2\u003c400\r\n%  1 is [  1:100,  1:150] 2 is [  1:100 151:400]\r\n%  4 is [101:400,  1:150] 3 is [101:400 151:400]\r\n% Color: 4 1 r g b sets all points in reg 1 to rgb, cost 5, 0\u003c=rgb\u003c=255\r\n% Swap: Not implemented\r\n% Merge: 6 idx1 idx2 0 0, Cost based on combined area idx1+idx2\r\n%  For XY example a cmd 6 1 2 0 0 sets idx2 to 1. [1:100 1:400] cost 1*4\r\n%\r\n% Commanding examples for the various regions\r\n% S=255*ones(400,400,3) is starting canvas, White\r\n%Image with (1,1,:)=0, Black square at pixel 1,1\r\n% Direct using XY and Color\r\n% 3 1 1 1 0    Cost 10*1\r\n% 4 1 255 255 255   Cost 5*160000   Coloring small points is costly\r\n% Using H,V,Color\r\n% 1 1 1 0 0    Cost 7*1  creates regions [1;2]\r\n% 2 1 1 0 0    Cost 7*400 with regions [1 3;2 2]\r\n% 5 1 255 255 255   Cost 5*160000   Coloring small points is costly\r\n% Using Color,V,Color,Reset,H,Color\r\n% 4 1 0 0 0   Cost 5   Coloring large areas is cheap\r\n% 2 1 1 0 0   Cost 7   [1 2], 1 is [1:400 1]  2 is [1:400 2:400]\r\n% 4 2 2555 255 255   Cost 5*round(400/400*400/399)=5  Low cost color\r\n% 0 0 0 0 0   Cost 1*1  Merge of 1,2 is whole img\r\n% 1 1 1 0 0   Cost 7   [1; 2], 1 is [1 1:400]  2 is [2:400 1:400]\r\n% 4 2 2555 255 255   Cost 5*round(400/399*400/400)=5  Low cost color\r\n% Total Cost 30\r\n%\r\n% Image with central rectangle [190:230, 210:240,:] set to blk [0 0 0]\r\n%Using  XY,XY,Color\r\n% 3 1 189 209 0   [1 2;4 3] regions [1:189 1:209] [1:189 210:400] 4[190:400 1:209]\r\n%   region 3: [190:400 210:400]  Cost 10\r\n% 3 3 230 240 0] regions [1 2 2;4 3 5;4 7 6] with 3 becoming [190:230, 210:240]\r\n%  New regions are numbers CW/L-R,T-B with base region value unchanged\r\n%  cost 10*round(400/211*400/191)=10*4=40\r\n% 4 3 0 0 0   Cost 5*round(400/41*400/31)=5*126=630  Moderate cost color\r\n% Total Cost 680    XY,XY,Color\r\n%Using V,V,H,H,C\r\n% 2 1 209 0 0  [1 2] regs [1:400 1:209] [1:400 210:400]  Cost 7\r\n% 2 2 240 0 0  [1 2 3] regs 2[1:400 210:240] 3[1:400 241:400]  Cost 14\r\n% 1 2 230 0 0  [1 2 3;1 4 3] regs 2[1:230 210:240] 4[231:400 210:240]  Cost 91\r\n% 1 2 209 0 0  [1 2 3;1 5 3;1 4 3] regs 2[1:209 210:240] 5[210:230 210:240]  Cost 154\r\n% 4 5 0 0 0   Cost 5*round(400/41*400/31)=5*126=630  Moderate cost color\r\n% Total Cost 896  V,V,H,H,C\r\n\r\n%Using XY,Color,Reset,V,Color,Reset,H,Color\r\n% 3 1 189 209 0  [1 2;4 3] regs [1:189 1:209] [1:189 210:400] 4[190:400 1:209]\r\n%   region 3: [190:400 210:400]  Cost 10\r\n% 4 3 0 0 0  Cost 5*round(400/211*400/191)=5*4=20\r\n% 0 0 0 0 0  Cost 1*round(160000/(44099+40301))=2   Reset\r\n% 2 1 240 0 0  [1 2] regs [1:400 1:240] [1:400 241:400]  Cost 7\r\n% 4 2 0 0 0  Cost 5*round(400/400*400/160)=5*3=15\r\n% 0 0 0 0 0  Cost 1   Reset\r\n% 1 1 230 0 0  [1; 2] regs [1:230 1:4000] [231:400 1:400]  Cost 7\r\n% 4 2 0 0 0  Cost 5*round(400/171*400/400)=5*2=10\r\n% Total Cost 72   XY,Color,Reset,V,Color,Reset,H,Color\r\n\r\n  cmds=[];\r\n  \r\n  %Suggested outline : Focus is on optimizing cuts in Best_Draw2\r\n  Gidx=ones(size(G,1));\r\n  bArea=400*400;\r\n  for ireg=1:size(regions,1) % Draw2\r\n   vrrcc=regions(ireg,:);\r\n   GregA=(vrrcc(2)-vrrcc(1)+1)*(vrrcc(4)-vrrcc(3)+1);\r\n   ptr=1; \r\n   Gidx=Gidx*0+1; % Assume start each region with a clean idx board\r\n  \r\n   while nnz(Gidx==ptr)\u003eGregA % Algorithm does not allow to be \u003c GregA\r\n    [bGidx,bcmd,p1,p2]=Best_Draw2(Gidx,vrrcc);\r\n    cmds=[cmds;bcmd ptr p1 p2 0]; % H/V/XY  Multiple H/V/XY cmds to create region\r\n    Gidx=bGidx;\r\n    ptr=Gidx(vrrcc(1),vrrcc(3)); % used in while for next H/V/XY cmd and  Color cmd\r\n   end\r\n  \r\n   cmds=[cmds;4 ptr vrrcc(5:7)]; % Color Command\r\n  \r\n   if nnz(Gidx==1)==bArea,continue;end\r\n   if ireg==size(regions,1),continue;end % No final reset\r\n   cmds=[cmds;0 0 0 0 0]; % Reset Command     ptr=1 Gidx(:,:)=1 \r\n  end % ireg \r\nend % create cmds\r\n\r\nfunction [bGidx,bcmd,p1,p2]=Best_Draw2(Gidx,vrrcc)\r\n %vrrcc goal region draw/color  r1 r2 c1 c2 r g b\r\n % Hr1 Hr2 Vc1 Vc2 xyTL xyLR xyTR xyLL\r\n bcmd=0;p1=0;p2=0;bGidx=Gidx;\r\n ptrmax=max(Gidx(:));\r\n Amax=0; %\r\n \r\n gr1=vrrcc(1);gr2=vrrcc(2);gc1=vrrcc(3);gc2=vrrcc(4); %goal region\r\n gA=(gr2-gr1+1)*(gc2-gc1+1); % Goal region Area\r\n ptr=Gidx(gr1,gc1); % region idx to process\r\n [r1, c1]=find(Gidx==ptr,1,'first'); %Common to H/V/XY/C\r\n [r2, c2]=find(Gidx==ptr,1,'last');\r\n \r\n %Update region that maximizes area unless cmd achieves r1 r2 c1 c2\r\n \r\n %H r1  Gidx(p1+1:r2,c1:c2)=ptrmax+1;  p1=cmd param\r\n  if gr1\u003er1\r\n   nGidx=Gidx;\r\n   nGidx(gr1:r2,c1:c2)=ptrmax+1; %Set new region\r\n   if nnz(nGidx==ptrmax+1)\u003eAmax || nnz(nGidx==ptrmax+1)==gA\r\n    Amax=nnz(nGidx==ptrmax+1);\r\n    p1=gr1-1; %r1\u003c=p1\u003cr2\u003c=400\r\n    bGidx=nGidx;\r\n    bcmd=1;\r\n    if nnz(nGidx==ptrmax+1)==gA, return;end\r\n   end\r\n  end\r\n  \r\n  \r\n  %H r2  Gidx(p1+1:r2,c1:c2)=ptrmax+1;  p1=cmd param\r\n  if r2\u003egr2\r\n   nGidx=Gidx;\r\n   \r\n  end\r\n  \r\n %V c1  Gidx(r1:r2,p1+1:c2)=ptrmax+1;\r\n  if gc1\u003ec1\r\n   nGidx=Gidx;\r\n   nGidx(r1:r2,gc1:c2)=ptrmax+1; %Set new region\r\n   if nnz(nGidx==ptrmax+1)\u003eAmax || nnz(nGidx==ptrmax+1)==gA\r\n    Amax=nnz(nGidx==ptrmax+1);\r\n    p1=gc1-1; %c1\u003c=p1\u003cc2\u003c=400\r\n    bGidx=nGidx;\r\n    bcmd=2;\r\n    if nnz(nGidx==ptrmax+1)==gA, return;end\r\n   end\r\n  end\r\n  \r\n %V c2  Gidx(r1:r2,p1+1:c2)=ptrmax+1;\r\n  if c2\u003egc2\r\n   nGidx=Gidx;\r\n   \r\n  end\r\n  \r\n%   Gidx(r1:p1,c1:p2)=ptr; % TL region\r\n%   Gidx(r1:p1,p2+1:c2)=ptrmax+1; % region to right is new\r\n%   Gidx(p1+1:r2,p2+1:c2)=ptrmax+2; % region to right and down is new\r\n%   Gidx(p1+1:r2,c1:p2)=ptrmax+3; % region to below  is new\r\n    \r\n % XY r1c1 gr1gc1 TL reg3\r\n  if r1\u003cgr1 \u0026\u0026 c1\u003cgc1 % Process only if gr1gc1 contained within r1, skip r1==gr1,c1=gc1\r\n   nGidx=Gidx; %p1=gr1-1  p2=gc1-1\r\n   %nGidx(r1:gr1-1,c1:gc1-1)=ptr; % Unchanged sectionID when move TL\r\n   nGidx(r1:gr1-1,gc1:c2)=ptrmax+1; \r\n   nGidx(gr1:r2,gc1:c2)=ptrmax+2; % Keep region TL to BR\r\n   nGidx(gr1:r2,c1:gc1-1)=ptrmax+3;\r\n   if nnz(nGidx==ptrmax+2)\u003eAmax || nnz(nGidx==ptrmax+2)==gA\r\n    p1=gr1-1; %r1\u003c=p1\u003cr2\u003c=400\r\n    p2=gc1-1; %c1\u003c=p2\u003cc2\u003c=400\r\n    bGidx=nGidx;\r\n    bcmd=3;\r\n    if nnz(nGidx==ptrmax+2)==gA, return;end\r\n   end\r\n  end\r\n    \r\n  % XY r2c2 gr2gc2  BR Corner gives reg1, +0\r\n  if r2\u003egr2 \u0026\u0026 c2\u003egc2 % Process only if gr2gc2 contained within r2, skip r2==gr2,c2=gc2\r\n   nGidx=Gidx; %p1=gr1-1  p2=gc1-1\r\n   \r\n  end\r\n    \r\n  % XY r1c2 gr1gc2  TR corner gives reg4, +3\r\n  if r1\u003cgr1 \u0026\u0026 c2\u003egc2 % Process only if gr1gc1 contained within r1, skip r1==gr1,c1=gc1\r\n   nGidx=Gidx; %p1=gr1-1  p2=gc1-1\r\n   \r\n  end\r\n  \r\n  % XY r2c1 gr2 gc1 BL corner gives reg2, +1\r\n  if r2\u003egr2 \u0026\u0026 c1\u003cgc1 % Process only if gr2gc1 contained within r2, skip r2==gr2,c1=gc1\r\n   nGidx=Gidx; %p1=gr1-1  p2=gc1-1\r\n   \r\n  end\r\n  \r\nend % Best_Draw2\r\n\r\n\r\n\r\nfunction [S,Gidx,CmdCost]=cmd_exec(cmd,S,Gidx,CmdCost)\r\n%This is how commands are executed and cmd costs evaluated\r\n%cmd: [cmd_id idx p1 p2 p3]\r\n%S image [400,400,3] initially all 255\r\n%Gidx working matrix of prior cmd idx updates. Set to all 1s upon Reset\r\n%CmdCost is running command costs based on area to be split/colored/reset\r\n ptrmax=max(Gidx(:));\r\n bArea=160000; % 400*400\r\n cmdscale=[7 7 10 5 1 3];\r\n \r\n %Calc cmd cost\r\n if cmd(1)==0 % reset  bArea/sum(max+min)\r\n  \r\n  qH=bArea; qL=0;\r\n  if ptrmax\u003e1\r\n   qH=0;\r\n   qL=bArea;\r\n  end\r\n  \r\n  for j=1:ptrmax\r\n   qt=nnz(Gidx(:)==j);\r\n   if qt\u003eqH\r\n    qH=qt;\r\n   end\r\n   if qt\u003cqL\r\n    qL=qt;\r\n   end\r\n  end\r\n  \r\n  Lcmdcost=1*round(bArea/(qH+qL));\r\n  CmdCost=CmdCost+Lcmdcost;\r\n else % H/V/XY/C  ignore merge and swap\r\n  Acmd=nnz(Gidx==cmd(2));\r\n  Lcmdcost=cmdscale(cmd(1))*round(bArea/Acmd);\r\n  CmdCost=CmdCost+Lcmdcost;\r\n end\r\n \r\n if cmd(1)==0 % reset\r\n  Gidx=0*Gidx+1;\r\n  return;\r\n end % Reset\r\n \r\n [r1, c1]=find(Gidx==cmd(2),1,'first'); %Common to H/V/XY/C\r\n [r2, c2]=find(Gidx==cmd(2),1,'last');\r\n \r\n if cmd(1)==4 % color 4 ptr r g b\r\n  S(r1:r2,c1:c2,1)=cmd(3); %r\r\n  S(r1:r2,c1:c2,2)=cmd(4); %g\r\n  S(r1:r2,c1:c2,3)=cmd(5); %b  \r\n end % Color\r\n \r\n if cmd(1)==1 %H  1 ptr p1 0 0\r\n  p1=cmd(3); %r r1\u003c=p1\u003cr2\u003c=400\r\n  Gidx(p1+1:r2,c1:c2)=ptrmax+1; % region below line gets increased\r\n end\r\n \r\n if cmd(1)==2 %V  2 ptr p1 0 0\r\n  p1=cmd(3); %c c1\u003c=p1\u003cc2\u003c=400\r\n  Gidx(r1:r2,p1+1:c2)=ptrmax+1; % region below line gets increased\r\n end\r\n \r\n if cmd(1)==3 %XY  3 ptr p1 p2 0 [1 1;1 1] becomes [1 2;4 3]\r\n  p1=cmd(3); %r r1\u003c=p1\u003cr2\u003c=400\r\n  p2=cmd(4); %c c1\u003c=p2\u003cc2\u003c=400\r\n  Gidx(r1:p1,p2+1:c2)=ptrmax+1; % region to right is new\r\n  Gidx(p1+1:r2,p2+1:c2)=ptrmax+2; % region to right and down is new\r\n  Gidx(p1+1:r2,c1:p2)=ptrmax+3; % region to below  is new\r\n end\r\n \r\nend % cmd_exec","test_suite":"%%\r\n%Google Drive Dowloads need to come from shared files\r\n% Tweak link: file/d/ to uc?export=download\u0026id=   while removing /view?usp=sharing\r\n% https://drive.google.com/file/d/1v3GsGgP3p905wzdvUqypL_-djYmxiyzK/view?usp=sharing\r\n% https://drive.google.com/uc?export=download\u0026id=1v3GsGgP3p905wzdvUqypL_-djYmxiyzK\r\n\r\n%21.png\r\nG=imread('https://drive.google.com/uc?export=download\u0026id=1ExUg4hujk4-kH9YWDvbFeRvKj2l5ujKl');\r\n% rT rBL cL cR r g b\r\nregions=[1 400 1 400 254 254 254 255 \r\n1 397 1 400 209 88 58 255 \r\n1 392 1 381 39 12 10 255 \r\n1 397 1 374 217 218 210 255 \r\n1 381 104 380 10 2 4 255 \r\n1 396 103 144 231 230 219 255 \r\n1 387 1 49 46 34 27 255 \r\n1 354 1 144 161 150 133 255 \r\n1 347 1 245 199 200 200 255 \r\n1 375 252 375 42 41 163 255 \r\n1 353 1 151 28 10 13 255 \r\n1 397 1 41 227 202 116 255 \r\n1 297 1 400 232 235 230 255 \r\n1 299 1 382 40 41 41 255 \r\n1 305 1 375 22 14 19 255 \r\n1 297 1 246 204 203 199 255 \r\n1 360 1 41 243 214 122 255 \r\n1 297 254 375 229 230 222 255 \r\n1 304 7 151 28 10 14 255 \r\n1 253 1 381 29 26 26 255 \r\n1 253 1 253 14 3 5 255 \r\n1 246 1 383 50 51 50 255 \r\n1 245 1 375 245 244 231 255 \r\n1 245 1 318 48 47 48 255 \r\n1 245 1 311 229 230 216 255 \r\n1 246 1 253 43 21 21 255 \r\n1 246 1 246 195 69 42 255 \r\n1 226 1 246 202 73 44 255 \r\n1 297 1 41 227 233 226 255 \r\n1 199 1 319 53 51 50 255 \r\n1 200 1 311 237 238 227 255 \r\n1 200 32 284 229 226 211 255 \r\n1 200 42 254 210 80 51 255 \r\n1 151 10 382 31 21 13 255 \r\n1 144 1 391 229 231 223 255 \r\n1 143 4 384 251 251 240 255 \r\n1 144 42 384 242 217 135 255 \r\n5 152 42 255 211 84 57 255 \r\n12 50 9 384 37 21 16 255 \r\n1 43 256 377 241 215 133 255 \r\n1 42 1 247 238 235 225 255];\r\n\r\ncmds = create_cmds(regions,G);\r\n\r\n%Evaluate cmds\r\nS=G*0+255;\r\nGidx=ones(400);\r\nCmdCost=0;\r\nbArea=400*400;\r\ncmdscale=[7 7 10 5 1 3]; %Reset/H/V/XY/C/M/S 1/7/7/10/5/1/3  [0:6] cmd ids\r\n\r\nfor icmd=1:size(cmds,1)\r\n cmd=cmds(icmd,:);\r\n ptrmax=max(Gidx(:));\r\n %Calc cmd cost\r\n if cmd(1)==0 % reset  bArea/sum(max+min)\r\n  \r\n  qH=bArea; qL=0;\r\n  if ptrmax\u003e1\r\n   qH=0;\r\n   qL=bArea;\r\n  end\r\n  \r\n  for j=1:ptrmax\r\n   qt=nnz(Gidx(:)==j);\r\n   if qt\u003eqH\r\n    qH=qt;\r\n   end\r\n   if qt\u003cqL\r\n    qL=qt;\r\n   end\r\n  end\r\n  Lcmdcost=1*round(bArea/(qH+qL));\r\n else % H/V/XY/C  ignore merge and swap\r\n  Acmd=nnz(Gidx==cmd(2));\r\n  Lcmdcost=cmdscale(cmd(1))*round(bArea/Acmd);\r\n end\r\n CmdCost=CmdCost+Lcmdcost;\r\n \r\n if cmd(1)==0 % reset\r\n  Gidx=0*Gidx+1;\r\n  continue;\r\n end % Reset\r\n \r\n [r1, c1]=find(Gidx==cmd(2),1,'first'); %Common to H/V/XY/C\r\n [r2, c2]=find(Gidx==cmd(2),1,'last');\r\n \r\n if cmd(1)==4 % color 4 ptr r g b\r\n  S(r1:r2,c1:c2,1)=cmd(3); %r\r\n  S(r1:r2,c1:c2,2)=cmd(4); %g\r\n  S(r1:r2,c1:c2,3)=cmd(5); %b  \r\n end % Color\r\n \r\n if cmd(1)==1 %H  1 ptr p1 0 0\r\n  p1=cmd(3); %r r1\u003c=p1\u003cr2\u003c=400\r\n  Gidx(p1+1:r2,c1:c2)=ptrmax+1; % region below line gets increased\r\n end\r\n \r\n if cmd(1)==2 %V  2 ptr p1 0 0\r\n  p1=cmd(3); %c c1\u003c=p1\u003cc2\u003c=400\r\n  Gidx(r1:r2,p1+1:c2)=ptrmax+1; % region below line gets increased\r\n end\r\n \r\n if cmd(1)==3 %XY  3 ptr p1 p2 0 [1 1;1 1] becomes [1 2;4 3]\r\n  p1=cmd(3); %r r1\u003c=p1\u003cr2\u003c=400\r\n  p2=cmd(4); %c c1\u003c=p2\u003cc2\u003c=400\r\n  Gidx(r1:p1,p2+1:c2)=ptrmax+1; % region to right is new\r\n  Gidx(p1+1:r2,p2+1:c2)=ptrmax+2; % region to right and down is new\r\n  Gidx(p1+1:r2,c1:p2)=ptrmax+3; % region to below  is new\r\n end\r\nend % icmd\r\n\r\n\r\n%Evaluate Img Score\r\n GmSsq=(double(G)-double(S)).^2;\r\n dis=sqrt(sum(GmSsq,3));\r\n scr=round(0.005*sum(dis(:)));\r\n \r\n fprintf('CmdScore: %i    Img Score:%i\\nTotal:%i\\n',CmdCost,scr,CmdCost+scr)\r\n if CmdCost+scr\u003e17000\r\n  fprintf('Combined Score Too High\\n')\r\n end\r\n \r\nvalid=(scr+CmdCost)\u003c=17000;\r\nassert(valid)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":3097,"edited_by":3097,"edited_at":"2023-06-28T01:46:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-06-27T23:57:46.000Z","updated_at":"2026-07-26T10:47:24.000Z","published_at":"2023-06-28T01:46:44.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://icfpcontest2023.github.io/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eICFP2023\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e Challenge is Jul 7-10, registraion opens late June. Updates at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://twitter.com/icfpcontest2023\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eTwitICFP2023\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. These contests are insanely complicated and competitive. The challenge evolves every 12 hours with new files and rule updates.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://icfpcontest2022.github.io/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eICFP2022 HomePage\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e has details of the RoboPaint contest. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://twitter.com/icfpcontest2022\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eTwit2022\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://icfpcontest2022.github.io/writeups/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWriteUps\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.icfpconference.org/contest.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePriorEvents\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://icfpcontest2022.github.io/Specifications/spec_v2_4.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSpec\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://gist.github.com/RafaelBocquet/e464c2d199f2d7a725cafdc22b30df7f\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eImageSubmissions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://github.com/icfpc-unagi/icfpc2022/tree/main/problems\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePuzzles\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSawickiSolutions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e are useful links. Posted 6/27/23.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe of Command Scripting is detailed in the function template. The commands have been matrixed and simplified but are based onthe Spec. Commands are Horiz split, Vertical split, Quad split, Color, and Reset.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a sequence of regions and colors writes that produce the Lower Right image, Img 13999, create commands to fill the image. The Goal 21.png.  Base costs  Cmds:1525, Img 13999, Submission combined score must be less than 17000.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVisualizations of Image creation: [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://drive.google.com/file/d/19MSfeGmn223KCGujl8Le6tQPqbW4EFXT/view?usp=drive_link\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e21 FBS Draw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e], adjust speed in settings.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput: Color regions  [M,7] of [r1 r2 c1 c2 r g b] where r1,c1 is TopLeft of a square and r2,c2 is BotRight\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput: cmds  [N,5] matrix of integer cmd, index, and parameters that vary based on cmd\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"360\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"360\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"360\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"360\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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Sequences 43: Least Common Fibonacci Number","description":"The Fibonacci sequence  is a series whose elements are numbers starting with  and , and subsequent Fibonacci numbers are defined recursively: . The first 20 Fibonacci numbers are:\r\n                            \r\nGiven two indices  and , write a program to return the least common Fibonacci number, , which is defined as the smallest Fibonacci number divisible by both  and . For example,, which is , since  and  both divide .\r\nSince. the value of  may become large even if the values of  and  are relatively small, please output a vector containing the number of digits and the last  digits of . Therefore, in the example above the output of , which has  digits, should be .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 216px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe Fibonacci sequence \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003eF\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e is a series whose elements are numbers starting with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"43.5\" height=\"20\" style=\"width: 43.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"43.5\" height=\"20\" style=\"width: 43.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, and subsequent \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Fibonacci_number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eFibonacci numbers\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e are defined recursively: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANYAAAAoCAYAAACCewRHAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAA1qADAAQAAAABAAAAKAAAAADl+puhAAAHM0lEQVR4Ae2bW4hVVRjH1YyZFMsymoxq5qHSLpiVjZZpw0RpWVJSqCVIUUhgEV2gB+n60oNQSWQSZQ+WUWYKqZlaU0aKYyKVmRmoUzaWRheL0czq9x/3wjXbffblzD7nzN5nffCf9a1v3f97rfWtvfaZXr2cOAYcA44Bx4BjwDHgGHAMOAYcA44Bx4BjwDHgGHAMOAYcA44Bx4BjwDHQTQZ6R5RfQPoEEJUvqJpHML4clJAx26X0dwWoKaLf+yhzThHlqqlILvntG/EEp5F+MlgCxlp516IvB78D1TEAnAdGAzOR2tHzIJsYxOlgIhAPRg6izAFt4F9QC04DmihjvPh3hE7CGahqfl+Am/887CfUQgoSLbJlQHnrgjJk2HaqNy7Dw5MhY9EGo8U2NySPS+rKQFXy2wIHZkIt7crHMbF7sOw6xpp9QxNDMBwovCRiSLtJvzMiT5aS36Wzn4BJJep0E/Xmht8+MUjqR55RVr73LT1I1U7dGpSQcds1Vv/3oG+24kFq3njQHNAR94ygwaZgqzp+b4A0eydpiEHicTHyZC3LBjpseHgtRufzxoHemTX+mTHGXkyWXPEbx2ONs1jahr7TikvVi71uv05SxJPDRslJqPP/ZdZYgrz2bNKfsfLkjQNraKmrVcmvFpPZqZ/zUaqFuRBot8mzTGVwhgMtmEG+wQ4nrltCefe8Sik9Vu74jbpub2CW6BrdyE8ojUC3gueDW0AzeBSUSkZSsa72uyufU8F1RVZie+291FEPhgJ56xFAx6MOsBo4Sc5A1fE7A47MTh0Wmm9XySmNLqGr67C246atj26qYI4fY/RhQcHS+UgopcfKHb9RHsveSdYyPx4CtUBn4ovBLPA1KOWH0C3UrwXeXWkrsoJhlBtslZ2GvgP0A2cB9U1edTFwkpyBquNXi06/rDAeQYvKL1sxPO435iyun2YZDn5F99/2Tcb2FzgBZFm0MfwSAn0+EA8aa1i+q0hPIrnkN8xjXQE7J1oMrbR0o+onPO+YSE7D8da41qD7b/vEwQrQYeWrpHo8jd8FdLJ4PkFHBpD3lBj55amFQqL2k0hW+NVFnXgdC8TTRvA62A6OkbCFZR8DdQb+yldaDemK2W/3Zct0tD+9t3fgDwJG8yW2TQH2cpv0LKeDWaABzANJ5Akyvx1SwNS3iDyrQvJtC0nzJ2WFX51StHleaw1gArourbQxaJHFllZymiPQ/Nil0s84kirDjh5x04IWRVRvRZ7hQGF9VIEKpusnVpPBXKC+vgTSlHYqU72aTGlJVvi9nwF/A24GOqFMB3Io4kOnmNiiywkdeVRQmAIqJZW8FZzDoA0HIjYLcgedVJ+zsLCywu8G+LzI9/CHejwfIKzxpXX+y4ffpri+9+ioJ9FDWt2pFfenN8XkSv/xiqsTBz09TrCFTDPiZIzI0xaRHpRsn/+L8Xh2nXr3OOQZxK04MXHPXHVBFvjV/H0V+F95tNH+CTSvYz9HuTezU2tiJxV5vGdBC/gNiMALwXqg26WFoKfLGDpoOFB4WxEdVhmNVQ/hM6DF9BgQJ3+AESBtyYrHyiq/5nnpx8iaF0uMwQ6NV7JtE4k0WwbdgNRZ8TiqrunfBKOAJtPPYBF4D+iIab8EEu1xotvQp3y9GkJcu1cSWUdmLSCVXQZeBMPAp0C3cOKnGiUP/GpjkCw4EnT9619Y35K8tGuWzp/t6FYwieeSa2wHNUBeaj7Qi5+uf9XmVtBTZQod2weafB18mrg8zVSfPSz6A4k6AkrqjwS9biU04zehl1QVQV74vZen9QqQwyir3E1rcpU6g07yWh7n2fzewEvOZfC9N+aPCbXRSNaBA8D+qKwbsv0JUEveICnVUXA3jel5zgxqtIK2uPyqizopxOU4bI7eRz36zGI/P6JHpe9RNXVNFyCSVWBxp3b0CLjSi+c9uIABnukNcgahLm0GgsvBR6ADGNmD8oaJRIR6T9WpoJzSTGODwI5yNhrRVhJ+VdVqEPfktbFA2+OxPwiagP38iJZe+tCEvi9pItVbzX2BruNUKRe01VzF1QfogXb5eVZP5L1le9iypamWymOl2ce06io3v1fScW0sQ3wDKHR68GXrfrSRKjR5jKdSjXWWTR/ZbpQx57Kc8YkHXVgY0QWGsd2OnvZDqaaFVU5+h/OsdgJ9iLdF/+DbCrocC+VZSiHmGGi/2Gm1S3aBt4DOxnmWGgZ3NdgO5KmNjEbR+5WOg9d7OkFq0ujVdHZqNfbMisrJrzyUXl+0eMxnpBZ0vbO1gc2gLMfCNTR0CAwERjTJtFPvBTcZY45DXcdqvLN9Y/yQuN6RloAuu5wvX9LouRQQ738DtXsYLATNII9SLn7lfOQMxGkhmM2sYjw30HK1vF8VIrk/CYMLJTp7txlw/HabQleBY8Ax4BhwDDgGHAOOAceAY8Ax4BhwDDgGHAOOAceAY8AxkJyB/wGm7xvGpD2IEAAAAABJRU5ErkJggg==\" width=\"107\" height=\"20\" style=\"width: 107px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. The first 20 Fibonacci numbers are:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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\" width=\"519.5\" height=\"19\" style=\"width: 519.5px; height: 19px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven two indices \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, write a program to return the least common Fibonacci number, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIoAAAAmCAYAAAAbWQPxAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAiqADAAQAAAABAAAAJgAAAACFxbEYAAAI1ElEQVR4Ae2YC9CWRRXHQcgLIslAmpT4mQ2mhkaaKI0CpZFmFydrLM1LZmVRmRSTqMNEFy/plMWMRZmVjTV5acpkkhI/wemiU1iaSWqOKRpmWqEoZubvh8+Zdtbned4rTHw8Z+b/7u45Z8/unj17dp932LCGGg80Hmg80Hig8UDjgcYDjQcaDzQeGHIeGMeKrgbzh9jKjmE9vwC7borrGs+kp4MjwSFgAASNpbJXNDZS6Zh3gFvBCzfSmBtrmJEMdA14COzWz0GvwNij4B8V+FGXg02l34/BavDfEqyCtxisBMtBSt+lUTenqrnKPzk1VFF3TQ+AiRXyTZ09mgX8FqwAW/dzMZ54Dacbei3tg4AR2glNRtkACVtuyOfBTLAnOAJcDkJuuRDk5Km/AaR6y2h/CpwCPgLmgW+BO0Hoab+OPo7wabBvndIQkE1gDX8FF/d7LRdhMJz9GPVuUvKh9Fub2DFbjQFldBbMGK8qCxhAobOG+nZlhuBFulV3xwod2fuDp8A3bWwG9FHWqE/e28+13lgY1fBlXRieRZ8nChtuxqktbLi5txf6bmAZDcKMQGl1BRps95YZKXjDKb3mnNsA2BzIa2cV8OB7HfVM22JhHYhNOa5Di4ej/2TS/31t9jereA1sU6I/Cl5q0+umjk5CaAarIq9R13dJlcIQ5c8p1t2XrOK9HkHyDPUXd+A0I/VvSf/vddD39ej+sULf4Is5WQ5U6KXsEWkjqy+irZ2jMv5Qb+5RrNv3Xc/0FSzEpvhS7oTmoRx9zUoTOumMblVKvDCxe0eJTYP5YdDOW8oU7BeRh2AcaEXjUfC9NRccmSjvQn02+CIwyPtBW2JkCvDEfyYx+ALqbwfng/eALUBKXvXngtNBWUZOdR+k4R69PGV2U0+/Gs7uwICb9AiIQLmkg76tVH1PhN0vZco6zcx1U8avas5EoC2/7OroAoT3gxjX0j+wpBOBd30qe42CLmka/TyUT4GweUNha4Dy1wlfuYEkbQ+uBtHH8mugjnxzquc7rpTyKCxTehnMNNKuLVOq4PmqHpvI+vU1MYDNSYnd1dR98HqKPdE/A0eDK0E7NLFQ8vFcR4sQngb+XSj5floMXOfXC/yUMmi/qHRRGuQfAP6VEKTvXwpuBFuBhSDIsUYDdaaCBcDNl2zXUWTkneuUWslOQSGi81/UTXnt0iCK0fdx6qbRfpAODLt1ZRrgdeOeUdjzOmtFrn8NcNylwKtnLXgDkD4GYk5vXM/p7efcxJ6Z73fAA+B1OQXEWHOpXwXuBi8BY4BXqfIloI4+jFC9yoM8sq53IZuV6FxPPU5Twq6sviKReEJMo/2gdE7LMTgH6LjxYB9wJjA73AXaIR0rPfxcUft7IFJPrvR78G3wfhCbsTf1IDe1V4rry7l5vVm+C+jLA0DQZCozwDSwChwGhgPJfaujvxdCs1VX5OkxixhtwuzSLvk+iX6Wl7bbsYWewf1PELYNkpz8UpqfM2vaP0Smvdk1OiH6bKGr/r1gUQiKciWlstsyfjdN/W8m1p5ZzADwMARdRkWZcJ9mgKDzqIRs32BWlGY+dW+ukLf8+93o3C7p7P3XLsW9H/oRtdHutvREm1aDyua0A8IrQ6GN8rFCx6zUiuKKUW8dSP84dM2TFEBl83pO0v7v/qiOKtTNYm8DZpSgGVGh9EE/mLRnFnX9viLhl1W3KZhPlwnlbVElKPhpir8T3p9b6Kfih9IG9XRzM1FHzXROD9AzP7mu6fwSft0g9xfCcXVKyJSnp/ODtNcmfdIgWpLwu62m9r6PkesSQ3tQ36loO//PJTK/fF5dtO3zTCIrq8a6ww/P0+kkUNLX/PMMJYxrqL8TrAapE3dNdHqppoFSthk65ewOB7iv0A+HVXU/BEH4zLGXZoqHFu0nKZdlsm6aXgmS18KC9bX//aRBdA5ss1vQwVTSeQa/qozrrDJQqjrK3wHo9Ljn3iSzBb0Vufq7F3qDRVueGWYr0A75mfYd4DsnJRf0HxBzOjoV9lB/S2HzJy1sXFzoOf5hma4b47WgrCyAM/WWzRehEWu9vkR7MTzHegKkzwNVvYaUiYmgFV2IgrpzWimWyY8tOseA+ablfXaDYUSmV0EETtg4Ne9U0jbI/gK84/PAeje8sGUQx0mg2hNNord2HwFxEssMmnnUM+hHZgpeSTG3TxQyA2tGUbcwq54I9rHRgo5HHvZOznS3pm22Vn5VJrN5C1C20gb0ZnDR+lr5zwrY6psxO6Yr6BET1YFVNALBUSCcuCBRHE59OQg7PqymJ/K8qkP8olkK4oGV6lxHI2z9IRX0oX5TYdsNLyPfBDH2ohIFD0HIp1D3zeC7Lg6YdiND+2g8HtTR5Qi1p+64THFWIVN+XCZzvMhEBsdU4BfREaCMPGzOaxWoOyRlfYe9Dq7/l8TCLQfBp8FpBU6nXAjuAaneq2in5MR/A0LHSX0DuMADgVE8F9wK1PkqGAVyiush7DyIwo65Ug/tD9FX286ljNJAKHP6eXSKuXk4DPi9E0NnJnL1bk9keXVLGG6ueoMgp7gqlE/IhPvRjnncQ915fDLTSZvvoKH+F1JmO/Xbio4xWCfl3RUDbAvfwHq0xvYvkZVtAOxhf6ro58npV2YZiy0foY5llszpBzD0xeOgLNsdDt9DoI6ncxpI6QAaa0D407lXnWB1Q88AzekWGMrdq5w8mOuAcv19EqijnyNUNw3qOv2NIhvFKEb8scDsdAYws5jW/x/oy0xCp53Q5WT2op9ZsiyQNLk92BP8ChiQG4p2wrCBOrrFANORu14PQUMdeMDH883AzGj63xC0C0Y98fM2hPEObS5D/y4wpsN+jToeGAA+ui8F/abJGLwPLAFVWaffY1bZOwuBAesju6EuPRDvDa/HfpJvlwvAiH4a7cLWMfTxypndRd+mS+aBE2h74vwq6BcN9MtQD3ZeS18f7fN7sNF0zTzwStpTMt6m3tydBfjQbajxQOOBxgONBxoPNB5oPNB4oPHA5uGBZwGduFP+0TlHHQAAAABJRU5ErkJggg==\" width=\"69\" height=\"19\" style=\"width: 69px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, which is defined as the smallest Fibonacci number divisible by both \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACIAAAAoCAYAAACb3CikAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAIqADAAQAAAABAAAAKAAAAABIyrn1AAACYElEQVRYCe2Wz0sVURTHNY0gEA2iWuVbhCK1CqwwMmiRkSnoKqJl4B8QgYJQRMsgF+5atAmCkGhTCVFEbaRWBSK1KiNEVEjcGOWPz5fugdPjPt+8mhkJ5sB3zpnvPXPOmTP33rl1dYUUHSg68J92oL5K3fcZ7wXV/GJhrkHejQ3EuMYY6bjL2HvAY9Dt+DfYT8EyUIwm0AZOgkNAMvdbpXsdJ9xGwApaiWOiop4A+e6POVTidlQaKOOPuPuX2ComJr8g1b1ZMB9zqMQlKWQ3D59wASadHTPXId/FBv6VO08A+yzSpQQBGxL4/OGSpCM97omP2J/dvcwDYBE06ybImhlpaiW3joyVBdaLPABvy/iab6st3xIRtSxNNAGPAa2aDjAAzoBhkKkMEd26sZW2vSOzYh65Ql5jd4JTQJ24AbRcP4BMRZ9NO6d14mok2wzc9QifKqU3tyKk/aZmiZYq8Daeir5FFCvkWySiVsxIhE+d0u5ohdxLPXrCgHvx06ZkhVxM+FzqbpdcEfp3qLC/FZ1lNPFNdpmRRL/AyboxneSBMh8Vfge8At/BOXAYTAG9mHbjqtKPhxUhPQdqOlvgvxMcB6tAR4ajQEt9FPwE+jdtKZ8Y9UWYrflSa2cOhljP0e9BO9CvQbF0wstNrpBJL6LddzBk7QnczXCfi3oYkj5z2W4HTmfbXESbnXbdH6DVZdR/SZPXryI3nL6po4I+i36aJprwxu3DvmAD0qo8Czkbgk644F3B/oLWZ/vqxjIztQ9pmba4DKex1ZEF0Of4bTFLZM1tfmzLGxZJiw7k1oFNRcOCfYg3LYMAAAAASUVORK5CYII=\" width=\"17\" height=\"20\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19.5\" height=\"20\" style=\"width: 19.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e For example,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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width=\"43.5\" height=\"20\" style=\"width: 43.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"43.5\" height=\"20\" style=\"width: 43.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e both divide \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"33\" height=\"18\" style=\"width: 33px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eSince. the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"33\" height=\"18\" style=\"width: 33px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e may become large even if the values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e are relatively small, please output a vector containing the number of digits and the last \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);\"\u003e6\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e digits of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"33\" height=\"18\" style=\"width: 33px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. Therefore, in the example above the output of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"65.5\" height=\"19\" style=\"width: 65.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, which has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);\"\u003e4\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e digits, should be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"58\" height=\"19\" style=\"width: 58px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = LCF(n,m)\r\n  y = x;\r\nend","test_suite":"%%\r\nn = 3; m = 4;\r\ny_correct = [4 6765];\r\nassert(isequal(LCF(n,m),y_correct))\r\n%%\r\nn = 31; m = 61;\r\ny_correct = [207 308229];\r\nassert(isequal(LCF(n,m),y_correct))\r\n%%\r\nn = 123; m = 456;\r\ny_correct = [11843 575091];\r\nassert(isequal(LCF(n,m),y_correct))\r\n%%\r\nn = 999; m = 99999;\r\ny_correct = [20899 746875];\r\nassert(isequal(LCF(n,m),y_correct))\r\n%%\r\nn = 98765; m = 43210;\r\ny_correct = [891912775 944568];\r\nassert(isequal(LCF(n,m),y_correct))\r\n%%\r\nn = double(intmax); m = 12345;\r\ny_correct = [2770427214858 134203];\r\nassert(isequal(LCF(n,m),y_correct))\r\n%%\r\nns = floor(double(intmax)./(1:100));\r\nys = arrayfun(@(i) log10(sum(LCF(ns(i-1),i))),2:101);\r\nss = round([sum(ys) mean(ys) median(ys) mode(ys) std(ys)],4);\r\nss_correct = [842.8233 8.4282 8.6618 7.1199 0.3808];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('LCF.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-21T07:09:35.000Z","updated_at":"2026-09-24T12:42:48.000Z","published_at":"2021-10-21T11:42:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Fibonacci sequence \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a series whose elements are numbers starting with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_{1} =1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_{2} =2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and subsequent \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Fibonacci_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eFibonacci numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e are defined recursively: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_{n} =F_{n-1}+F_{n-2} \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The first 20 Fibonacci numbers are:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{1, \\t2, \\t3, \\t5, \\t8, \\t13, \\t21, \\t34, \\t55, \\t89, \\t144, \\t233, \\t377, \\t610, \\t987, \\t1597, \\t2584, \\t4181, \\t6765, 10946\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven two indices \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, write a program to return the least common Fibonacci number, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eLCF(n,m)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, which is defined as the smallest Fibonacci number divisible by both \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_{n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_{m}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e For example,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eLCF(3,4)=6765\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, which is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_{19}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, since \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_{3}=3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_{4}=5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e both divide \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e6765\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince. the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eLCF\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e may become large even if the values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are relatively small, please output a vector containing the number of digits and the last \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e digits of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eLCF\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore, in the example above the output of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eLCF(3,4)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, which has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e digits, should be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[4\\\\  6765]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1917,"title":"click away","description":"Write a function that clicks on a GUI button.\r\n\r\n*Description*:\r\n\r\nSome times one wishes to use Matlab to automate some time consuming repetitive process that requires filling fields or clicking buttons on the screen. Matlab offers a simple way to control the cursor position (e.g. |set(0,'pointerlocation',...)|, but it is not so clear how one would perform mouse or keyboard clicks.\r\n\r\nThis problem creates a simple message box:\r\n\r\n msgbox('Click the OK button','')\r\n\r\nwhich displays the above message and an 'OK' button. \r\n\r\nYour function just needs to actually click on the OK button (or use equivalent keyboard shortcuts) to pass this problem. Simple, right?\r\n\r\n","description_html":"\u003cp\u003eWrite a function that clicks on a GUI button.\u003c/p\u003e\u003cp\u003e\u003cb\u003eDescription\u003c/b\u003e:\u003c/p\u003e\u003cp\u003eSome times one wishes to use Matlab to automate some time consuming repetitive process that requires filling fields or clicking buttons on the screen. Matlab offers a simple way to control the cursor position (e.g. \u003ctt\u003eset(0,'pointerlocation',...)\u003c/tt\u003e, but it is not so clear how one would perform mouse or keyboard clicks.\u003c/p\u003e\u003cp\u003eThis problem creates a simple message box:\u003c/p\u003e\u003cpre\u003e msgbox('Click the OK button','')\u003c/pre\u003e\u003cp\u003ewhich displays the above message and an 'OK' button.\u003c/p\u003e\u003cp\u003eYour function just needs to actually click on the OK button (or use equivalent keyboard shortcuts) to pass this problem. Simple, right?\u003c/p\u003e","function_template":"function y = clickOK()\r\nend","test_suite":"%%\r\nh=msgbox('Click the OK button','');\r\nclickOK();\r\nassert(ishandle(h),'do not simply delete the figure');\r\ndrawnow;\r\nassert(~ishandle(h),'failed to click the OK button');\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":29,"created_by":43,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2013-10-06T17:23:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-10-06T06:04:42.000Z","updated_at":"2026-09-24T15:38:05.000Z","published_at":"2013-10-06T08:41:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that clicks on a GUI button.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDescription\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSome times one wishes to use Matlab to automate some time consuming repetitive process that requires filling fields or clicking buttons on the screen. Matlab offers a simple way to control the cursor position (e.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eset(0,'pointerlocation',...)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, but it is not so clear how one would perform mouse or keyboard clicks.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem creates a simple message box:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ msgbox('Click the OK button','')]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhich displays the above message and an 'OK' button.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour function just needs to actually click on the OK button (or use equivalent keyboard shortcuts) to pass this problem. Simple, right?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1000,"title":"Image Processing 004: Zernike Coefficients","description":"*Fit Zernike Terms to a wavefront.*\r\n\r\nThe class notes of \u003chttp://www.visualopticslab.com/OPTI535/Lectures/Class06_08.pdf Schwiegerling UofA\u003e on ANSI Standard Zernike terms is the basis for this challenge.  Pages 13 and 14 give the term definitions implemented in the zern_data_v01.m routine provided in the function template.\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/_/rsrc/1350774824076/matlab_cody/Zernike_UA_480.jpg\u003e\u003e\r\n\r\n\r\nANSI Standard Zernike Chart:\r\n\r\n\r\n\r\n*Algorithm Description:*\r\n\r\n  M=surface array to be fit by Zernike terms; \r\n  -valid data is circle of normalized radius\u003c=1\r\n  Use the R and T arrays to create the A array\r\n  R=radial normalized distance from center of array\r\n  T=angular radian value from center of array\r\n  A=fitting array [valid_data_pts,terms]\r\n\r\n  Create A * z_fit = M(valid_data_pts)\r\n  [valid_pts,terms] * [terms,1] = [valid_pts,1]\r\n\r\n  Loop term=0:terms-1\r\n  - Create the 2-D array of z-terms uisng z=zern_data_v01(term,R,T)\r\n  - A(:,term+1) = z(valid_data_pts)\r\n  End Loop\r\n  \r\n  Solve for z_fit: pinv(A)*M(valid_pts)  or A\\M(valid_pts)\r\n\r\n*Inputs:* [M N R T] where N is number of Zernike terms for fit\r\n\r\n*Outputs:* [v] Zernike fit vector of length N\r\n\r\nCreation of the M surface and expected v fit vector can be seen in the Test Suite.\r\n\r\n\r\n\r\n\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 888.85px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 444.433px; transform-origin: 407px 444.433px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109.15px 7.91667px; transform-origin: 109.15px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFit Zernike Terms to a wavefront.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.7833px 7.91667px; transform-origin: 56.7833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe class notes of\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://www.visualopticslab.com/OPTI535/Lectures/Class06_08.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSchwiegerling UofA\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 253.6px 7.91667px; transform-origin: 253.6px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e on ANSI Standard Zernike terms is the basis for this challenge. Pages 13 and 14 give the term definitions implemented in the zern_data_v01.m routine provided in the function template.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 319.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 159.967px; text-align: center; transform-origin: 384px 159.967px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.9667px 7.91667px; transform-origin: 92.9667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eANSI Standard Zernike Chart:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75.8333px 7.91667px; transform-origin: 75.8333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eAlgorithm Description:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 326.933px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 163.467px; transform-origin: 404px 163.467px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 169.4px 7.91667px; transform-origin: 169.4px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 61.6px 7.91667px; transform-origin: 61.6px 7.91667px; \"\u003eM=surface array \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 100.1px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 100.1px 7.91667px; \"\u003eto be fit by Zernike terms\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; \"\u003e; \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 173.25px 7.91667px; transform-origin: 173.25px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 46.2px 7.91667px; transform-origin: 46.2px 7.91667px; \"\u003e-valid data \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 127.05px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 127.05px 7.91667px; \"\u003eis circle of normalized radius\u0026lt;=1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 169.4px 7.91667px; transform-origin: 169.4px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; \"\u003eUse \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 154px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 154px 7.91667px; \"\u003ethe R and T arrays to create the A array\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 188.65px 7.91667px; transform-origin: 188.65px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 77px 7.91667px; transform-origin: 77px 7.91667px; \"\u003eR=radial normalized \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 111.65px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 111.65px 7.91667px; \"\u003edistance from center of array\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 165.55px 7.91667px; transform-origin: 165.55px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 65.45px 7.91667px; transform-origin: 65.45px 7.91667px; \"\u003eT=angular radian \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 100.1px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 100.1px 7.91667px; \"\u003evalue from center of array\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 146.3px 7.91667px; transform-origin: 146.3px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 61.6px 7.91667px; transform-origin: 61.6px 7.91667px; \"\u003eA=fitting array \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 84.7px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 84.7px 7.91667px; \"\u003e[valid_data_pts,terms]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 138.6px 7.91667px; transform-origin: 138.6px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 26.95px 7.91667px; transform-origin: 26.95px 7.91667px; \"\u003eCreate \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 111.65px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 111.65px 7.91667px; \"\u003eA * z_fit = M(valid_data_pts)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 173.25px 7.91667px; transform-origin: 173.25px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e[valid_pts,terms] * [terms,1] = [valid_pts,1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 73.15px 7.91667px; transform-origin: 73.15px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 19.25px 7.91667px; transform-origin: 19.25px 7.91667px; \"\u003eLoop \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 53.9px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 53.9px 7.91667px; \"\u003eterm=0:terms-1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 250.25px 7.91667px; transform-origin: 250.25px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 7.91667px; transform-origin: 50.05px 7.91667px; \"\u003e- Create the \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 200.2px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 200.2px 7.91667px; \"\u003e2-D array of z-terms uisng z=zern_data_v01(term,R,T)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 127.05px 7.91667px; transform-origin: 127.05px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e- A(:,term+1) = z(valid_data_pts)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 7.91667px; transform-origin: 30.8px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; \"\u003eEnd \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 15.4px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 15.4px 7.91667px; \"\u003eLoop\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 215.6px 7.91667px; transform-origin: 215.6px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 23.1px 7.91667px; transform-origin: 23.1px 7.91667px; \"\u003eSolve \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 119.35px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 119.35px 7.91667px; \"\u003efor z_fit: pinv(A)*M(valid_pts)\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; \"\u003e  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 65.45px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 65.45px 7.91667px; \"\u003eor A\\M(valid_pts)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.3333px 7.91667px; transform-origin: 23.3333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInputs:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 162.55px 7.91667px; transform-origin: 162.55px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e [M N R T] where N is number of Zernike terms for fit\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.1667px 7.91667px; transform-origin: 29.1667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutputs:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.7833px 7.91667px; transform-origin: 98.7833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e [v] Zernike fit vector of length N\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 250.083px 7.91667px; transform-origin: 250.083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCreation of the M surface and expected v fit vector can be seen in the Test Suite.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function v = Zernike_Fit(M,N,R,T)\r\n% M surface array\r\n% N Number of Zernike terms for fit  0:N-1\r\n% R Radial distance from center of M array for each M location\r\n% T angle from center of M array to each M location\r\n  v=zeros(N,1);\r\nend\r\n\r\n% The function zern_data_v01 has been loaded and rehashed\r\n% z = zern_data_v01(j,r,t) % is sufficient in the main routine\r\n\r\n%% zern_data_v01.m\r\n% Author: Team\r\n% function to create a zernike polynomial\r\n% Using ANSI standard zernikes\r\n\r\n% input\r\n%  j = term #\r\n%  r = normalized radial vector\r\n%  t = theta\r\n\r\nfunction z = zern_data_v01(j,r,t)\r\n\r\n    % Convert single index term to standard\r\n    n= ceil((sqrt(9+8*j)-1)/2)-1; % 0-0; 2-1; 5-2; 9-3; ...\r\n    m= 2*j-n*(n+2);\r\n    \r\n    % zernike term\r\n   \r\n    z = r*0; %zeros(size(r));\r\n        \r\n        % radial component\r\n    for s = 0:(n-abs(m))/2\r\n     z = z + (-1)^s * factorial(n-s) * r.^(n-2*s) ./ ...\r\n        (factorial(s) * factorial((n+abs(m))/2 - s) * factorial((n-abs(m))/2 - s));\r\n    end\r\n        \r\n        % angular component\r\n    z = z .* ((m\u003e=0)*cos(m*t) - (m\u003c0)*sin(m*t));\r\n    \r\n    % normalization\r\n    z = z * sqrt(2*(n+1)/(1+(m==0)));\r\n    \r\n    % value added processing\r\n    z = z .* (r\u003c=1);\r\n    \r\nend\r\n\r\n","test_suite":"fname='https://sites.google.com/site/razapor/matlab_cody/zern_data_v01.m?attredirects=0\u0026d=1';\r\nurlwrite(fname,'zern_data_v01.m')\r\n%urlwrite('http://tinyurl.com/matlab-zernike','zern_data_v01.m')\r\nrehash path\r\n% z = zern_data_v01(j,r,t) % is sufficient in the main routine\r\n%%\r\nM=zeros(256);\r\nterms=6; % Number of Terms to fit  0:terms-1\r\n% Test Suite portion using zern_data_v01\r\n[ ydim xdim ] = size(M);\r\nx = linspace(-1,1,xdim);\r\ny = linspace(1,-1,ydim);\r\n[X Y] = meshgrid(x,y);\r\nR = sqrt(X.^2 + Y.^2);\r\nT = atan2(Y,X);\r\n% Create surface\r\nz_fit=zeros(terms,1); % Map 0:9 to 1:10\r\nz_fit(2)=1.0;\r\n\r\n% Build a Surface\r\nM = M +  zern_data_v01(0,R,T); % Force NaN for non-data\r\nM(M==0)=NaN;\r\nM(M\u003e0)=0;\r\nfor term = 0:terms-1\r\n M = M + z_fit(term+1) * zern_data_v01(term,R,T);\r\n% figure(3);imagesc(data_fit) % Visualization\r\n% pause (0.5)\r\nend\r\n\r\n% Data is a circle\r\n% Non-data is assigned NaN\r\n\r\ntic\r\nv = Zernike_Fit(M,terms,R,T)\r\ntoc\r\nassert(max(abs(v-z_fit))\u003c0.01,sprintf('v=%i %i %i %i %i %i',v))\r\n\r\n\r\n%%\r\nM=zeros(256);\r\nterms=10; % Number of Terms to fit  0:terms-1\r\n% Test Suite portion using zern_data_v01\r\n[ ydim xdim ] = size(M);\r\nx = linspace(-1,1,xdim);\r\ny = linspace(1,-1,ydim);\r\n[X Y] = meshgrid(x,y);\r\nR = sqrt(X.^2 + Y.^2);\r\nT = atan2(Y,X);\r\n\r\n% Create surface\r\nz_fit= round(2*rand(terms,1)-1).*rand(terms,1);\r\n\r\n% Build a Surface\r\nM = M +  zern_data_v01(0,R,T); % Force NaN for non-data\r\nM(M==0)=NaN;\r\nM(M\u003e0)=0;\r\nfor term = 0:terms-1\r\n M = M + z_fit(term+1) * zern_data_v01(term,R,T);\r\n% figure(3);imagesc(data_fit) % Visualization\r\n% pause (0.5)\r\nend\r\n\r\ntic\r\nv = Zernike_Fit(M,terms,R,T)\r\ntoc\r\nassert(max(abs(v-z_fit))\u003c0.01)\r\n\r\n\r\n%%\r\nM=zeros(128);\r\nterms=15; % Number of Terms to fit  0:terms-1\r\n% Test Suite portion using zern_data_v01\r\n[ ydim xdim ] = size(M);\r\nx = linspace(-1,1,xdim);\r\ny = linspace(1,-1,ydim);\r\n[X Y] = meshgrid(x,y);\r\nR = sqrt(X.^2 + Y.^2);\r\nT = atan2(Y,X);\r\n\r\n% Create surface\r\nz_fit= round(2*rand(terms,1)-1).*rand(terms,1);\r\n\r\n% Build a Surface\r\nM = M +  zern_data_v01(0,R,T); % Force NaN for non-data\r\nM(M==0)=NaN;\r\nM(M\u003e0)=0;\r\nfor term = 0:terms-1\r\n M = M + z_fit(term+1) * zern_data_v01(term,R,T);\r\n% figure(3);imagesc(data_fit) % Visualization\r\n% pause (0.5)\r\nend\r\n\r\ntic\r\nv = Zernike_Fit(M,terms,R,T)\r\ntoc\r\nassert(max(abs(v-z_fit))\u003c0.01)\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":5,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2020-09-29T23:07:58.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2012-10-18T13:25:52.000Z","updated_at":"2026-09-24T16:53:35.000Z","published_at":"2012-10-21T01:08:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFit Zernike Terms to a wavefront.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe class notes of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.visualopticslab.com/OPTI535/Lectures/Class06_08.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSchwiegerling UofA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e on ANSI Standard Zernike terms is the basis for this challenge. Pages 13 and 14 give the term definitions implemented in the zern_data_v01.m routine provided in the function template.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eANSI Standard Zernike Chart:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAlgorithm Description:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[M=surface array to be fit by Zernike terms; \\n-valid data is circle of normalized radius\u003c=1\\nUse the R and T arrays to create the A array\\nR=radial normalized distance from center of array\\nT=angular radian value from center of array\\nA=fitting array [valid_data_pts,terms]\\n\\nCreate A * z_fit = M(valid_data_pts)\\n[valid_pts,terms] * [terms,1] = [valid_pts,1]\\n\\nLoop term=0:terms-1\\n- Create the 2-D array of z-terms uisng z=zern_data_v01(term,R,T)\\n- A(:,term+1) = z(valid_data_pts)\\nEnd Loop\\n\\nSolve for z_fit: pinv(A)*M(valid_pts)  or A\\\\M(valid_pts)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [M N R T] where N is number of Zernike terms for fit\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [v] Zernike fit vector of length N\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreation of the M surface and expected v fit vector can be seen in the Test 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46838,"title":"The most decentralized RGB colors","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 222px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 111px; transform-origin: 407px 111px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eInput number of colors and try to find the most decentralized combination.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor n=1, any color is OK.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor n=2, the 2 colors should have an euclidean distance of sqrt(255^2*3), such as [0 0 0] and [255 255 255].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor n=3, the 3 colors have 3 distances. We measure the smallest one, which should be sqrt(255^2*2). One possible combination may be [255 255 255;255 0 0;0 0 255].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor n=8, apparently we capture the 8 vertecies of the cube, the smallest distance is 255.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThen, more?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYour function should return a n×3 matrix with each row represent an RGB color.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Colors=ColorDistribute(N)\r\nColors=[0 0 0];\r\nend","test_suite":"%%\r\nassert(MinDistance(ColorDistribute(1),1)\u003e=500);\r\nfunction Md=MinDistance(ColorMatrix,NumberOfColors)\r\narguments\r\n    ColorMatrix(:,3)uint8\r\n\tNumberOfColors(1,1)uint8\r\nend\r\nMd=500;\r\nColorMatrix=double(ColorMatrix);\r\nfor a=1:NumberOfColors-1\r\n    Color1=ColorMatrix(a,:);\r\n    for b=a+1:NumberOfColors\r\n        Md=min(Md,norm(Color1-ColorMatrix(b,:)));\r\n    end\r\nend\r\nend\r\n%%\r\nassert(MinDistance(ColorDistribute(2),2)\u003e441);\r\nfunction Md=MinDistance(ColorMatrix,NumberOfColors)\r\narguments\r\n    ColorMatrix(:,3)uint8\r\n\tNumberOfColors(1,1)uint8\r\nend\r\nMd=500;\r\nColorMatrix=double(ColorMatrix);\r\nfor a=1:NumberOfColors-1\r\n    Color1=ColorMatrix(a,:);\r\n    for b=a+1:NumberOfColors\r\n        Md=min(Md,norm(Color1-ColorMatrix(b,:)));\r\n    end\r\nend\r\nend\r\n%%\r\nassert(MinDistance(ColorDistribute(3),3)\u003e360);\r\nfunction Md=MinDistance(ColorMatrix,NumberOfColors)\r\narguments\r\n    ColorMatrix(:,3)uint8\r\n\tNumberOfColors(1,1)uint8\r\nend\r\nMd=500;\r\nColorMatrix=double(ColorMatrix);\r\nfor a=1:NumberOfColors-1\r\n    Color1=ColorMatrix(a,:);\r\n    for b=a+1:NumberOfColors\r\n        Md=min(Md,norm(Color1-ColorMatrix(b,:)));\r\n    end\r\nend\r\nend\r\n%%\r\nassert(MinDistance(ColorDistribute(4),4)\u003e360);\r\nfunction Md=MinDistance(ColorMatrix,NumberOfColors)\r\narguments\r\n    ColorMatrix(:,3)uint8\r\n\tNumberOfColors(1,1)uint8\r\nend\r\nMd=500;\r\nColorMatrix=double(ColorMatrix);\r\nfor a=1:NumberOfColors-1\r\n    Color1=ColorMatrix(a,:);\r\n    for b=a+1:NumberOfColors\r\n        Md=min(Md,norm(Color1-ColorMatrix(b,:)));\r\n    end\r\nend\r\nend\r\n%%\r\nassert(MinDistance(ColorDistribute(5),5)\u003e284);\r\nfunction Md=MinDistance(ColorMatrix,NumberOfColors)\r\narguments\r\n    ColorMatrix(:,3)uint8\r\n\tNumberOfColors(1,1)uint8\r\nend\r\nMd=500;\r\nColorMatrix=double(ColorMatrix);\r\nfor a=1:NumberOfColors-1\r\n    Color1=ColorMatrix(a,:);\r\n    for b=a+1:NumberOfColors\r\n        Md=min(Md,norm(Color1-ColorMatrix(b,:)));\r\n    end\r\nend\r\nend\r\n%%\r\nassert(MinDistance(ColorDistribute(6),6)\u003e266);\r\nfunction Md=MinDistance(ColorMatrix,NumberOfColors)\r\narguments\r\n    ColorMatrix(:,3)uint8\r\n\tNumberOfColors(1,1)uint8\r\nend\r\nMd=500;\r\nColorMatrix=double(ColorMatrix);\r\nfor a=1:NumberOfColors-1\r\n    Color1=ColorMatrix(a,:);\r\n    for b=a+1:NumberOfColors\r\n        Md=min(Md,norm(Color1-ColorMatrix(b,:)));\r\n    end\r\nend\r\nend\r\n%%\r\nassert(MinDistance(ColorDistribute(7),7)\u003e255);\r\nfunction Md=MinDistance(ColorMatrix,NumberOfColors)\r\narguments\r\n    ColorMatrix(:,3)uint8\r\n\tNumberOfColors(1,1)uint8\r\nend\r\nMd=500;\r\nColorMatrix=double(ColorMatrix);\r\nfor a=1:NumberOfColors-1\r\n    Color1=ColorMatrix(a,:);\r\n    for b=a+1:NumberOfColors\r\n        Md=min(Md,norm(Color1-ColorMatrix(b,:)));\r\n    end\r\nend\r\nend\r\n%%\r\nassert(MinDistance(ColorDistribute(8),8)\u003e=255);\r\nfunction Md=MinDistance(ColorMatrix,NumberOfColors)\r\narguments\r\n    ColorMatrix(:,3)uint8\r\n\tNumberOfColors(1,1)uint8\r\nend\r\nMd=500;\r\nColorMatrix=double(ColorMatrix);\r\nfor a=1:NumberOfColors-1\r\n    Color1=ColorMatrix(a,:);\r\n    for b=a+1:NumberOfColors\r\n        Md=min(Md,norm(Color1-ColorMatrix(b,:)));\r\n    end\r\nend\r\nend\r\n%%\r\nassert(MinDistance(ColorDistribute(9),9)\u003e=219);\r\nfunction Md=MinDistance(ColorMatrix,NumberOfColors)\r\narguments\r\n    ColorMatrix(:,3)uint8\r\n\tNumberOfColors(1,1)uint8\r\nend\r\nMd=500;\r\nColorMatrix=double(ColorMatrix);\r\nfor a=1:NumberOfColors-1\r\n    Color1=ColorMatrix(a,:);\r\n    for b=a+1:NumberOfColors\r\n        Md=min(Md,norm(Color1-ColorMatrix(b,:)));\r\n    end\r\nend\r\nend\r\n%%\r\nassert(MinDistance(ColorDistribute(64),64)\u003e=85);\r\nfunction Md=MinDistance(ColorMatrix,NumberOfColors)\r\narguments\r\n    ColorMatrix(:,3)uint8\r\n\tNumberOfColors(1,1)uint8\r\nend\r\nMd=500;\r\nColorMatrix=double(ColorMatrix);\r\nfor a=1:NumberOfColors-1\r\n    Color1=ColorMatrix(a,:);\r\n    for b=a+1:NumberOfColors\r\n        Md=min(Md,norm(Color1-ColorMatrix(b,:)));\r\n    end\r\nend\r\nend","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":362068,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-17T04:34:30.000Z","updated_at":"2026-09-22T12:08:38.000Z","published_at":"2020-10-17T04:34:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput number of colors and try to find the most decentralized combination.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor n=1, any color is OK.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor n=2, the 2 colors should have an euclidean distance of sqrt(255^2*3), such as [0 0 0] and [255 255 255].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor n=3, the 3 colors have 3 distances. We measure the smallest one, which should be sqrt(255^2*2). One possible combination may be [255 255 255;255 0 0;0 0 255].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor n=8, apparently we capture the 8 vertecies of the cube, the smallest distance is 255.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen, more?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour function should return a n×3 matrix with each row represent an RGB color.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54275,"title":"Get twenty-four","description":"Inpur four integers in 1 to 10, you may use plus, minus, multiply and divid to get 24. Note that every integer should be used once and only once. Brackets are of no limit, and the result should exactly be 24 once you calculate by hand. (Calculation in computer will lead to a tolerance to the computer precision.) \r\nYou need to return a format and a vector with the same four integers, such that you can print the expression.\r\nE.g., input                            x = [5 5 7 7]\r\n        you may return            f  = '(%d*%d)-(%d/%d)'\r\n                     and                 z = [5 5 7 7]\r\n      so  24 is obatined by     eval(sprintf(f,z)).\r\n     The answer is not necessary unique, e.g., other acceptable answers are\r\n                                            f  = '(%d*%d)-(%d*%d)'  \r\n                                            z =  [7 7 5 5]\r\n                   and                   f = '(%d-%d)*(%d+%d)'\r\n                                            z = [7 5 7 5]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 363px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 181.5px; transform-origin: 407px 181.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInpur four integers in 1 to 10, you may use plus, minus, multiply and divid to get 24. Note that every integer should be used once and only once. Brackets are of no limit, and the result should exactly be 24 once you calculate by hand. (Calculation in computer will lead to a tolerance to the computer precision.) \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou need to return a format and a vector with the same four integers, such that you can print the expression.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eE.g., input                            x = [5 5 7 7]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        you may return            f  = '(%d*%d)-(%d/%d)'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                     and                 z = [5 5 7 7]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e      so  24 is obatined by     eval(sprintf(f,z)).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e     The answer is not necessary unique, e.g., other acceptable answers are\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                            f  = '(%d*%d)-(%d*%d)'  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                            z =  [7 7 5 5]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                   and                   f = '(%d-%d)*(%d+%d)'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                            z = [7 5 7 5]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [f,z] = get24(x)\r\n  z = 23;\r\n  f = '(%d%d+%s%s)'\r\nend","test_suite":"%%\r\nx = [1 2 3 4];\r\ntry \r\n    [f,z] = get24(x);\r\n    s = sprintf(f,z); s(s\u003e'9'|s\u003c'0')=' '; assert(length(str2num(s))==4);    \r\n    assert(ischar(f));\r\n    assert(all( sort(z)==sort(x) ));\r\n    assert(length(f(f=='-'|f=='+'|f=='*'|f=='/'))==3);\r\n    assert( abs( eval(sprintf(f,z))-24 )\u003c=1e-8 );\r\n    w = f(f~='('\u0026f~=')'\u0026f~='+'\u0026f~='-'\u0026f~='*'\u0026f~='/'\u0026f~='%'\u0026f~='s'\u0026f~='d');\r\n    assert(isempty(w),'unusual format character!');\r\ncatch\r\n    assert(false,'no result or something wrong!');\r\nend\r\n%%\r\nx = [6 9 9 10];\r\ntry \r\n    [f,z] = get24(x);\r\n    s = sprintf(f,z); s(s\u003e=9'|s\u003c'0')=' '; assert(length(str2num(s))==4);    \r\n    assert(ischar(f));\r\n    assert(all( sort(z)==sort(x) ));\r\n    assert(length(f(f=='-'|f=='+'|f=='*'|f=='/'))==3);\r\n    assert( abs( eval(sprintf(f,z))-24 )\u003c=1e-8 );\r\n    w = f(f~='('\u0026f~=')'\u0026f~='+'\u0026f~='-'\u0026f~='*'\u0026f~='/'\u0026f~='%'\u0026f~='s'\u0026f~='d');\r\n    assert(isempty(w),'unusual format character!');\r\ncatch\r\n    assert(false,'no result or something wrong!');\r\nend\r\n%%\r\nx = [4 4 10 10];\r\ntry \r\n    [f,z] = get24(x);\r\n    s = sprintf(f,z); s(s\u003e'9'|s\u003c'0')=' '; assert(length(str2num(s))==4);    \r\n    assert(ischar(f));\r\n    assert(all( sort(z)==sort(x) ));\r\n    assert(length(f(f=='-'|f=='+'|f=='*'|f=='/'))==3);\r\n    assert( abs( eval(sprintf(f,z))-24 )\u003c=1e-8 );\r\n    w = f(f~='('\u0026f~=')'\u0026f~='+'\u0026f~='-'\u0026f~='*'\u0026f~='/'\u0026f~='%'\u0026f~='s'\u0026f~='d');\r\n    assert(isempty(w),'unusual format character!');\r\ncatch\r\n    assert(false,'no result or something wrong!');\r\nend\r\n%%\r\nx = [3 3 7 7];\r\ntry \r\n    [f,z] = get24(x);\r\n    s = sprintf(f,z); s(s\u003e'9'|s\u003c'0')=' '; assert(length(str2num(s))==4);    \r\n    assert(ischar(f));\r\n    assert(all( sort(z)==sort(x) ));\r\n    assert(length(f(f=='-'|f=='+'|f=='*'|f=='/'))==3);\r\n    assert( abs( eval(sprintf(f,z))-24 )\u003c=1e-8 );\r\n    w = f(f~='('\u0026f~=')'\u0026f~='+'\u0026f~='-'\u0026f~='*'\u0026f~='/'\u0026f~='%'\u0026f~='s'\u0026f~='d');\r\n    assert(isempty(w),'unusual format character!');\r\ncatch\r\n    assert(false,'no result or something wrong!');\r\nend\r\n%%\r\nx = [1 4 5 6];\r\ntry \r\n    [f,z] = get24(x);\r\n    s = sprintf(f,z); s(s\u003e'9'|s\u003c'0')=' '; assert(length(str2num(s))==4);    \r\n    assert(ischar(f));\r\n    assert(all( sort(z)==sort(x) ));\r\n    assert(length(f(f=='-'|f=='+'|f=='*'|f=='/'))==3);\r\n    assert( abs( eval(sprintf(f,z))-24 )\u003c=1e-8 );\r\n    w = f(f~='('\u0026f~=')'\u0026f~='+'\u0026f~='-'\u0026f~='*'\u0026f~='/'\u0026f~='%'\u0026f~='s'\u0026f~='d');\r\n    assert(isempty(w),'unusual format character!');\r\ncatch\r\n    assert(false,'no result or something wrong!');\r\nend","published":true,"deleted":false,"likes_count":0,"comments_count":3,"created_by":2197980,"edited_by":2197980,"edited_at":"2024-08-29T05:32:43.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2024-08-29T05:32:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-04-13T12:52:09.000Z","updated_at":"2026-09-26T12:16:40.000Z","published_at":"2022-04-13T12:52:22.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInpur four integers in 1 to 10, you may use plus, minus, multiply and divid to get 24. Note that every integer should be used once and only once. Brackets are of no limit, and the result should exactly be 24 once you calculate by hand. (Calculation in computer will lead to a tolerance to the computer precision.) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou need to return a format and a vector with the same four integers, such that you can print the expression.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eE.g., input                            x = [5 5 7 7]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        you may return            f  = '(%d*%d)-(%d/%d)'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                     and                 z = [5 5 7 7]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e      so  24 is obatined by     eval(sprintf(f,z)).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e     The answer is not necessary unique, e.g., other acceptable answers are\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                            f  = '(%d*%d)-(%d*%d)'  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                            z =  [7 7 5 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                   and                   f = '(%d-%d)*(%d+%d)'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                            z = [7 5 7 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46691,"title":"Kaggle: Planetoid Game of Life - Solve 40 non-trivial Puzzles","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 482.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 241.083px; transform-origin: 407px 241.083px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.kaggle.com/c/conways-reverse-game-of-life-2020\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eKaggle's Conway's Reverse Game of Life 2020 \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 203.05px 7.91667px; transform-origin: 203.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003econtest inspires this Life challenge. The kaggle contest runs from Oct-01-2020 thru Nov-30-2020. References:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://mathworld.wolfram.com/GameofLife.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eGame of Life at Wolfram\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWiki Life\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 138.467px 7.91667px; transform-origin: 138.467px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The Kaggle event is 50K cases to solve for a state 1 to 5 iterations prior to a given state. Imperfect solutions are allowed but penalized. Input file to Kaggle is a csv so Matlab solutions can be posted at the Kaggle site for this event.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 7.91667px; transform-origin: 384px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis Challenge is to Solve at least 40, excluding trivials, of the 50K puzzles per these revised Life Laws. Trivial solutions are where the Final state may match the Start State.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 51.0833px; transform-origin: 404px 51.0833px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 350.35px 7.91667px; transform-origin: 350.35px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 26.95px 7.91667px; transform-origin: 26.95px 7.91667px; \"\u003e1. Any \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 188.65px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 188.65px 7.91667px; \"\u003elive cell with fewer than two live neighbors dies\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 19.25px 7.91667px; transform-origin: 19.25px 7.91667px; \"\u003e, as \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 115.5px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 115.5px 7.91667px; \"\u003eif caused by under-population.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 315.7px 7.91667px; transform-origin: 315.7px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 26.95px 7.91667px; transform-origin: 26.95px 7.91667px; \"\u003e2. Any \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 288.75px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 288.75px 7.91667px; \"\u003elive cell with two or three live neighbors lives on to the next generation.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 311.85px 7.91667px; transform-origin: 311.85px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 26.95px 7.91667px; transform-origin: 26.95px 7.91667px; \"\u003e3. Any \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 192.5px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 192.5px 7.91667px; \"\u003elive cell with more than three live neighbors dies\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 19.25px 7.91667px; transform-origin: 19.25px 7.91667px; \"\u003e, as \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 73.15px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 73.15px 7.91667px; \"\u003eif by overcrowding.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 361.9px 7.91667px; transform-origin: 361.9px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 26.95px 7.91667px; transform-origin: 26.95px 7.91667px; \"\u003e4. Any \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 242.55px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 242.55px 7.91667px; \"\u003edead cell with exactly three live neighbors becomes a live cell\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 19.25px 7.91667px; transform-origin: 19.25px 7.91667px; \"\u003e, as \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 73.15px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 73.15px 7.91667px; \"\u003eif by reproduction.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 265.65px 7.91667px; transform-origin: 265.65px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 34.65px 7.91667px; transform-origin: 34.65px 7.91667px; \"\u003e5. Edges \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 231px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 231px 7.91667px; \"\u003ewrap around. Eight Neighbors. (Change to normal planar life)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 221.317px 7.91667px; transform-origin: 221.317px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNote: The edges wrap so the matrix represents the surface of a sphere.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4333px 7.91667px; transform-origin: 19.4333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 354.317px 7.91667px; transform-origin: 354.317px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (mtest,numtosolve) the Finish state matrix of 50K rows of [casenumber, iterations, 625 values], number of case to solve (40)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.2667px 7.91667px; transform-origin: 25.2667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 339.533px 7.91667px; transform-origin: 339.533px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (mstart) the Starting state matrix of at least 40 puzzles all with perfect zero error solutions, [casenumber, 625 values]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.95px 7.91667px; transform-origin: 15.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHint:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 364.467px 7.91667px; transform-origin: 364.467px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e There are 40 non-trivial solutions for iterations 1 and 2 where a solving Start state has a single bit flip that is adjacent to a set bit or is a set bit. Cases where there are more than 40 set bits in the final state may consume significant time for no solutions. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function mstart = solveLife(mtest,numtosolve)\r\n  mstart=zeros(numtosolve,626)\r\nend","test_suite":"%%\r\n%'https://sites.google.com/site/razapor/matlab_cody/mtest.mat?attredirects=0\u0026d=1';\r\n%mtest format is [casenumer, iterations, start1:625,finish1:625] for 50K cases 0:49999\r\n%'https://sites.google.com/site/razapor/matlab_cody/mtrain.mat?attredirects=0\u0026d=1';\r\ntic\r\nfname='https://sites.google.com/site/razapor/matlab_cody/mtest.mat?attredirects=0\u0026d=1';\r\nurlwrite(fname,'mtest.mat') %1.22s\r\nload('mtest.mat'); %0.42s\r\ntoc\r\n\r\nnumtosolve=40;\r\nmstart = solveLife(mtest,numtosolve);\r\ntoc\r\nmstart=unique(mstart,'rows'); % remove exact duplicate solutions\r\n\r\n%Check for Trivial solutions; Life(mtest(case))==mtest(case)\r\nvalid=1;\r\nfor i=1:size(mstart,1)  % \r\n icase=mstart(i,1); %50000:99999\r\n iter=mtest(icase-49999,2); %Test cases start at 50000\r\n \r\n A=reshape(mtest(icase-49999,3:end),25,25);\r\n Abase=A;\r\n for j=1:iter\r\n  C=0;\r\n  for r=-1:1 % -1 Up   Using circshift to perform wrap convolution\r\n   Ar=circshift(A,r,1);\r\n   for c=-1:1 % -1 Left\r\n     Arc=circshift(Ar,c,2);\r\n     C=C+Arc;\r\n   end\r\n  end\r\n  A = C==3 | A\u0026C==4;\r\n end %j\r\n\r\n if isequal(Abase,A) % mtest [case, iter, data1:625]\r\n  valid=0; %Trivial solution entered\r\n  break;\r\n end\r\nend %main loop i\r\ntoc  % Trivial check timer\r\n\r\nLprocess=size(mstart,1)*valid;\r\nvalid=0; % Reset valid as counter for solutions\r\nfor i=1:Lprocess  % skip if any were trivial\r\n icase=mstart(i,1); %50000:99999\r\n iter=mtest(icase-49999,2); %Test cases start at 50000\r\n \r\n A=reshape(mstart(i,2:end),25,25);\r\n for j=1:iter\r\n  C=0;\r\n  for r=-1:1 % -1 Up   Using circshift to perform wrap convolution\r\n   Ar=circshift(A,r,1);\r\n   for c=-1:1 % -1 Left\r\n     Arc=circshift(Ar,c,2);\r\n     C=C+Arc;\r\n   end\r\n  end\r\n  A = C==3 | A\u0026C==4;\r\n end %j\r\n\r\n if ~isequal(A(:)',mtest(icase-49999,3:end)) % mtest [case, iter, data1:625]\r\n  valid=0; %Evolved does not match goal\r\n  break;\r\n else\r\n  valid=valid+1;\r\n end\r\nend %main loop i\r\ntoc\r\n\r\nassert(valid\u003e=40)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-06T18:14:45.000Z","updated_at":"2026-09-25T21:57:25.000Z","published_at":"2020-10-06T18:41:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.kaggle.com/c/conways-reverse-game-of-life-2020\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKaggle's Conway's Reverse Game of Life 2020 \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003econtest inspires this Life challenge. The kaggle contest runs from Oct-01-2020 thru Nov-30-2020. References:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://mathworld.wolfram.com/GameofLife.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGame of Life at Wolfram\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWiki Life\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The Kaggle event is 50K cases to solve for a state 1 to 5 iterations prior to a given state. Imperfect solutions are allowed but penalized. Input file to Kaggle is a csv so Matlab solutions can be posted at the Kaggle site for this event.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to Solve at least 40, excluding trivials, of the 50K puzzles per these revised Life Laws. Trivial solutions are where the Final state may match the Start State.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[1. Any live cell with fewer than two live neighbors dies, as if caused by under-population.\\n2. Any live cell with two or three live neighbors lives on to the next generation.\\n3. Any live cell with more than three live neighbors dies, as if by overcrowding.\\n4. Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.\\n5. Edges wrap around. Eight Neighbors. (Change to normal planar life)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: The edges wrap so the matrix represents the surface of a sphere.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (mtest,numtosolve) the Finish state matrix of 50K rows of [casenumber, iterations, 625 values], number of case to solve (40)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (mstart) the Starting state matrix of at least 40 puzzles all with perfect zero error solutions, [casenumber, 625 values]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHint:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e There are 40 non-trivial solutions for iterations 1 and 2 where a solving Start state has a single bit flip that is adjacent to a set bit or is a set bit. Cases where there are more than 40 set bits in the final state may consume significant time for no solutions. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42396,"title":"the proud tradition of zero scores in Cody","description":"The short version is: *_your function should return a zero and also have a zero score/size_*\r\n\r\nThe long version comes with a little history:\r\n\r\nThere is a long tradition of attempting to modify the scoring function in Cody to be able to create problems that score solutions, for example, based on the solution running-time instead of the solution code-complexity. There is, of course, a parallel tradition of Cody players trying to \"game\" the system into getting the lowest possible score for their solutions.\r\n \r\nCody players are a very resourceful crowd, and very early into the game they found that overwriting the solution file (after it was evaluated) did the trick: Cody would then evaluate your solution size/code-complexity from the contents of the overwritten file so problem creators could overwrite the solutions with specially-crafted files that would return the desired solution score. Also solvers could overwrite their own files to get a 0 score if they so wished, simply adding\r\n\r\n  !echo \"%\" \u003e my_fcn_name.m\r\n\r\nto their solutions. \r\n\r\nThat state of affairs, naturally, perhaps sadly, did not last long, and Cody machinery was modified to score the solutions _before_ the testsuite was run. \r\n\r\nOf course this fix lasted even shorter, and Cody players found that the variable where that score was being stored could be accessed from the testsuite code using evalin('caller',...) or assignin('caller',...) syntax (yes, that variable was very amicably named _score_). So cody creators could now add the line\r\n\r\n  assignin('caller','score',0);\r\n\r\nto their testsuite to give players a 0 (or any arbitrary) score. \r\n\r\nThis new scenario lasted for quite some time, probably because while problem creators could still modify the scoring function as they wish and create all forms of problems that departed from the size/complexity-based scoring, problem solvers could not do the same to get any arbitrary score. From the solution function perspective the variable _score_ was two(!) steps up in the stack, and there is simply no way to use evalin('caller',...) syntax recursively along the lines of\r\n\r\n  evalin('caller','assignin(''caller'',''score'',0)');\r\n \r\nSomewhat recently this situation changed again and Cody started using the Unit Testing framework to run solutions. That put _a lot_ of layers between the testsuite and the coveted workspace where the _score_ variable lived, making the assignin trick obsolete. In addition key Cody functionality was hidden into .p files, which added a small burden to exploring the inner workings of Cody, and the old _score_ variable was nowhere to be found in those new functions.\r\n\r\nYour job in this problem, following this proud tradition, is to get a zero score. Also your solution function should return a 0 as well, just to make it _do_ something. \r\n\r\nA few pointers to get you started would be:\r\n\r\n* the now somewhat obsolete \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1769-singularity-2-0-easier singularity\u003e series\r\n* the folder ~/+cody\r\n* \u003chttp://www.mathworks.com/help/matlab/ref/dbstack.html dbstack\u003e\r\n\r\nGood luck and please hack responsibly!\r\n\r\nps1. if you are thinking of submitting an empty solution, no, that does not count (that is not a function and that is not returning any number).\r\n\r\nps2. if you are thinking of copy/pasting my own _SetSolutionScore_ trick, that will not work here, sorry! (it is protected so that it only works when the testsuite code uses it; if you manage to disable this protection and make it work from within your solution file I will accept that as well as a valid solution)\r\n\r\nps3. if you want to use _SetSolutionScore_ to be able to assign not-size-based scores in your own problems, simply copy/paste the relevant code in \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1192-say-something-funny/solutions/new#test_suite_body this problem testsuite\u003e. _SetSolutionScore_, like the old _assignin_ trick, will not interfere with other problems (solvers cannot copy/paste your testsuite code to get zero-scores in other problems)\r\n\r\n*note: please refrain from using this sort of Cody tricks to get leading scores in general non-hacking problems. That is just discorteous to other players* (add here rant about the regexp trick and how leading scores used to be worth pursuing).\r\n\r\n","description_html":"\u003cp\u003eThe short version is: \u003cb\u003e\u003ci\u003eyour function should return a zero and also have a zero score/size\u003c/i\u003e\u003c/b\u003e\u003c/p\u003e\u003cp\u003eThe long version comes with a little history:\u003c/p\u003e\u003cp\u003eThere is a long tradition of attempting to modify the scoring function in Cody to be able to create problems that score solutions, for example, based on the solution running-time instead of the solution code-complexity. There is, of course, a parallel tradition of Cody players trying to \"game\" the system into getting the lowest possible score for their solutions.\u003c/p\u003e\u003cp\u003eCody players are a very resourceful crowd, and very early into the game they found that overwriting the solution file (after it was evaluated) did the trick: Cody would then evaluate your solution size/code-complexity from the contents of the overwritten file so problem creators could overwrite the solutions with specially-crafted files that would return the desired solution score. Also solvers could overwrite their own files to get a 0 score if they so wished, simply adding\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e!echo \"%\" \u0026gt; my_fcn_name.m\r\n\u003c/pre\u003e\u003cp\u003eto their solutions.\u003c/p\u003e\u003cp\u003eThat state of affairs, naturally, perhaps sadly, did not last long, and Cody machinery was modified to score the solutions \u003ci\u003ebefore\u003c/i\u003e the testsuite was run.\u003c/p\u003e\u003cp\u003eOf course this fix lasted even shorter, and Cody players found that the variable where that score was being stored could be accessed from the testsuite code using evalin('caller',...) or assignin('caller',...) syntax (yes, that variable was very amicably named \u003ci\u003escore\u003c/i\u003e). So cody creators could now add the line\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eassignin('caller','score',0);\r\n\u003c/pre\u003e\u003cp\u003eto their testsuite to give players a 0 (or any arbitrary) score.\u003c/p\u003e\u003cp\u003eThis new scenario lasted for quite some time, probably because while problem creators could still modify the scoring function as they wish and create all forms of problems that departed from the size/complexity-based scoring, problem solvers could not do the same to get any arbitrary score. From the solution function perspective the variable \u003ci\u003escore\u003c/i\u003e was two(!) steps up in the stack, and there is simply no way to use evalin('caller',...) syntax recursively along the lines of\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eevalin('caller','assignin(''caller'',''score'',0)');\r\n\u003c/pre\u003e\u003cp\u003eSomewhat recently this situation changed again and Cody started using the Unit Testing framework to run solutions. That put \u003ci\u003ea lot\u003c/i\u003e of layers between the testsuite and the coveted workspace where the \u003ci\u003escore\u003c/i\u003e variable lived, making the assignin trick obsolete. In addition key Cody functionality was hidden into .p files, which added a small burden to exploring the inner workings of Cody, and the old \u003ci\u003escore\u003c/i\u003e variable was nowhere to be found in those new functions.\u003c/p\u003e\u003cp\u003eYour job in this problem, following this proud tradition, is to get a zero score. Also your solution function should return a 0 as well, just to make it \u003ci\u003edo\u003c/i\u003e something.\u003c/p\u003e\u003cp\u003eA few pointers to get you started would be:\u003c/p\u003e\u003cul\u003e\u003cli\u003ethe now somewhat obsolete \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1769-singularity-2-0-easier\"\u003esingularity\u003c/a\u003e series\u003c/li\u003e\u003cli\u003ethe folder ~/+cody\u003c/li\u003e\u003cli\u003e\u003ca href = \"http://www.mathworks.com/help/matlab/ref/dbstack.html\"\u003edbstack\u003c/a\u003e\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eGood luck and please hack responsibly!\u003c/p\u003e\u003cp\u003eps1. if you are thinking of submitting an empty solution, no, that does not count (that is not a function and that is not returning any number).\u003c/p\u003e\u003cp\u003eps2. if you are thinking of copy/pasting my own \u003ci\u003eSetSolutionScore\u003c/i\u003e trick, that will not work here, sorry! (it is protected so that it only works when the testsuite code uses it; if you manage to disable this protection and make it work from within your solution file I will accept that as well as a valid solution)\u003c/p\u003e\u003cp\u003eps3. if you want to use \u003ci\u003eSetSolutionScore\u003c/i\u003e to be able to assign not-size-based scores in your own problems, simply copy/paste the relevant code in \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1192-say-something-funny/solutions/new#test_suite_body\"\u003ethis problem testsuite\u003c/a\u003e. \u003ci\u003eSetSolutionScore\u003c/i\u003e, like the old \u003ci\u003eassignin\u003c/i\u003e trick, will not interfere with other problems (solvers cannot copy/paste your testsuite code to get zero-scores in other problems)\u003c/p\u003e\u003cp\u003e\u003cb\u003enote: please refrain from using this sort of Cody tricks to get leading scores in general non-hacking problems. That is just discorteous to other players\u003c/b\u003e (add here rant about the regexp trick and how leading scores used to be worth pursuing).\u003c/p\u003e","function_template":"function y = zeroscore(~)\r\ny = 0;\r\n","test_suite":"%%\r\n\r\n% gets expected output/score\r\nfh=fopen('zeroscore.m');str=fread(fh,'*char')'; fclose(fh);\r\nresults=scoringengine.verifyCode(str,'assert(isequal(zeroscore(),0))');\r\n\r\n% pass/fail\r\nstr={'Failed','Passed'};\r\nif results.pass\u0026results.score=='0'\u0026ischar(results.score), \r\n    fprintf('Congrats! Solution score: %s; Solution status: %s\\n',results.score, str{1+results.pass}); \r\nelse \r\n    fprintf('Sorry! Solution score: %s; Solution status: %s\\n',results.score, str{1+results.pass}); \r\n    [a,b]=1; \r\nend\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":43,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":"2017-10-28T00:51:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-06-19T20:20:19.000Z","updated_at":"2026-09-28T14:58:36.000Z","published_at":"2015-06-21T03:36:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe short version is:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eyour function should return a zero and also have a zero score/size\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe long version comes with a little history:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere is a long tradition of attempting to modify the scoring function in Cody to be able to create problems that score solutions, for example, based on the solution running-time instead of the solution code-complexity. There is, of course, a parallel tradition of Cody players trying to \\\"game\\\" the system into getting the lowest possible score for their solutions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCody players are a very resourceful crowd, and very early into the game they found that overwriting the solution file (after it was evaluated) did the trick: Cody would then evaluate your solution size/code-complexity from the contents of the overwritten file so problem creators could overwrite the solutions with specially-crafted files that would return the desired solution score. Also solvers could overwrite their own files to get a 0 score if they so wished, simply adding\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[!echo \\\"%\\\" \u003e my_fcn_name.m]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eto their solutions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThat state of affairs, naturally, perhaps sadly, did not last long, and Cody machinery was modified to score the solutions\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ebefore\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the testsuite was run.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOf course this fix lasted even shorter, and Cody players found that the variable where that score was being stored could be accessed from the testsuite code using evalin('caller',...) or assignin('caller',...) syntax (yes, that variable was very amicably named\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003escore\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e). So cody creators could now add the line\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[assignin('caller','score',0);]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eto their testsuite to give players a 0 (or any arbitrary) score.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis new scenario lasted for quite some time, probably because while problem creators could still modify the scoring function as they wish and create all forms of problems that departed from the size/complexity-based scoring, problem solvers could not do the same to get any arbitrary score. From the solution function perspective the variable\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003escore\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e was two(!) steps up in the stack, and there is simply no way to use evalin('caller',...) syntax recursively along the lines of\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[evalin('caller','assignin(''caller'',''score'',0)');]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSomewhat recently this situation changed again and Cody started using the Unit Testing framework to run solutions. That put\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea lot\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of layers between the testsuite and the coveted workspace where the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003escore\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e variable lived, making the assignin trick obsolete. In addition key Cody functionality was hidden into .p files, which added a small burden to exploring the inner workings of Cody, and the old\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003escore\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e variable was nowhere to be found in those new functions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour job in this problem, following this proud tradition, is to get a zero score. Also your solution function should return a 0 as well, just to make it\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edo\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e something.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA few pointers to get you started would be:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe now somewhat obsolete\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1769-singularity-2-0-easier\\\"\u003e\u003cw:r\u003e\u003cw:t\u003esingularity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e series\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe folder ~/+cody\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/help/matlab/ref/dbstack.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003edbstack\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood luck and please hack responsibly!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eps1. if you are thinking of submitting an empty solution, no, that does not count (that is not a function and that is not returning any number).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eps2. if you are thinking of copy/pasting my own\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSetSolutionScore\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e trick, that will not work here, sorry! (it is protected so that it only works when the testsuite code uses it; if you manage to disable this protection and make it work from within your solution file I will accept that as well as a valid solution)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eps3. if you want to use\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSetSolutionScore\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to be able to assign not-size-based scores in your own problems, simply copy/paste the relevant code in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1192-say-something-funny/solutions/new#test_suite_body\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ethis problem testsuite\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSetSolutionScore\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, like the old\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e trick, will not interfere with other problems (solvers cannot copy/paste your testsuite code to get zero-scores in other problems)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enote: please refrain from using this sort of Cody tricks to get leading scores in general non-hacking problems. That is just discorteous to other players\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (add here rant about the regexp trick and how leading scores used to be worth pursuing).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":907,"title":"Now! (Anticheating version 1)","description":"By now, _Problem 901. Now!_ has not been solved without the use of cheats or hacks.\r\n\r\n\u003chttp://www.mathworks.com/matlabcentral/cody/problems/901-now\u003e\r\n\r\nThe goal of this Problem is to progressively design an anticheating test suite by learning from the solutions proposed by solvers of previous problems in the Now! series.","description_html":"\u003cp\u003eBy now, \u003ci\u003eProblem 901. Now!\u003c/i\u003e has not been solved without the use of cheats or hacks.\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://www.mathworks.com/matlabcentral/cody/problems/901-now\"\u003ehttp://www.mathworks.com/matlabcentral/cody/problems/901-now\u003c/a\u003e\u003c/p\u003e\u003cp\u003eThe goal of this Problem is to progressively design an anticheating test suite by learning from the solutions proposed by solvers of previous problems in the Now! series.\u003c/p\u003e","function_template":"function ans = ISaidNow\r\n   now;\r\nend","test_suite":"%%\r\n%#######################################################################%\r\nclear matlabCode;\r\n[~]=urlwrite('http://files4codygame.appspot.com/files/game.p','game.p');\r\nrehash;\r\nprotected_objs={'assert','isequal','now','error'};\r\ngame.status(protected_objs{:});\r\n%#######################################################################%\r\n\r\nnow1=ISaidNow;\r\n\r\n%#######################################################################%\r\n\r\nprotected_objs={'assert','isequal','now','error'};\r\ns2=game.status(protected_objs{:});\r\nallowed_vars={'now1'};\r\ncheated=game.cheated(allowed_vars{:});\r\n\r\nfprintf('Cheated = %d\\n',cheated)\r\nif cheated\r\nwhile 1\r\n%TIMEOUT EXPIRATION\r\nend\r\nend\r\n%#######################################################################%\r\n\r\n[~]=fft(rand(1,1000000));\r\nassert(isequal(now1,1))\r\n\r\n\r\n%%\r\n%#######################################################################%\r\n\r\nclear matlabCode;\r\n[~]=urlwrite('http://files4codygame.appspot.com/files/game.p','game.p');\r\nrehash;\r\nprotected_objs={'assert','isequal','now','error'};\r\ngame.status(protected_objs{:});\r\n\r\n%#######################################################################%\r\n\r\nnow1=ISaidNow;\r\n\r\n%#######################################################################%\r\n\r\nprotected_objs={'assert','isequal','now','error'};\r\ns2=game.status(protected_objs{:});\r\nallowed_vars={'now1'};\r\ncheated=game.cheated(allowed_vars{:});\r\n\r\nfprintf('Cheated = %d\\n',cheated)\r\nif cheated\r\nwhile 1\r\n%TIMEOUT EXPIRATION\r\nend\r\nend\r\n\r\n%#######################################################################%\r\n\r\n[~]=fft(rand(1,1000000));\r\nnow2=now;\r\nassert(isequal(now1,now2),sprintf('now1 = %.11f, now2 = %.11f',now1,now2))","published":true,"deleted":false,"likes_count":2,"comments_count":9,"created_by":5925,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2012-08-16T07:18:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-08-12T19:17:48.000Z","updated_at":"2026-09-28T15:00:20.000Z","published_at":"2012-08-16T07:06:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBy now,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem 901. Now!\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has not been solved without the use of cheats or hacks.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/901-now\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://www.mathworks.com/matlabcentral/cody/problems/901-now\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe goal of this Problem is to progressively design an anticheating test suite by learning from the solutions proposed by solvers of previous problems in the Now! series.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44270,"title":"Assert yourself!  Hack the assert function to pass this test.","description":"Have you ever wanted to test out one of those hacks you have seen which \"games\" the problem by simply overwriting the assert method?  Perhaps you have held off in good conscience or in consideration of the difficulty it brings to others wanting to find an actual, correct solution that they can learn from.  Well, this question is for you!  Please use whatever method you can to pass this test, which is otherwise stacked completely and unfairly against you.\r\n\r\n*Example 1*\r\n\r\n  y = assertYourself(10,1);\r\n  % Test is assert(false);\r\n\r\n*Example 2*\r\n\r\n  [v,y] = assertYourself(rand(10,1), 'blah','eh?');\r\n  % Test is assert(false);\r\n\r\nSee, just not fair.  \r\n\r\nNote: More unfair test cases added.","description_html":"\u003cp\u003eHave you ever wanted to test out one of those hacks you have seen which \"games\" the problem by simply overwriting the assert method?  Perhaps you have held off in good conscience or in consideration of the difficulty it brings to others wanting to find an actual, correct solution that they can learn from.  Well, this question is for you!  Please use whatever method you can to pass this test, which is otherwise stacked completely and unfairly against you.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample 1\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ey = assertYourself(10,1);\r\n% Test is assert(false);\r\n\u003c/pre\u003e\u003cp\u003e\u003cb\u003eExample 2\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e[v,y] = assertYourself(rand(10,1), 'blah','eh?');\r\n% Test is assert(false);\r\n\u003c/pre\u003e\u003cp\u003eSee, just not fair.\u003c/p\u003e\u003cp\u003eNote: More unfair test cases added.\u003c/p\u003e","function_template":"function varargout = assertYourself(varargin)\r\n  \r\nend","test_suite":"%%\r\nx = 'Try this one';\r\ny_correct = rand(1);\r\nassert(isequal(assertYourself(x),y_correct))\r\n\r\n%%\r\nclear all;\r\nx = rand(10);\r\ny_correct = rand(1);\r\nassertYourself();\r\nassert(isequal(true,false))\r\n\r\n%%\r\nclear all;\r\nx = rand(10);\r\ny = assertYourself(x,'blah')\r\ny_correct = rand(1);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nclear all;\r\nx = randi(26,10);\r\ny_correct = rand(1);\r\n[v,z]= assertYourself(x,x,x);\r\nz;\r\nmsg = ['That is not even fair!  ',char(randi(26,1,10)+'A')]\r\nassert(isequal(x,y_correct));\r\n\r\n%% \r\nclear all;\r\n[v,z]= assertYourself();\r\nv;\r\nassert(false);","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":130819,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2017-07-30T04:46:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-07-28T03:49:16.000Z","updated_at":"2026-09-28T14:59:50.000Z","published_at":"2017-07-28T03:58:18.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHave you ever wanted to test out one of those hacks you have seen which \\\"games\\\" the problem by simply overwriting the assert method? Perhaps you have held off in good conscience or in consideration of the difficulty it brings to others wanting to find an actual, correct solution that they can learn from. Well, this question is for you! Please use whatever method you can to pass this test, which is otherwise stacked completely and unfairly against you.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[y = assertYourself(10,1);\\n% Test is assert(false);]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[[v,y] = assertYourself(rand(10,1), 'blah','eh?');\\n% Test is assert(false);]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee, just not fair.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: More unfair test cases added.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"problems":[{"id":2323,"title":"Pandigital number n°3 (Inspired by Project Euler 32)","description":"After Problem 2319 and 2320.\r\n\r\nAn n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE. For example, the 5-digit number 15234, is 1 through 5 pandigital.\r\n\r\nThe product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital ([391867254]).\r\n\r\nFind the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through n pandigital (n is given in input).\r\n\r\nHINT1: Some products can be obtained in more than one way so be sure to only include it once in your sum.\r\n\r\nHINT2: All in good time...  \r\n\r\n","description_html":"\u003cp\u003eAfter Problem 2319 and 2320.\u003c/p\u003e\u003cp\u003eAn n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE. For example, the 5-digit number 15234, is 1 through 5 pandigital.\u003c/p\u003e\u003cp\u003eThe product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital ([391867254]).\u003c/p\u003e\u003cp\u003eFind the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through n pandigital (n is given in input).\u003c/p\u003e\u003cp\u003eHINT1: Some products can be obtained in more than one way so be sure to only include it once in your sum.\u003c/p\u003e\u003cp\u003eHINT2: All in good time...\u003c/p\u003e","function_template":"function y = pandigital_sum(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 3;\r\ny_correct = [];\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n%%\r\nx = 4;\r\ny_correct = 12;\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n%%\r\nx = 5;\r\ny_correct = 52;\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n%%\r\nx = 6;\r\ny_correct = 162;\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n%%\r\nx = 7;\r\ny_correct = []; % Strange no ?\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n\r\n%%\r\nx = 8;\r\ny_correct = 13458;\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n\r\n\r\n%% You obtain the Project Euler n°32 solution with n=9\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":5390,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":48,"test_suite_updated_at":"2019-10-23T23:21:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-05-15T10:08:43.000Z","updated_at":"2026-10-15T13:54:29.000Z","published_at":"2014-05-15T10:20:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAfter Problem 2319 and 2320.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE. For example, the 5-digit number 15234, is 1 through 5 pandigital.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital ([391867254]).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through n pandigital (n is given in input).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHINT1: Some products can be obtained in more than one way so be sure to only include it once in your sum.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHINT2: All in good time...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":46066,"title":"Evaluate the logarithmic integral","description":"The \u003chttps://en.wikipedia.org/wiki/Logarithmic_integral_function logarithmic integral\u003e li(x) plays a role in number theory because the related function Li(x) = li(x) - li(2) provides an estimate for the number of primes less than x. MATLAB's Symbolic Toolbox has the function \u003chttps://www.mathworks.com/help/symbolic/sym.logint.html |logint|\u003e, but it is not available in basic MATLAB or Cody. \r\n\r\nWrite a function to evaluate the logarithmic integral.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 123px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 61.5px; transform-origin: 407px 61.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.0667px 7.91667px; transform-origin: 12.0667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Logarithmic_integral_function\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003elogarithmic integral\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"li(x)\" style=\"width: 30.5px; height: 19px;\" width=\"30.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 184px 7.91667px; transform-origin: 184px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e plays a role in number theory because the related function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPwAAAAmCAYAAADgDvYuAAAFLElEQVR4nO2dXbXrIBCFt4c4iIEYiIIqqIM6qINaiIZKqIdaqIZaOOeBzuq0DTDAQH7WfGvlpbmHJDtsmAHCBQzDMAzDMAzDMAzDMAzDMIQcX4cWE4Besby9YXrX5wJgUCqrf5XXlRRyBHCOHDllnhJv7AhXYTTpAdyhJ/gSDHBa3gFcPf/G9C5jhDPSA07Hb7rX76mN4yT4mxFvn50Q126E0zjb9AOAw6uQP3Y8X7+PieUdWRmXhL+5JV5HygD3IrfW8/RwBn/greec4U3vfEY4HZ54azhn+ImdPwjLnhDuLEd8vlt+XBE29BHOr0X0XxeVPtjczaRUwAFO8JoVREWgheDvRcPwpvcvXEMNw1NE5mNk5d3w2+jQ7yHTT5A38F74BUvCMsoNJWHHA3lpQyq3RtepQcjwgOldCjdgKKSXmJ0aaF9k3MG9gxt+G90j4tEGL+cZuI4ILcNLoQcsGoQQcoB7ri2Emt/EDC/F9J4nZvgUJoTTpSOc4X3vgEcbsbSLxh2yaW34BxTCkhVfTwstw5ve82gZnnr3UCRwi5wH3r38U+F6QVoannqAopAkkQviIq4RDcOb3n60DH95lRFCMptyg8zwQHj2JopmDn+N3AgNhKTQwVXcM34rLuVZobxxiUqvgSSHN73zkebwd895gnLzUsjwEiNLGhkvJYbv4SoVH3QI3XCKODRFxUczeR404PO6vrlPCoFyBpN6xNcrSI6cyj+n5971bonP8COcDn+e8xzNZyVtJaE65fxZjapGDz9AVgFzQ9QzK3/Ee9STepu50U+N6/JKUXLkhIwhPfeqd0tiPfwpcp6XUTroR+9Turim6LpaIX2sAtJN5rSGvIKf4CpcysM+kRd2afXwObrG9Nyj3i2JGV6S41PDWJq+UOolLYfeT1ZksQXDA5+jmKnLQylM3RJLGh5orzdfbtoidVqL4cm8qTMb2VHUVgzP86rUeV4aENkSSxu+td48jWiROq3B8B3yR9z/kBlFbcXwPKdKXURihk+ntd4aPXxK/V2D4WnBTs6iqN0bnq9tTv2CKXfqZG2j9Cnnt6h3S5Y2fInZi2YHcgzf4feFxipgh7xcBXgvTaS8MjWnzG0N1zpKLzm/Rb1bomF4WnOQuuqtxOz83poZ/ozfL4NiFRDIG72lTy/5/GjKWmKq+EvOwy8xSg9sT++WaBg+Z7ScpjVDZj8gXGeKFjelGp4WYHw/pKQCXpE2ekuDGhRS8rySBpKuCLew9OKy1x4vhIbhTW8/GoYHnL7SQTf6kCk0CEr+CjUIlEokRwip38PzT/m+WxdJBaQVQqEHvuA973vHZ0jK54cvcKFRLNykZYgtvhbTgnrJUsOb3n6olyw1/ARZBETvgsY3fIckhbojY++BgV2AH6EboYO3QB0+p1Ro15w5qCKHBOTXmavMsd1gvrlDf1unmtDyWZ+epnc5Az53e/reoouWGfvOc6jhCEXH/PNXyREK1emdJg2kSva0Cx1UwUI5rq+SxVpEmp4JrdUOnedQD7X2DzmImJ6mdzmh6b+D4PwcD4QbuRRvxQZ4T2i3v4EKPRR27RAyYf1rumtjetfngHYm9G26uWpOKNy1Q8CI+vu4bQXTuz5X1E9l5mbHNsOEejuj0Nddax8pbonpXRea4ailQYuNSKtzg+5/ikBcK5W7dUzvutTao58ak63t/T/LBN3KclEub2+Y3nWhVaha5uzgGtRdmJ3QHOzYdMjTCNO7Pload4plGYZhGIZhGIZhGIZhGIaxFP/Ka2gIYQHNwgAAAABJRU5ErkJggg==\" alt=\"Li(x) = li(x) - li(2)\" style=\"width: 126px; height: 19px;\" width=\"126\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.0667px 7.91667px; transform-origin: 40.0667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e provides an estimate for the number of primes less than x. MATLAB's Symbolic Toolbox has the function\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/symbolic/sym.logint.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003elogint\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75px 7.91667px; transform-origin: 75px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, but it is not available in basic MATLAB or Cody.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 158.967px 7.91667px; transform-origin: 158.967px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to evaluate the logarithmic integral.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.1833px 7.91667px; transform-origin: 29.1833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSee also \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46081-set-soldner-s-constant\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 46081 \"Set Soldner's constant\"\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logarithmicIntegral(x)\r\n  y = f(x);\r\nend","test_suite":"%%\r\nx = 0;\r\ny_correct = 0;\r\nassert(abs(logarithmicIntegral(x)-y_correct)\u003c1e-8)\r\n\r\n%%\r\nx = 0.2;\r\ny_correct = -0.085126486728794;\r\nassert(abs(logarithmicIntegral(x)-y_correct)\u003c1e-8)\r\n\r\n%%\r\nx = 0.5;\r\ny_correct = -0.378671043061088;\r\nassert(abs(logarithmicIntegral(x)-y_correct)\u003c1e-8)\r\n\r\n%%\r\nx = 1;\r\ny = logarithmicIntegral(x);\r\nassert(isinf(y) \u0026\u0026 sign(y) == -1)\r\n\r\n%%\r\nx = 2;\r\ny_correct = 1.045163780117493;\r\nassert(abs(logarithmicIntegral(x)-y_correct)\u003c1e-8)\r\n\r\n%%\r\nx = 5;\r\ny_correct = 3.634588310032652;\r\nassert(abs(logarithmicIntegral(x)-y_correct)\u003c1e-8)\r\n\r\n%%\r\nx = 8;\r\ny_correct = 5.253718299558931;\r\nassert(abs(logarithmicIntegral(x)-y_correct)\u003c1e-8)\r\n\r\n%%\r\nx = 3+2i;\r\ny_correct = 2.558790740400258 + 1.594445119241119i;\r\ny = logarithmicIntegral(x);\r\nassert(abs(real(y)-real(y_correct))\u003c1e-8 \u0026\u0026 abs(imag(y)-imag(y_correct))\u003c1e-8)\r\n\r\n%%\r\nx = 3-0.2i;\r\ny_correct = 2.169086896211800 - 0.181703645882027i;\r\ny = logarithmicIntegral(x);\r\nassert(abs(real(y)-real(y_correct))\u003c1e-8 \u0026\u0026 abs(imag(y)-imag(y_correct))\u003c1e-8)\r\n\r\n%%\r\nx = -0.3-2i;\r\ny_correct = 0.999726888286245 - 3.238096925989443i;\r\ny = logarithmicIntegral(x);\r\nassert(abs(real(y)-real(y_correct))\u003c1e-8 \u0026\u0026 abs(imag(y)-imag(y_correct))\u003c1e-8)\r\n\r\n%%\r\nx = -5-3i;\r\ny_correct = 0.500720609942772 - 5.020802115037742i;\r\ny = logarithmicIntegral(x);\r\nassert(abs(real(y)-real(y_correct))\u003c1e-8 \u0026\u0026 abs(imag(y)-imag(y_correct))\u003c1e-8)\r\n\r\n%%\r\nx = 0.3i;\r\ny_correct = 0.074754684076440 + 3.053886180297906i;\r\ny = logarithmicIntegral(x);\r\nassert(abs(real(y)-real(y_correct))\u003c1e-8 \u0026\u0026 abs(imag(y)-imag(y_correct))\u003c1e-8)\r\n \r\n%%\r\nx = 0.4-2i;\r\ny_correct = 1.171012435933119 - 2.861745062394908i;\r\ny = logarithmicIntegral(x);\r\nassert(abs(real(y)-real(y_correct))\u003c1e-8 \u0026\u0026 abs(imag(y)-imag(y_correct))\u003c1e-8)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-07-28T15:11:20.000Z","updated_at":"2026-10-01T13:27:39.000Z","published_at":"2020-07-29T01:46:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Logarithmic_integral_function\\\"\u003e\u003cw:r\u003e\u003cw:t\u003elogarithmic integral\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"li(x)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{\\\\rm li}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e plays a role in number theory because the related function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Li(x) = li(x) - li(2)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{\\\\rm Li}(x) = {\\\\rm li}(x) - {\\\\rm li}(2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e provides an estimate for the number of primes less than x. MATLAB's Symbolic Toolbox has the function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/symbolic/sym.logint.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elogint\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, but it is not available in basic MATLAB or Cody.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to evaluate the logarithmic integral.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee also \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46081-set-soldner-s-constant\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 46081 \\\"Set Soldner's constant\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44374,"title":"Tautology","description":"Check if the given expression is always true. For example, the sentence\r\n\r\n  '~(A \u0026 B) == (~A | ~B)'\r\n\r\nis always true.\r\n\r\nCharacters in the input sequences may include *~ \u0026 | == ( )*, whitespace, 0 for false, 1 for true and letters for variables.","description_html":"\u003cp\u003eCheck if the given expression is always true. For example, the sentence\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e'~(A \u0026 B) == (~A | ~B)'\r\n\u003c/pre\u003e\u003cp\u003eis always true.\u003c/p\u003e\u003cp\u003eCharacters in the input sequences may include \u003cb\u003e~ \u0026 | == ( )\u003c/b\u003e, whitespace, 0 for false, 1 for true and letters for variables.\u003c/p\u003e","function_template":"function y = tautology(x)\r\n  y = true;\r\nend","test_suite":"%%\r\nx = '0';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '1';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|1';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '1\u0026A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A\u0026B';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|~A';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '0==0';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~0';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~(A \u0026 B) == (~A | ~B)';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~(Z \u0026 Y) == (~Y | ~Z)';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|X|V|W|Y|Z';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B|C|D|E|F|G|H|I|J|K|L|M|~A|O|P|Q|R|S|T|U|X|V|W|Y|Z';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nassert(isequal(tautology('(A|B)|C'),false));\r\n%%\r\nassert(isequal(tautology('(A|B)|(C == C)'),true));\r\n%%\r\nassert(isequal(tautology('(A == B)|(B == C)|(C == A)'),true));\r\n%%\r\nassert(isequal(tautology('~(~(~(~(~(~(0))))))'),false)); \r\n%%\r\nassert(isequal(tautology('~(~(~(~(~(~(~0))))))'),true));\r\n% provided by Alfonso:\r\nassert(isequal(tautology('((0\u00261)|~B)\u0026~B'),false)); \r\n%%\r\nassert(isequal(tautology('((0\u0026~B)\u0026~B)'),false)); \r\n%%\r\nassert(isequal(tautology('((0|A)\u0026~A)'),false)); \r\n%%\r\nassert(isequal(tautology('((0|A)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((0|~B)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((1\u00260)|B)'),false)); \r\n%%\r\nassert(isequal(tautology('((1\u00261)\u0026A)'),false)); \r\n%%\r\nassert(isequal(tautology('((1|0)|A)'),true)); \r\n%%\r\nassert(isequal(tautology('((1|A)|0)'),true)); \r\n%%\r\nassert(isequal(tautology('((1|~A)\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('((A\u00261)|~A)|A'),true)); \r\n%%\r\nassert(isequal(tautology('((A\u0026~A)\u0026~B)|~A'),false)); \r\n%%\r\nassert(isequal(tautology('((A\u0026~B)\u00261)|B'),false)); \r\n%%\r\nassert(isequal(tautology('((A|0)\u00261)\u0026~B'),false)); \r\n%%\r\nassert(isequal(tautology('((A|A)\u0026A)|~A'),true)); \r\n%%\r\nassert(isequal(tautology('((B|0)\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('((B|1)\u0026B)\u0026A'),false)); \r\n%%\r\nassert(isequal(tautology('((B|A)|~A)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)\u00260)\u0026B'),false)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)|0)'),false)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)|~A)|1'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|A)|~B)\u00261'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|B)|A)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|~A)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|~B)\u00260)'),false)); \r\n%%\r\nassert(isequal(tautology('((~B\u00260)\u0026A)'),false)); \r\n%%\r\nassert(isequal(tautology('(0\u00261)|1\u00261'),true)); \r\n%%\r\nassert(isequal(tautology('(0|~A\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('(1|A\u00260)'),true)); \r\n%%\r\nassert(isequal(tautology('(A\u0026A\u0026~B)'),false)); \r\n%%\r\nassert(isequal(tautology('(A\u0026~A|1)'),true)); \r\n%%\r\nassert(isequal(tautology('(A|1)|B'),true)); \r\n%%\r\nassert(isequal(tautology('(A|A)|A|1'),true)); \r\n%%\r\nassert(isequal(tautology('(B\u00261)|~B'),true)); \r\n%%\r\nassert(isequal(tautology('(B\u0026~B)\u0026~B\u00260'),false)); \r\n%%\r\nassert(isequal(tautology('(B|~B)|B'),true)); \r\n%%\r\nassert(isequal(tautology('(~A\u0026B\u00260)'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|0)|~B\u0026~A'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|1)|1'),true)); \r\n%%\r\nassert(isequal(tautology('(~A|B\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|B)|~B'),true)); \r\n%%\r\nassert(isequal(tautology('(~A|~A)|0'),false)); \r\n%%\r\nassert(isequal(tautology('(~B\u00260)\u00261|1'),true)); \r\n%%\r\nassert(isequal(tautology('1\u0026B|~B|0'),true)); \r\n%%\r\nassert(isequal(tautology('B\u00261\u0026A\u00261'),false)); \r\n%%\r\nassert(isequal(tautology('~A\u00260\u00261|1'),true)); \r\n%%\r\nassert(isequal(tautology('~B\u00260\u0026~A|B'),false)); \r\n%%\r\nassert(isequal(tautology('~B|1|1|~B'),true)); \r\n%%\r\nassert(isequal(tautology('~B|~B\u00261|1'),true));\r\n%%\r\nassert(isequal(tautology('A==~A'),false));\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":30,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":45,"test_suite_updated_at":"2017-10-31T07:45:16.000Z","rescore_all_solutions":true,"group_id":35,"created_at":"2017-10-10T23:20:08.000Z","updated_at":"2026-08-07T05:32:19.000Z","published_at":"2017-10-16T01:51:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCheck if the given expression is always true. For example, the sentence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA['~(A \u0026 B) == (~A | ~B)']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eis always true.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCharacters in the input sequences may include\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e~ \u0026amp; | == ( )\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, whitespace, 0 for false, 1 for true and letters for variables.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45451,"title":"Don't be Too Greedy!!","description":"Refer to the prev problem \u003chttps://www.mathworks.com/matlabcentral/cody/problems/45450-don-t-be-too-greedy\u003e\r\n\r\nFor this time, calculate the maximum number of marks he can achieve after finishing all his assignments.","description_html":"\u003cp\u003eRefer to the prev problem \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/45450-don-t-be-too-greedy\"\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/45450-don-t-be-too-greedy\u003c/a\u003e\u003c/p\u003e\u003cp\u003eFor this time, calculate the maximum number of marks he can achieve after finishing all his assignments.\u003c/p\u003e","function_template":"function y = greedy_3(p,t,mark)","test_suite":"%%\r\np=[ 10,  4,  1,  2,  5,  2];\r\nt=[  2,  4,  3,  8,  1, 10];\r\nassert(isequal(greedy_3(p,t,100),515))\r\n\r\n%%\r\n p=[4,2,1, 5, 3, 2, 6];\r\n t=[1,8,2, 3, 1, 4, 2];\r\nassert(isequal(greedy_3(p,t,10),-16))\r\n\r\n%%\r\np=[9,10,2,10,7,1,3,6,10,10,2,10];\r\nt=[48    25    41     8    22    46    40    48    33     2    43    47];\r\nassert(isequal(greedy_3(p,t,200),-4008))\r\n\r\n%%\r\np=[1,3,1,2,4];\r\nt=[1,4,10,2,5];\r\nassert(isequal(greedy_3(p,t,200),950))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-13T12:04:50.000Z","updated_at":"2026-08-28T01:44:40.000Z","published_at":"2020-04-13T12:04:50.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRefer to the prev problem\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45450-don-t-be-too-greedy\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/45450-don-t-be-too-greedy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this time, calculate the maximum number of marks he can achieve after finishing all his assignments.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":51783,"title":"Solve an ODE: equation B","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.25px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 106.625px; transform-origin: 407px 106.625px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.358px 7.91667px; transform-origin: 211.358px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to solve the following ordinary differential equation:  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 39px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.5px; text-align: left; transform-origin: 384px 19.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y\u0026quot; + (1/x) y' - (a^2 + p^2/x^2) y = 0\" style=\"width: 181.5px; height: 39px;\" width=\"181.5\" height=\"39\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.125px; text-align: left; transform-origin: 384px 21.125px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.3917px 7.91667px; transform-origin: 14.3917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewith \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y(x1) = y1\" style=\"width: 64.5px; height: 20px;\" width=\"64.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.0083px 7.91667px; transform-origin: 35.0083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and either \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y(x0) = y0\" style=\"width: 64.5px; height: 20px;\" width=\"64.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 7.91667px; transform-origin: 10.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y'(x0) = y'0\" style=\"width: 74px; height: 20px;\" width=\"74\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38.1167px 7.91667px; transform-origin: 38.1167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Along with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ey1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.275px 7.91667px; transform-origin: 25.275px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, one of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ey0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 7.91667px; transform-origin: 11.55px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eyp0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109.708px 7.91667px; transform-origin: 109.708px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be assigned numerical values, and the other will be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 7.91667px; transform-origin: 11.55px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eNaN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 128.742px 7.91667px; transform-origin: 128.742px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The function should return the values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.9px 7.91667px; transform-origin: 80.9px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at the specified values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 194.483px 7.91667px; transform-origin: 194.483px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOne of the applications for this equation is in groundwater. For \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a = 1\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEwAAAAkCAYAAAAjMNwcAAAB2UlEQVRoge2ZUZGDMBRFjwccYKAGUFAFOKiDOKiFalgJeMDCasAC+xFeeTCEkpRCdvrOTGY/CAl7uXk3pGAYhmEYhrFEAVwBN7TruY+TNw7ogAdQ4cVqh2bCzXgA/fBXU+BF7DHRnlzxgvR4gebUw7XfwPWv4xcvSBO4XjAKej/qoXJFu8ut9GsZXfbVSO16VaN0v0vMBAVjgrhhICmUJd6yzdAc+a/5hm1CONXvFjOBCPbDdF07vF3vTN9GS5xobodWR8zXEy/YPEk3UakBGryAGv3mYuK436HNn2XrfOVKv1vi+E+04ksD6OsxybKHw1JeUPeinzZIkmCSGh3LbyZVsKPRgq05rOYNwfS+JHTzXfXJeYcsu/iP1jC9dwkV2JZtteFsPp6SMKZgx3IClqTb9+iU1Cuh2qHfIvIpsWU5Rm3y1H1HpaReLWvOESeGTBJEu2dpgpKxLqx9aoQ4OiXhw9+SOi2W3CO1Kyl6T0JcFkrKmkR3wXSHP785dKb0H1g7DxMHJqW9jmEZQJ9MRhfEjJDaOz9x7UgU68J0LdeMqZTz1iGGkvH/crxpAL0XiU2/r0RHq/GCLZ9DhmLrBu/rkR82JVrFYRX5n6aegpywLjUTzDCM3PgDF8YKvLGFg5UAAAAASUVORK5CYII=\" alt=\"p = 0\" style=\"width: 38px; height: 18px;\" width=\"38\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 136.567px 7.91667px; transform-origin: 136.567px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the equation arises in the flow of water to a well pumping in a leaky confined aquifer; the independent variable \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 141.975px 7.91667px; transform-origin: 141.975px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the normalized distance from the well, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.94167px 7.91667px; transform-origin: 8.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is related to the piezometric head, a combination of the elevation and pressure of the water. Specifying the derivative at a point amounts to specifying the flow to the well.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = solveODEB(x,coeff,Xbc,bc)\r\n%  y = values of the solution\r\n%  x = values of the independent variable where the solution is requested\r\n%  coeff = [a p], the two parameters in the ODE\r\n%  Xbc = values of x where the boundary conditions are specifified\r\n%  bc = [y0 yp0 y1] = boundary values (see description)\r\n\r\n  y = f(x,coeff,Xbc,bc);\r\nend","test_suite":"%%\r\ncoeff = [1 0];\r\nXbc = [1 4];\r\nbc = [1 NaN 0];\r\nx = linspace(1,4,7);\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [1 0.505461057363874 0.265959532078956 0.140787844664873 0.071276733472728 0.029333752731051 0];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\ncoeff = [3 1];\r\nXbc = [0.5 4.5];\r\nbc = [0 NaN 2];\r\nx = [cos(pi/4) cos(pi/6) sqrt(2) (1+sqrt(5))/2 sqrt(3) sqrt(5) exp(1) pi 4+psi(1)];\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [0.000035290165611 0.000065476121971 0.000315436935125 0.000552779648598 0.000757412623201 0.003086031722519 0.012031119481478 0.040129255417251 0.089700339919646];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\ncoeff = [1 1/2];\r\nXbc = [1 5];\r\nbc = [4 NaN -1];\r\nx = 1.2:0.75:4.95;\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [2.974028994378906 1.041176175714286 0.308462205553512 -0.076175488441917 -0.426089583908447 -0.952692417292867];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\ncoeff = [2 4];\r\nXbc = [1 Inf];\r\nbc = [3 NaN 0];\r\nx = 1:2:9;\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [3 0.005688558853080 0.000051725255081 0.000000653418086 0.000000009396692];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n%-------------------------------\r\n%%\r\ncoeff = [1 0];\r\nXbc = [1 4];\r\nbc = [NaN 1 0];\r\nx = linspace(1,4,7);\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [-0.696760997897786 -0.352185550727323 -0.185310228971762 -0.098095479140575 -0.049662847941353 -0.020438614824974 0];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n \r\n%%\r\ncoeff = [3 1];\r\nXbc = [0.5 4.5];\r\nbc = [NaN 0 2];\r\nx = [cos(pi/4) cos(pi/6) sqrt(2) (1+sqrt(5))/2 sqrt(3) sqrt(5) exp(1) pi 4+psi(1)];\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [0.000053997354167 0.000075728700374 0.000316920386259 0.000553525214653 0.000757922298088 0.003086129240342 0.012031140116004 0.040129260776539 0.089700342119009];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\ncoeff = [1 1/2];\r\nXbc = [1 5];\r\nbc = [NaN 4 -1];\r\nx = 1.2:0.75:4.95;\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [-2.047695617799804 -0.816404083826666 -0.431398160565887 -0.374418157507686 -0.532801281305956 -0.958228725044217];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\ncoeff = [1 0];\r\nXbc = [1 Inf];\r\nbc = [NaN 3 0];\r\nx = 1:2:9;\r\ny = solveODEB(x,coeff,Xbc,bc);\r\ny_correct = [-2.098451806781317 -0.173147136186896 -0.018397012773047 -0.002117248575316 -0.000253600440751];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-05-16T01:10:22.000Z","updated_at":"2026-09-15T06:59:48.000Z","published_at":"2021-05-16T01:19:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to solve the following ordinary differential equation:  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\u0026quot; + (1/x) y' - (a^2 + p^2/x^2) y = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{d^2y}{dx^2} +\\\\frac{1}{x} \\\\frac{dy}{dx}-\\\\left(a^2+\\\\frac{p^2}{x^2}\\\\right)y = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewith \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y(x1) = y1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey(x_1) = y_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and either \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y(x0) = y0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey(x_0) = y_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y'(x0) = y'0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\\\\prime(x_0) = y\\\\prime_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Along with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, one of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eyp0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be assigned numerical values, and the other will be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNaN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The function should return the values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at the specified values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOne of the applications for this equation is in groundwater. For \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the equation arises in the flow of water to a well pumping in a leaky confined aquifer; the independent variable \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the normalized distance from the well, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is related to the piezometric head, a combination of the elevation and pressure of the water. Specifying the derivative at a point amounts to specifying the flow to the well.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61175,"title":"[Master Regular Expression] Goat Latin","description":"You are given a string sentence that consist of words separated by spaces. Each word consists of lowercase and uppercase letters only.\r\nWe would like to convert the sentence to \"Goat Latin\" (a made-up language similar to Pig Latin.) The rules of Goat Latin are as follows:\r\nIf a word begins with a vowel ('a', 'e', 'i', 'o', or 'u'), append \"ma\" to the end of the word.\r\nFor example, the word \"apple\" becomes \"applema\".\r\nIf a word begins with a consonant (i.e., not a vowel), remove the first letter and append it to the end, then add \"ma\".\r\nFor example, the word \"goat\" becomes \"oatgma\".\r\nAdd one letter 'a' to the end of each word per its word index in the sentence, starting with 1.\r\nFor example, the first word gets \"a\" added to the end, the second word gets \"aa\" added to the end, and so on.\r\nReturn the final sentence representing the conversion from sentence to Goat Latin.\r\n \r\nExample 1:\r\nInput: sentence = \"I speak Goat Latin\"\r\nOutput: \"Imaa peaksmaaa oatGmaaaa atinLmaaaaa\"\r\nExample 2:\r\nInput: sentence = \"The quick brown fox jumped over the lazy dog\"\r\nOutput: \"heTmaa uickqmaaa rownbmaaaa oxfmaaaaa umpedjmaaaaaa overmaaaaaaa hetmaaaaaaaa azylmaaaaaaaaa ogdmaaaaaaaaaa\"\r\n \r\nConstraints:\r\n1 \u003c= sentence.length \u003c= 150\r\nsentence consists of English letters and spaces.\r\nsentence has no leading or trailing spaces.\r\nAll the words in sentence are separated by a single space.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 809.375px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 404.688px; transform-origin: 408px 404.688px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given a string sentence that consist of words separated by spaces. Each word consists of lowercase and uppercase letters only.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe would like to convert the sentence to \"Goat Latin\" (a made-up language similar to Pig Latin.) The rules of Goat Latin are as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf a word begins with a vowel ('a', 'e', 'i', 'o', or 'u'), append \"ma\" to the end of the word.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the word \"apple\" becomes \"applema\".\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf a word begins with a consonant (i.e., not a vowel), remove the first letter and append it to the end, then add \"ma\".\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the word \"goat\" becomes \"oatgma\".\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAdd one letter 'a' to the end of each word per its word index in the sentence, starting with 1.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the first word gets \"a\" added to the end, the second word gets \"aa\" added to the end, and so on.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e the final sentence representing the conversion from sentence to Goat Latin\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 1:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sentence = \"I speak Goat Latin\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \"Imaa peaksmaaa oatGmaaaa atinLmaaaaa\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 2:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sentence = \"The quick brown fox jumped over the lazy dog\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \"heTmaa uickqmaaa rownbmaaaa oxfmaaaaa umpedjmaaaaaa overmaaaaaaa hetmaaaaaaaa azylmaaaaaaaaa ogdmaaaaaaaaaa\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConstraints:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1 \u0026lt;= sentence.length \u0026lt;= 150\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esentence consists of English letters and spaces.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esentence has no leading or trailing spaces.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAll the words in sentence are separated by a single space.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function result = solution(sentence)\r\n\r\nend","test_suite":"%%\r\nsentence = 'I speak Goat Latin';\r\ncorrect_answer = 'Imaa peaksmaaa oatGmaaaa atinLmaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'The quick brown fox jumped over the lazy dog';\r\ncorrect_answer = 'heTmaa uickqmaaa rownbmaaaa oxfmaaaaa umpedjmaaaaaa overmaaaaaaa hetmaaaaaaaa azylmaaaaaaaaa ogdmaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'YLI Tdy kh dXKaa yRlPm WCVHO jVA tkLqg KWvQP Vo x aF IJSb DJUn q';\r\ncorrect_answer = 'LIYmaa dyTmaaa hkmaaaa XKaadmaaaaa RlPmymaaaaaa CVHOWmaaaaaaa VAjmaaaaaaaa kLqgtmaaaaaaaaa WvQPKmaaaaaaaaaa oVmaaaaaaaaaaa xmaaaaaaaaaaaa aFmaaaaaaaaaaaaa IJSbmaaaaaaaaaaaaaa JUnDmaaaaaaaaaaaaaaa qmaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'win QKDZ zoI pFP OFxhk XHUl qbQw W Em tzur Nm Wolnm wQ kQZh mvqwr I';\r\ncorrect_answer = 'inwmaa KDZQmaaa oIzmaaaa FPpmaaaaa OFxhkmaaaaaa HUlXmaaaaaaa bQwqmaaaaaaaa Wmaaaaaaaaa Emmaaaaaaaaaa zurtmaaaaaaaaaaa mNmaaaaaaaaaaaa olnmWmaaaaaaaaaaaaa Qwmaaaaaaaaaaaaaa QZhkmaaaaaaaaaaaaaaa vqwrmmaaaaaaaaaaaaaaaa Imaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'zo';\r\ncorrect_answer = 'ozmaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'cUS j E NlYz j Tc HR P p';\r\ncorrect_answer = 'UScmaa jmaaa Emaaaa lYzNmaaaaa jmaaaaaa cTmaaaaaaa RHmaaaaaaaa Pmaaaaaaaaa pmaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'FAMfT ain J z oEo aDttb';\r\ncorrect_answer = 'AMfTFmaa ainmaaa Jmaaaa zmaaaaa oEomaaaaaa aDttbmaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'NPm t gwad PVVG d MGLk Yvmy SXgK f A xPB zrnY Pz Ga';\r\ncorrect_answer = 'PmNmaa tmaaa wadgmaaaa VVGPmaaaaa dmaaaaaa GLkMmaaaaaaa vmyYmaaaaaaaa XgKSmaaaaaaaaa fmaaaaaaaaaa Amaaaaaaaaaaa PBxmaaaaaaaaaaaa rnYzmaaaaaaaaaaaaa zPmaaaaaaaaaaaaaa aGmaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'VRVJO kxPa';\r\ncorrect_answer = 'RVJOVmaa xPakmaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'dwR MWqM wBHyj va dwCF eod sHzt ft zP SASy GD uvh';\r\ncorrect_answer = 'wRdmaa WqMMmaaa BHyjwmaaaa avmaaaaa wCFdmaaaaaa eodmaaaaaaa Hztsmaaaaaaaa tfmaaaaaaaaa Pzmaaaaaaaaaa ASySmaaaaaaaaaaa DGmaaaaaaaaaaaa uvhmaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'W UvuC AEg Hsqo r mdzgu';\r\ncorrect_answer = 'Wmaa UvuCmaaa AEgmaaaa sqoHmaaaaa rmaaaaaa dzgummaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'rDIH peGn';\r\ncorrect_answer = 'DIHrmaa eGnpmaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'Lr EV XM S Drre IDu sXbwK AFMP DS ASJ A x cXjtk w fz sD vut jg';\r\ncorrect_answer = 'rLmaa EVmaaa MXmaaaa Smaaaaa rreDmaaaaaa IDumaaaaaaa XbwKsmaaaaaaaa AFMPmaaaaaaaaa SDmaaaaaaaaaa ASJmaaaaaaaaaaa Amaaaaaaaaaaaa xmaaaaaaaaaaaaa Xjtkcmaaaaaaaaaaaaaa wmaaaaaaaaaaaaaaa zfmaaaaaaaaaaaaaaaa Dsmaaaaaaaaaaaaaaaaa utvmaaaaaaaaaaaaaaaaaa gjmaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'ALNn';\r\ncorrect_answer = 'ALNnmaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'w YCcE Cx t';\r\ncorrect_answer = 'wmaa CcEYmaaa xCmaaaa tmaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'KYgHu kur tf Qrz D sSr mOo BTW Y dlsw VGXN SQg GuRb X BU IL';\r\ncorrect_answer = 'YgHuKmaa urkmaaa ftmaaaa rzQmaaaaa Dmaaaaaa Srsmaaaaaaa Oommaaaaaaaa TWBmaaaaaaaaa Ymaaaaaaaaaa lswdmaaaaaaaaaaa GXNVmaaaaaaaaaaaa QgSmaaaaaaaaaaaaa uRbGmaaaaaaaaaaaaaa Xmaaaaaaaaaaaaaaa UBmaaaaaaaaaaaaaaaa ILmaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'xFC oTW YBfHj XfpPw bDD';\r\ncorrect_answer = 'FCxmaa oTWmaaa BfHjYmaaaa fpPwXmaaaaa DDbmaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'O B ZYpNk IfEYR Kmcy i IYo WiP T YNL k eM rhIRJ t AYnT';\r\ncorrect_answer = 'Omaa Bmaaa YpNkZmaaaa IfEYRmaaaaa mcyKmaaaaaa imaaaaaaa IYomaaaaaaaa iPWmaaaaaaaaa Tmaaaaaaaaaa NLYmaaaaaaaaaaa kmaaaaaaaaaaaa eMmaaaaaaaaaaaaa hIRJrmaaaaaaaaaaaaaa tmaaaaaaaaaaaaaaa AYnTmaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'e ttpp yZ Xi NSFfx cbpW TtT Ufl';\r\ncorrect_answer = 'emaa tpptmaaa Zymaaaa iXmaaaaa SFfxNmaaaaaa bpWcmaaaaaaa tTTmaaaaaaaa Uflmaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'at uj EE W k NhW cJo YJzf Ba Ei J CYG BS RsMWI oEr';\r\ncorrect_answer = 'atmaa ujmaaa EEmaaaa Wmaaaaa kmaaaaaa hWNmaaaaaaa Jocmaaaaaaaa JzfYmaaaaaaaaa aBmaaaaaaaaaa Eimaaaaaaaaaaa Jmaaaaaaaaaaaa YGCmaaaaaaaaaaaaa SBmaaaaaaaaaaaaaa sMWIRmaaaaaaaaaaaaaaa oErmaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'YJK WRiRy BR nsj jR aq oOBiB LM jho PIoh Jd ZVD MKJo GQa ZQ JQoI C TjW rGBxs eu';\r\ncorrect_answer = 'JKYmaa RiRyWmaaa RBmaaaa sjnmaaaaa Rjmaaaaaa aqmaaaaaaa oOBiBmaaaaaaaa MLmaaaaaaaaa hojmaaaaaaaaaa IohPmaaaaaaaaaaa dJmaaaaaaaaaaaa VDZmaaaaaaaaaaaaa KJoMmaaaaaaaaaaaaaa QaGmaaaaaaaaaaaaaaa QZmaaaaaaaaaaaaaaaa QoIJmaaaaaaaaaaaaaaaaa Cmaaaaaaaaaaaaaaaaaa jWTmaaaaaaaaaaaaaaaaaaa GBxsrmaaaaaaaaaaaaaaaaaaaa eumaaaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'KhQ RzIxv W y BZ';\r\ncorrect_answer = 'hQKmaa zIxvRmaaa Wmaaaa ymaaaaa ZBmaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'O uQT kTpvQ we MprM KeyHB o PWskJ wV uMppp V mzPt LO GNAr E k A y w';\r\ncorrect_answer = 'Omaa uQTmaaa TpvQkmaaaa ewmaaaaa prMMmaaaaaa eyHBKmaaaaaaa omaaaaaaaa WskJPmaaaaaaaaa Vwmaaaaaaaaaa uMpppmaaaaaaaaaaa Vmaaaaaaaaaaaa zPtmmaaaaaaaaaaaaa OLmaaaaaaaaaaaaaa NArGmaaaaaaaaaaaaaaa Emaaaaaaaaaaaaaaaa kmaaaaaaaaaaaaaaaaa Amaaaaaaaaaaaaaaaaaa ymaaaaaaaaaaaaaaaaaaa wmaaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'Qem sv v CsIJ';\r\ncorrect_answer = 'emQmaa vsmaaa vmaaaa sIJCmaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'WDE mKpD umWx';\r\ncorrect_answer = 'DEWmaa KpDmmaaa umWxmaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'IwiK tHUzG fff WGW p aiNRF XMK TYZV dQ b CrES';\r\ncorrect_answer = 'IwiKmaa HUzGtmaaa fffmaaaa GWWmaaaaa pmaaaaaa aiNRFmaaaaaaa MKXmaaaaaaaa YZVTmaaaaaaaaa Qdmaaaaaaaaaa bmaaaaaaaaaaa rESCmaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'Cjm nX RuiM sjZXi wlhnC F x Xp Ith p GkYwR baO pSI';\r\ncorrect_answer = 'jmCmaa Xnmaaa uiMRmaaaa jZXismaaaaa lhnCwmaaaaaa Fmaaaaaaa xmaaaaaaaa pXmaaaaaaaaa Ithmaaaaaaaaaa pmaaaaaaaaaaa kYwRGmaaaaaaaaaaaa aObmaaaaaaaaaaaaa SIpmaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'njtB MhagV fXgz yd nm bVtIX';\r\ncorrect_answer = 'jtBnmaa hagVMmaaa Xgzfmaaaa dymaaaaa mnmaaaaaa VtIXbmaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'vfzy IoIHU';\r\ncorrect_answer = 'fzyvmaa IoIHUmaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'wP TzEWi nR o Gvn tfg IRzp c tD OEf dtoM N ma k Vo O FrJm sl';\r\ncorrect_answer = 'Pwmaa zEWiTmaaa Rnmaaaa omaaaaa vnGmaaaaaa fgtmaaaaaaa IRzpmaaaaaaaa cmaaaaaaaaa Dtmaaaaaaaaaa OEfmaaaaaaaaaaa toMdmaaaaaaaaaaaa Nmaaaaaaaaaaaaa ammaaaaaaaaaaaaaa kmaaaaaaaaaaaaaaa oVmaaaaaaaaaaaaaaaa Omaaaaaaaaaaaaaaaaa rJmFmaaaaaaaaaaaaaaaaaa lsmaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'asmW tJKE OBeUn rNP TeIAr skn h Eh a JgLi J d a d';\r\ncorrect_answer = 'asmWmaa JKEtmaaa OBeUnmaaaa NPrmaaaaa eIArTmaaaaaa knsmaaaaaaa hmaaaaaaaa Ehmaaaaaaaaa amaaaaaaaaaa gLiJmaaaaaaaaaaa Jmaaaaaaaaaaaa dmaaaaaaaaaaaaa amaaaaaaaaaaaaaa dmaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'Au';\r\ncorrect_answer = 'Aumaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'hOM y vw KabmF rxfLL WcPy cO ORrjt bp ks gkz MpP NrLbG c b BNEMq zfQIt vcEp Eqh frbVt';\r\ncorrect_answer = 'OMhmaa ymaaa wvmaaaa abmFKmaaaaa xfLLrmaaaaaa cPyWmaaaaaaa Ocmaaaaaaaa ORrjtmaaaaaaaaa pbmaaaaaaaaaa skmaaaaaaaaaaa kzgmaaaaaaaaaaaa pPMmaaaaaaaaaaaaa rLbGNmaaaaaaaaaaaaaa cmaaaaaaaaaaaaaaa bmaaaaaaaaaaaaaaaa NEMqBmaaaaaaaaaaaaaaaaa fQItzmaaaaaaaaaaaaaaaaaa cEpvmaaaaaaaaaaaaaaaaaaa Eqhmaaaaaaaaaaaaaaaaaaaa rbVtfmaaaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'Djl lWo Qsbrt Y i Act ZwK h cbDrl Jtukm VOmEk J NQluv fBGok siU Iky z JM DM Edtb';\r\ncorrect_answer = 'jlDmaa Wolmaaa sbrtQmaaaa Ymaaaaa imaaaaaa Actmaaaaaaa wKZmaaaaaaaa hmaaaaaaaaa bDrlcmaaaaaaaaaa tukmJmaaaaaaaaaaa OmEkVmaaaaaaaaaaaa Jmaaaaaaaaaaaaa QluvNmaaaaaaaaaaaaaa BGokfmaaaaaaaaaaaaaaa iUsmaaaaaaaaaaaaaaaa Ikymaaaaaaaaaaaaaaaaa zmaaaaaaaaaaaaaaaaaa MJmaaaaaaaaaaaaaaaaaaa MDmaaaaaaaaaaaaaaaaaaaa Edtbmaaaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'DYwO bAv lw qoszQ bp Qh SCaAL UKWa bAHNo';\r\ncorrect_answer = 'YwODmaa Avbmaaa wlmaaaa oszQqmaaaaa pbmaaaaaa hQmaaaaaaa CaALSmaaaaaaaa UKWamaaaaaaaaa AHNobmaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":4945898,"edited_by":4945898,"edited_at":"2026-01-31T12:14:26.000Z","deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2026-01-31T12:12:55.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-31T12:12:09.000Z","updated_at":"2026-09-15T09:03:55.000Z","published_at":"2026-01-31T12:12:09.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given a string sentence that consist of words separated by spaces. Each word consists of lowercase and uppercase letters only.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe would like to convert the sentence to \\\"Goat Latin\\\" (a made-up language similar to Pig Latin.) The rules of Goat Latin are as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf a word begins with a vowel ('a', 'e', 'i', 'o', or 'u'), append \\\"ma\\\" to the end of the word.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the word \\\"apple\\\" becomes \\\"applema\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf a word begins with a consonant (i.e., not a vowel), remove the first letter and append it to the end, then add \\\"ma\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the word \\\"goat\\\" becomes \\\"oatgma\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAdd one letter 'a' to the end of each word per its word index in the sentence, starting with 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the first word gets \\\"a\\\" added to the end, the second word gets \\\"aa\\\" added to the end, and so on.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e the final sentence representing the conversion from sentence to Goat Latin\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e sentence = \\\"I speak Goat Latin\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \\\"Imaa peaksmaaa oatGmaaaa atinLmaaaaa\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e sentence = \\\"The quick brown fox jumped over the lazy dog\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \\\"heTmaa uickqmaaa rownbmaaaa oxfmaaaaa umpedjmaaaaaa overmaaaaaaa hetmaaaaaaaa azylmaaaaaaaaa ogdmaaaaaaaaaa\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConstraints:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1 \u0026lt;= sentence.length \u0026lt;= 150\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esentence consists of English letters and spaces.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esentence has no leading or trailing spaces.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAll the words in sentence are separated by a single space.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1092,"title":"Decimation","description":"When dealing to the Roman Army, the term decimate meant that the entire unit would be broken up into groups of ten soldiers, and lots would be drawn.  The person who was unlucky enough to draw the short straw would be executed by the other nine members of his group.\r\n\r\nThe bloodthirsty Roman Centurion Carnage Maximus decided to apply this to his prisoners, with a few gruesome differences.  Rather than kill every tenth prisoner and allow the rest to live, he is going to leave only one prisoner alive and kill all of the others.  Instead of killing every tenth prisoner, he chooses a number (kill_every).  If kill_every=3, he kills every third prisoner.  If kill_every=5, he kills every fifth prisoner.  He always chooses a number between 2 and the number of prisoners he has, and this process will be repeated until there is only one prisoner left.  For example, if there are 10 prisoners, and kill_every=3\r\n\r\nFirst iteration: 1 2 3 4 5 6 7 8 9 10\r\n\r\n1-2-3 4-5-6 7-8-9 10\r\n\r\nPrisoners 3, 6 and 9 will be killed.\r\n\r\nSecond iteration: 1 2 4 5 7 8 10\r\n\r\nBecause Prisoner 10 was counted during the first iteration, the executions\r\nwill proceed as such: 10-1-2 4-5-7 8-10, so prisoners 2 and 7 will be killed\r\n\r\nThird iteration: 1 4 5 8 10\r\n8-10-1 4-5-8 10, so prisoners 1 and 8 executed.\r\n\r\nFourth Iteration:  10-4-5 10\r\nPrisoner 5 is executed.\r\n\r\nFifth iteration:  10-4 10\r\nPrisoner 10 is executed\r\n\r\nSince the sole survivor is prisoner 4, he is released.\r\n\r\nYou are an unlucky prisoner caught by Carnage Maximum.  Prior to lining up the prisoners, he reveals the number of prisoners he has and his value of kill_every for the day.  Your job is to figure out which prisoner you need to be in order to survive.  Write a MATLAB script that takes the values of num_prisoners and kill_every.  The output will be survivor, which is the position of the person who survives.  If you write your script quickly enough, that person will be you.\r\n\r\nGood luck!","description_html":"\u003cp\u003eWhen dealing to the Roman Army, the term decimate meant that the entire unit would be broken up into groups of ten soldiers, and lots would be drawn.  The person who was unlucky enough to draw the short straw would be executed by the other nine members of his group.\u003c/p\u003e\u003cp\u003eThe bloodthirsty Roman Centurion Carnage Maximus decided to apply this to his prisoners, with a few gruesome differences.  Rather than kill every tenth prisoner and allow the rest to live, he is going to leave only one prisoner alive and kill all of the others.  Instead of killing every tenth prisoner, he chooses a number (kill_every).  If kill_every=3, he kills every third prisoner.  If kill_every=5, he kills every fifth prisoner.  He always chooses a number between 2 and the number of prisoners he has, and this process will be repeated until there is only one prisoner left.  For example, if there are 10 prisoners, and kill_every=3\u003c/p\u003e\u003cp\u003eFirst iteration: 1 2 3 4 5 6 7 8 9 10\u003c/p\u003e\u003cp\u003e1-2-3 4-5-6 7-8-9 10\u003c/p\u003e\u003cp\u003ePrisoners 3, 6 and 9 will be killed.\u003c/p\u003e\u003cp\u003eSecond iteration: 1 2 4 5 7 8 10\u003c/p\u003e\u003cp\u003eBecause Prisoner 10 was counted during the first iteration, the executions\r\nwill proceed as such: 10-1-2 4-5-7 8-10, so prisoners 2 and 7 will be killed\u003c/p\u003e\u003cp\u003eThird iteration: 1 4 5 8 10\r\n8-10-1 4-5-8 10, so prisoners 1 and 8 executed.\u003c/p\u003e\u003cp\u003eFourth Iteration:  10-4-5 10\r\nPrisoner 5 is executed.\u003c/p\u003e\u003cp\u003eFifth iteration:  10-4 10\r\nPrisoner 10 is executed\u003c/p\u003e\u003cp\u003eSince the sole survivor is prisoner 4, he is released.\u003c/p\u003e\u003cp\u003eYou are an unlucky prisoner caught by Carnage Maximum.  Prior to lining up the prisoners, he reveals the number of prisoners he has and his value of kill_every for the day.  Your job is to figure out which prisoner you need to be in order to survive.  Write a MATLAB script that takes the values of num_prisoners and kill_every.  The output will be survivor, which is the position of the person who survives.  If you write your script quickly enough, that person will be you.\u003c/p\u003e\u003cp\u003eGood luck!\u003c/p\u003e","function_template":"function survivor=decimate(num_prisoners,kill_every)\r\nsurvivor=4;\r\nend","test_suite":"%%\r\nassert(isequal(decimate(10,3),4))\r\n%%\r\nassert(isequal(decimate(1024,3),676))\r\n%%\r\nassert(isequal(decimate(2012,50),543))\r\n%%\r\nassert(isequal(decimate(30,5),3))\r\n%%\r\nassert(isequal(decimate(10,10),8))\r\n%%\r\nassert(isequal(decimate(2048,2),1))","published":true,"deleted":false,"likes_count":20,"comments_count":14,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":328,"test_suite_updated_at":"2012-12-04T21:28:04.000Z","rescore_all_solutions":false,"group_id":13,"created_at":"2012-12-04T19:47:49.000Z","updated_at":"2026-09-15T02:14:07.000Z","published_at":"2012-12-04T19:53:55.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen dealing to the Roman Army, the term decimate meant that the entire unit would be broken up into groups of ten soldiers, and lots would be drawn. The person who was unlucky enough to draw the short straw would be executed by the other nine members of his group.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe bloodthirsty Roman Centurion Carnage Maximus decided to apply this to his prisoners, with a few gruesome differences. Rather than kill every tenth prisoner and allow the rest to live, he is going to leave only one prisoner alive and kill all of the others. Instead of killing every tenth prisoner, he chooses a number (kill_every). If kill_every=3, he kills every third prisoner. If kill_every=5, he kills every fifth prisoner. He always chooses a number between 2 and the number of prisoners he has, and this process will be repeated until there is only one prisoner left. For example, if there are 10 prisoners, and kill_every=3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFirst iteration: 1 2 3 4 5 6 7 8 9 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1-2-3 4-5-6 7-8-9 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrisoners 3, 6 and 9 will be killed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSecond iteration: 1 2 4 5 7 8 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBecause Prisoner 10 was counted during the first iteration, the executions will proceed as such: 10-1-2 4-5-7 8-10, so prisoners 2 and 7 will be killed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThird iteration: 1 4 5 8 10 8-10-1 4-5-8 10, so prisoners 1 and 8 executed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFourth Iteration: 10-4-5 10 Prisoner 5 is executed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFifth iteration: 10-4 10 Prisoner 10 is executed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince the sole survivor is prisoner 4, he is released.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are an unlucky prisoner caught by Carnage Maximum. Prior to lining up the prisoners, he reveals the number of prisoners he has and his value of kill_every for the day. Your job is to figure out which prisoner you need to be in order to survive. Write a MATLAB script that takes the values of num_prisoners and kill_every. The output will be survivor, which is the position of the person who survives. If you write your script quickly enough, that person will be you.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood luck!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":364,"title":"Matrix spiral","description":"Make a spiral in a (n*n) matrix. The spiral has to start in the top left, and has to rotate clockwise to the center. The spiral has to have a padding of zeros between itself.\r\n\r\nThe (n*n) matrix is filled with zeros except for the spiral, that has to be made of 11 (elevens, for visual reference).\r\nThe final matrix has to have the same or more zeros than elevens.\r\n\r\nExample:\r\nn=8\r\n\r\nA =\r\n\r\n    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11     0    11\r\n     0     0    11     0     0    11     0    11\r\n     0     0    11     0    11    11     0    11\r\n     0     0    11     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0","description_html":"\u003cp\u003eMake a spiral in a (n*n) matrix. The spiral has to start in the top left, and has to rotate clockwise to the center. The spiral has to have a padding of zeros between itself.\u003c/p\u003e\u003cp\u003eThe (n*n) matrix is filled with zeros except for the spiral, that has to be made of 11 (elevens, for visual reference).\r\nThe final matrix has to have the same or more zeros than elevens.\u003c/p\u003e\u003cp\u003eExample:\r\nn=8\u003c/p\u003e\u003cp\u003eA =\u003c/p\u003e\u003cpre\u003e    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11     0    11\r\n     0     0    11     0     0    11     0    11\r\n     0     0    11     0    11    11     0    11\r\n     0     0    11     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0\u003c/pre\u003e","function_template":"function A = Matrix_Spiral(n)\r\n  A = n;\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct =[0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n%%\r\nn = 2;\r\ny_correct =[11    11\r\n     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n%%\r\nn = 3;\r\ny_correct =[11    11    11\r\n     0     0    11\r\n     0     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n%%\r\nn = 4;\r\ny_correct =[11    11    11    11\r\n     0     0     0    11\r\n     0     0    11    11\r\n     0     0     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n\r\n%%\r\nn = 5;\r\ny_correct =[11    11    11    11    11\r\n     0     0     0     0    11\r\n     0     0    11     0    11\r\n     0     0    11    11    11\r\n     0     0     0     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n%%\r\nn = 10;\r\ny_correct =[11    11    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11     0    11\r\n     0     0    11     0     0     0     0    11     0    11\r\n     0     0    11     0    11    11     0    11     0    11\r\n     0     0    11     0    11     0     0    11     0    11\r\n     0     0    11     0    11    11    11    11     0    11\r\n     0     0    11     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n\r\n%%\r\nn = 17;\r\ny_correct =[11    11    11    11    11    11    11    11    11    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11    11    11    11    11    11    11    11     0    11\r\n     0     0    11     0     0     0     0     0     0     0     0     0     0     0    11     0    11\r\n     0     0    11     0    11    11    11    11    11    11    11    11    11     0    11     0    11\r\n     0     0    11     0    11     0     0     0     0     0     0     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11    11    11    11    11     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11     0     0     0    11     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11     0    11     0    11     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11     0    11    11    11     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11     0     0     0     0     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11    11    11    11    11    11    11     0    11     0    11\r\n     0     0    11     0    11     0     0     0     0     0     0     0     0     0    11     0    11\r\n     0     0    11     0    11    11    11    11    11    11    11    11    11    11    11     0    11\r\n     0     0    11     0     0     0     0     0     0     0     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11    11    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))","published":true,"deleted":false,"likes_count":5,"comments_count":3,"created_by":872,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":98,"test_suite_updated_at":"2012-02-20T12:29:13.000Z","rescore_all_solutions":false,"group_id":18,"created_at":"2012-02-20T12:17:08.000Z","updated_at":"2026-04-28T18:06:26.000Z","published_at":"2012-02-20T12:29:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a spiral in a (n*n) matrix. The spiral has to start in the top left, and has to rotate clockwise to the center. The spiral has to have a padding of zeros between itself.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe (n*n) matrix is filled with zeros except for the spiral, that has to be made of 11 (elevens, for visual reference). The final matrix has to have the same or more zeros than elevens.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: n=8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA =\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    11    11    11    11    11    11    11    11\\n     0     0     0     0     0     0     0    11\\n     0     0    11    11    11    11     0    11\\n     0     0    11     0     0    11     0    11\\n     0     0    11     0    11    11     0    11\\n     0     0    11     0     0     0     0    11\\n     0     0    11    11    11    11    11    11\\n     0     0     0     0     0     0     0     0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":3084,"title":"Scrabble Scores - 11","description":"This problem builds on the previous problem, wherein you were provided a letter of an existing word on the board and from which you played a word to find the highest scoring word. See the previous problem for more details.\r\n\r\nNow, you will be provided a multiplier character array that represents the fifteen possible squares that can be played on, ranging from seven above the existing letter (in which case the existing letter is the last letter in an eight-letter word) to seven below the existing letter (in which case the existing letter is the first letter in an eight-letter word) with the existing letter fixed in the 8th position. The multipliers are the same as in previous problems:\r\n\r\n * D: double word\r\n * T: triple word\r\n * Q: quadruple word\r\n * d: double letter\r\n * t: triple letter\r\n * q: quadruple letter\r\n\r\nThe center multiplier square will be left blank, since it's already covered by a tile. Write a routine to determine the highest scoring word(s) based on the multiplier squares.\r\n\r\nOnce again, you will be provided a cell array of strings containing all possible words based on the existing letter and the letters on your tray. In addition to providing the highest score, also provide the word(s) that achieve that score in a cell array. See the test suite for examples. Due to high-scoring tiles, the highest score may not be achieved by the longest word(s).\r\n\r\nRelated problems:\r\n\r\nPrevious problem: 10 - \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3082-scrabble-scores-10 Word score optimization (known letter)\u003e. Next problem: 12 - \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12 Word score optimization (first word)\u003e.","description_html":"\u003cp\u003eThis problem builds on the previous problem, wherein you were provided a letter of an existing word on the board and from which you played a word to find the highest scoring word. See the previous problem for more details.\u003c/p\u003e\u003cp\u003eNow, you will be provided a multiplier character array that represents the fifteen possible squares that can be played on, ranging from seven above the existing letter (in which case the existing letter is the last letter in an eight-letter word) to seven below the existing letter (in which case the existing letter is the first letter in an eight-letter word) with the existing letter fixed in the 8th position. The multipliers are the same as in previous problems:\u003c/p\u003e\u003cpre\u003e * D: double word\r\n * T: triple word\r\n * Q: quadruple word\r\n * d: double letter\r\n * t: triple letter\r\n * q: quadruple letter\u003c/pre\u003e\u003cp\u003eThe center multiplier square will be left blank, since it's already covered by a tile. Write a routine to determine the highest scoring word(s) based on the multiplier squares.\u003c/p\u003e\u003cp\u003eOnce again, you will be provided a cell array of strings containing all possible words based on the existing letter and the letters on your tray. In addition to providing the highest score, also provide the word(s) that achieve that score in a cell array. See the test suite for examples. Due to high-scoring tiles, the highest score may not be achieved by the longest word(s).\u003c/p\u003e\u003cp\u003eRelated problems:\u003c/p\u003e\u003cp\u003ePrevious problem: 10 - \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3082-scrabble-scores-10\"\u003eWord score optimization (known letter)\u003c/a\u003e. Next problem: 12 - \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12\"\u003eWord score optimization (first word)\u003c/a\u003e.\u003c/p\u003e","function_template":"function [score,max_word] = scrabble_scores_11(words,mult,existing_letter)\r\n\r\nscore = 0;\r\nmax_word = {''};\r\n\r\nend","test_suite":"%%\r\nexisting_letter = 's'; %the word must contain this letter, which is in an already played word\r\ntray_letters = 'aethilm'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including the first letter with your tray letters\r\nwords = {'ae','ah','ai','al','am','as','at','eh','el','em','es','et','ha','he','hi','hm','is','it','la','li','ma','me','mi','sh','si','ta','te','ti','ahi','ahs','ail','aim','ais','ait','ale','als','alt','ami','ash','ate','eat','elm','els','ems','est','eta','eth','hae','ham','has','hat','hem','hes','het','hie','him','his','hit','ism','its','lah','lam','las','lat','lea','lei','let','lie','lis','lit','mae','mas','mat','meh','mel','met','mil','mis','sae','sal','sat','sea','sei','sel','set','sha','she','sim','sit','tae','tam','tas','tea','tel','tes','the','tie','til','tis','ahem','ahis','ails','aims','aits','ales','alit','alme','alms','alts','amie','amis','ates','east','eath','eats','elhi','elms','emit','etas','eths','haem','haes','haet','hail','hale','halm','halt','hame','hams','hast','hate','hats','heal','heat','heil','helm','hems','hest','hets','hies','hila','hilt','hims','hist','hits','ilea','isle','item','lahs','lame','lams','lase','lash','last','late','lath','lati','lats','leas','leis','lest','lets','lias','lies','lima','lime','list','lite','lits','maes','mail','male','malt','mash','mast','mate','math','mats','meal','meat','mels','melt','mesa','mesh','meta','meth','mile','mils','milt','mise','mist','mite','sail','sale','salt','same','sate','sati','seal','seam','seat','semi','seta','sham','shea','shim','sial','silt','sima','site','sith','slam','slat','slim','slit','smit','stem','tael','tail','tale','tali','tame','tams','tase','teal','team','teas','tela','tels','thae','them','this','ties','tile','tils','time','aisle','alist','almeh','almes','amies','email','emits','haems','haets','hails','hales','halms','halts','hames','haste','hates','heals','heats','heils','heist','helms','hemal','hilts','islet','istle','items','laith','lames','lathe','lathi','laths','leash','least','limas','limes','litas','lites','lithe','maile','mails','maist','males','malts','mates','maths','meals','meats','melts','metal','meths','metis','miles','milts','mites','saith','salmi','satem','selah','setal','shale','shalt','shame','sheal','shiel','slate','slime','smalt','smelt','smile','smite','smith','stale','steal','steam','stela','stile','stime','taels','tails','tales','tames','tamis','teals','teams','telia','tesla','thali','tiles','times','almehs','emails','halest','halite','hamlet','haslet','hiemal','lamest','lathes','lathis','latish','mailes','mashie','mesial','metals','misate','miseat','saithe','saltie','samiel','samite','samlet','sheila','shelta','smalti','stelai','tahsil','thalis','theism','atheism','halites','hamlets','heliast'};\r\nmult = ' T   d   d   T '; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\nmax_score_corr = 39;\r\nmax_word_corr = {'hamlets'};\r\n[max_score,max_word] = scrabble_scores_11(words,mult,existing_letter);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(max_word,max_word_corr))\r\n\r\n\r\n%%\r\nind = randi(4);\r\nexisting_letter = 's'; %the word must contain this letter, which is in an already played word\r\ntray_letters = 'aethilm'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including the first letter with your tray letters\r\nwords = {'ae','ah','ai','al','am','as','at','eh','el','em','es','et','ha','he','hi','hm','is','it','la','li','ma','me','mi','sh','si','ta','te','ti','ahi','ahs','ail','aim','ais','ait','ale','als','alt','ami','ash','ate','eat','elm','els','ems','est','eta','eth','hae','ham','has','hat','hem','hes','het','hie','him','his','hit','ism','its','lah','lam','las','lat','lea','lei','let','lie','lis','lit','mae','mas','mat','meh','mel','met','mil','mis','sae','sal','sat','sea','sei','sel','set','sha','she','sim','sit','tae','tam','tas','tea','tel','tes','the','tie','til','tis','ahem','ahis','ails','aims','aits','ales','alit','alme','alms','alts','amie','amis','ates','east','eath','eats','elhi','elms','emit','etas','eths','haem','haes','haet','hail','hale','halm','halt','hame','hams','hast','hate','hats','heal','heat','heil','helm','hems','hest','hets','hies','hila','hilt','hims','hist','hits','ilea','isle','item','lahs','lame','lams','lase','lash','last','late','lath','lati','lats','leas','leis','lest','lets','lias','lies','lima','lime','list','lite','lits','maes','mail','male','malt','mash','mast','mate','math','mats','meal','meat','mels','melt','mesa','mesh','meta','meth','mile','mils','milt','mise','mist','mite','sail','sale','salt','same','sate','sati','seal','seam','seat','semi','seta','sham','shea','shim','sial','silt','sima','site','sith','slam','slat','slim','slit','smit','stem','tael','tail','tale','tali','tame','tams','tase','teal','team','teas','tela','tels','thae','them','this','ties','tile','tils','time','aisle','alist','almeh','almes','amies','email','emits','haems','haets','hails','hales','halms','halts','hames','haste','hates','heals','heats','heils','heist','helms','hemal','hilts','islet','istle','items','laith','lames','lathe','lathi','laths','leash','least','limas','limes','litas','lites','lithe','maile','mails','maist','males','malts','mates','maths','meals','meats','melts','metal','meths','metis','miles','milts','mites','saith','salmi','satem','selah','setal','shale','shalt','shame','sheal','shiel','slate','slime','smalt','smelt','smile','smite','smith','stale','steal','steam','stela','stile','stime','taels','tails','tales','tames','tamis','teals','teams','telia','tesla','thali','tiles','times','almehs','emails','halest','halite','hamlet','haslet','hiemal','lamest','lathes','lathis','latish','mailes','mashie','mesial','metals','misate','miseat','saithe','saltie','samiel','samite','samlet','sheila','shelta','smalti','stelai','tahsil','thalis','theism','atheism','halites','hamlets','heliast'};\r\nswitch ind\r\n\tcase 1\r\n\t\tmult = ' T   d   d   T '; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 39;\r\n\t\tmax_word_corr = {'hamlets'};\r\n\tcase 2\r\n\t\tmult = 'T  D  d d  D  T'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 32;\r\n\t\tmax_word_corr = {'atheism'};\r\n\tcase 3\r\n\t\tmult = 'Q  t  T T  t  Q'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 153;\r\n\t\tmax_word_corr = {'halest'};\r\n\tcase 4\r\n\t\tmult = 'Q t T d d T t Q'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 60;\r\n\t\tmax_word_corr = {'heliast'};\r\nend\r\n[max_score,max_word] = scrabble_scores_11(words,mult,existing_letter);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(max_word,max_word_corr))\r\n\r\n\r\n%%\r\nind = randi(4);\r\nexisting_letter = 't'; %the word must contain this letter, which is in an already played word\r\ntray_letters = 'eodnirl'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including the first letter with your tray letters\r\nwords = {'de','do','ed','el','en','er','et','id','in','it','li','lo','ne','no','od','oe','oi','on','or','re','te','ti','to','del','den','die','din','dit','doe','dol','don','dor','dot','eld','end','eon','ern','ion','ire','led','lei','let','lid','lie','lin','lit','lot','net','nil','nit','nod','nor','not','ode','oil','old','ole','one','ore','ort','red','rei','ret','rid','rin','rod','roe','rot','ted','tel','ten','tie','til','tin','tod','toe','ton','tor','deil','deli','delt','deni','dent','diel','diet','dine','dino','dint','diol','dire','dirl','dirt','dite','doer','doit','dole','dolt','done','dore','dote','edit','enol','idle','idol','inro','into','ired','iron','lend','leno','lent','lido','lied','lien','lier','line','lino','lint','lion','lire','lite','lode','loid','loin','lone','lord','lore','lorn','loti','nerd','nide','nite','node','nodi','noel','noil','noir','nori','note','olde','orle','redo','rein','rend','reno','rent','ride','riel','rile','rind','riot','rite','rode','roil','role','rote','roti','rotl','tein','tend','tern','tide','tied','tier','tile','tine','tire','tirl','tiro','toed','toil','told','tole','tone','tore','tori','torn','trio','trod','diner','doter','droit','drone','elint','eloin','enrol','ident','idler','indol','inert','inlet','inter','intro','irone','lento','lined','liner','lirot','liter','litre','loden','loner','nerol','niter','nitre','nitro','noted','noter','oiled','oiler','olden','older','oldie','olein','oriel','redon','relit','reoil','riled','ronde','teind','teloi','tenor','tilde','tiled','tiler','tined','tired','toile','toled','tondi','toned','toner','trend','tried','trine','triol','trode','trone','dentil','dinero','dotier','editor','entoil','indole','ironed','linted','linter','loiter','neroli','norite','orient','retold','rident','rioted','rodent','roiled','rondel','tinder','tirled','toiled','toiler','tonier','trined','triode','lentoid','retinol','tendril','trindle'};\r\nswitch ind\r\n\tcase 1\r\n\t\tmult = ' T   d   d   T '; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 27;\r\n\t\tmax_word_corr = {'tendril','trindle'};\r\n\tcase 2\r\n\t\tmult = 'T  D  d d  D  T'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 18;\r\n\t\tmax_word_corr = {'retinol','tendril','trindle'};\r\n\tcase 3\r\n\t\tmult = 'Q  t  T T  t  Q'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 81;\r\n\t\tmax_word_corr = {'retinol'};\r\n\tcase 4\r\n\t\tmult = 'Q t T d d T t Q'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 90;\r\n\t\tmax_word_corr = {'lentoid'};\r\nend\r\n[max_score,max_word] = scrabble_scores_11(words,mult,existing_letter);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(max_word,max_word_corr))\r\n\r\n\r\n%% anti-cheating test case 3\r\nind = randi(4);\r\nexisting_letter = 'n'; %the word must contain this letter, which is in an already played word\r\ntray_letters = 'dmvxeao'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including the first letter with your tray letters\r\nwords = {'ad','ae','am','an','ax','da','de','do','ed','em','en','ex','ma','me','mo','na','ne','no','od','oe','om','on','ox','ado','and','ane','ave','avo','axe','dam','dan','den','dev','dex','doe','dom','don','emo','end','eon','mad','mae','man','max','med','men','moa','mod','mon','nae','nam','nav','nod','nom','oda','ode','oma','one','ova','van','vex','voe','vox','aeon','amen','axed','axon','dame','damn','dean','demo','deva','dome','dona','done','dove','exam','exon','made','mane','mano','mead','mean','mend','meno','moan','mode','move','moxa','name','nave','nema','node','noma','nome','nova','odea','omen','oven','oxen','vane','vena','vend','admen','amend','anode','axmen','axone','daven','demon','devon','doven','maned','maven','maxed','menad','monad','monde','moved','named','nomad','novae','vaned','venom','daemon','moaned'};\r\nswitch ind\r\n\tcase 1\r\n\t\tmult = ' T   d   d   T '; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 20;\r\n\t\tmax_word_corr = {'axone'};\r\n\tcase 2\r\n\t\tmult = 'T  D  d d  D  T'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 30;\r\n\t\tmax_word_corr = {'axmen'};\r\n\tcase 3\r\n\t\tmult = 'Q  t  T T  t  Q'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 108;\r\n\t\tmax_word_corr = {'axone'};\r\n\tcase 4\r\n\t\tmult = 'Q t T d d T t Q'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 45;\r\n\t\tmax_word_corr = {'axmen'};\r\nend\r\n[max_score,max_word] = scrabble_scores_11(words,mult,existing_letter);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(max_word,max_word_corr))\r\n\r\n\r\n%% anti-cheating test case 4\r\nind = randi(4);\r\nexisting_letter = 'z'; %the word must contain this letter, which is in an already played word\r\ntray_letters = 'aehcmdi'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including the first letter with your tray letters\r\nwords = {'ad','ae','ah','ai','am','da','de','ed','eh','em','ha','he','hi','hm','id','ma','me','mi','za','ace','adz','ahi','aid','aim','ami','cad','cam','chi','dah','dam','die','dim','edh','had','hae','ham','hem','hic','hid','hie','him','ice','ich','mac','mad','mae','med','meh','mic','mid','zed','aced','ache','acid','acme','adze','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','cazh','cedi','chad','chai','cham','chem','chez','chia','chid','dace','dame','daze','dice','dime','each','emic','hade','haed','haem','hame','haze','head','hide','hied','iced','idea','idem','mace','mach','made','maid','maze','mead','mech','mica','mice','zeda','ached','aimed','amice','amide','azide','chide','chime','demic','hazed','hemic','maced','mache','maize','mazed','media','medic','miche','chimed','haemic','miched','zaideh'};\r\nswitch ind\r\n\tcase 1\r\n\t\tmult = ' T   d   d   T '; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 24;\r\n\t\tmax_word_corr = {'hazed'};\r\n\tcase 2\r\n\t\tmult = 'T  D  d d  D  T'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 40;\r\n\t\tmax_word_corr = {'zaideh'};\r\n\tcase 3\r\n\t\tmult = 'Q  t  T T  t  Q'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 162;\r\n\t\tmax_word_corr = {'cazh','hazed'};\r\n\tcase 4\r\n\t\tmult = 'Q t T d d T t Q'; %all possible multiplier squares, from seven above the first letter (meaning your word would end with the first letter) to seven below the first letter (meaning your word would start with the first letter)\r\n\t\tmax_score_corr = 84;\r\n\t\tmax_word_corr = {'zaideh'};\r\nend\r\n[max_score,max_word] = scrabble_scores_11(words,mult,existing_letter);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(max_word,max_word_corr))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":7,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":"2015-03-17T13:10:14.000Z","rescore_all_solutions":false,"group_id":40,"created_at":"2015-03-15T00:22:34.000Z","updated_at":"2026-07-15T09:52:04.000Z","published_at":"2015-03-17T01:47:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem builds on the previous problem, wherein you were provided a letter of an existing word on the board and from which you played a word to find the highest scoring word. See the previous problem for more details.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNow, you will be provided a multiplier character array that represents the fifteen possible squares that can be played on, ranging from seven above the existing letter (in which case the existing letter is the last letter in an eight-letter word) to seven below the existing letter (in which case the existing letter is the first letter in an eight-letter word) with the existing letter fixed in the 8th position. The multipliers are the same as in previous problems:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ * D: double word\\n * T: triple word\\n * Q: quadruple word\\n * d: double letter\\n * t: triple letter\\n * q: quadruple letter]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe center multiplier square will be left blank, since it's already covered by a tile. Write a routine to determine the highest scoring word(s) based on the multiplier squares.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnce again, you will be provided a cell array of strings containing all possible words based on the existing letter and the letters on your tray. In addition to providing the highest score, also provide the word(s) that achieve that score in a cell array. See the test suite for examples. Due to high-scoring tiles, the highest score may not be achieved by the longest word(s).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRelated problems:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrevious problem: 10 -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3082-scrabble-scores-10\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWord score optimization (known letter)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Next problem: 12 -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWord score optimization (first word)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1231,"title":"PACMAT Easy","description":"The Classic PACMAN game brought to Cody.\r\n\r\nPACMAT_Easy is the simple case of clearing the board of Yellow Dots while not bumping into the non-moving ghosts.\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/PACMAT_300.jpg\u003e\u003e\r\n\r\nTo aid in development of your routine, a PACMAT.m file that creates a video has been posted at \u003chttps://sites.google.com/site/razapor/matlab_cody/PACMAT_Easy.m?attredirects=0\u0026d=1 PACMAT_Easy.m\u003e. (Right click, 'save link as'). Using patches (not sprites).\r\n\r\n\r\nAn example video of the first Player \u003chttps://sites.google.com/site/razapor/matlab_cody/pac_s314_motMP4_v004.mp4?attredirects=0\u0026d=1 PACMAT_Easy_Video\u003e  (MP4: Left click and Windows Media Player)\r\n\r\nAlfonso Nieto-Castanon's 298 \u003chttps://sites.google.com/site/razapor/matlab_cody/PACMAT_Easy_ANC_298.mp4?attredirects=0\u0026d=1 PACMAT Video\u003e\r\n\r\nAlfonso employed a Local Optimum Monte-Carlo approach to find a best solution. Solution #8 is the very compact non-apriori PACMAT solver.\r\n\r\n*Inputs:* Map   Definitions: -1=Wall, 0=Empty, 1=Dot, 2=PACMAT, \u003e2=Ghost\r\n\r\n*Output:* Direction  Definitions: 1-Up, 2-Right, 3-Down, 4-Left, 0-No move\r\n\r\n*Scoring:* Total # of Moves to Clear the Yellow Dots\r\n\r\n\r\n*Near Future:* Ghosts will move with various algorithms.\r\n\r\n*Far Future:* Asteroids and Space Invaders","description_html":"\u003cp\u003eThe Classic PACMAN game brought to Cody.\u003c/p\u003e\u003cp\u003ePACMAT_Easy is the simple case of clearing the board of Yellow Dots while not bumping into the non-moving ghosts.\u003c/p\u003e\u003cimg src=\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_300.jpg\"\u003e\u003cp\u003eTo aid in development of your routine, a PACMAT.m file that creates a video has been posted at \u003ca href=\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_Easy.m?attredirects=0\u0026amp;d=1\"\u003ePACMAT_Easy.m\u003c/a\u003e. (Right click, 'save link as'). Using patches (not sprites).\u003c/p\u003e\u003cp\u003eAn example video of the first Player \u003ca href=\"https://sites.google.com/site/razapor/matlab_cody/pac_s314_motMP4_v004.mp4?attredirects=0\u0026amp;d=1\"\u003ePACMAT_Easy_Video\u003c/a\u003e  (MP4: Left click and Windows Media Player)\u003c/p\u003e\u003cp\u003eAlfonso Nieto-Castanon's 298 \u003ca href=\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_Easy_ANC_298.mp4?attredirects=0\u0026amp;d=1\"\u003ePACMAT Video\u003c/a\u003e\u003c/p\u003e\u003cp\u003eAlfonso employed a Local Optimum Monte-Carlo approach to find a best solution. Solution #8 is the very compact non-apriori PACMAT solver.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInputs:\u003c/b\u003e Map   Definitions: -1=Wall, 0=Empty, 1=Dot, 2=PACMAT, \u003e2=Ghost\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e Direction  Definitions: 1-Up, 2-Right, 3-Down, 4-Left, 0-No move\u003c/p\u003e\u003cp\u003e\u003cb\u003eScoring:\u003c/b\u003e Total # of Moves to Clear the Yellow Dots\u003c/p\u003e\u003cp\u003e\u003cb\u003eNear Future:\u003c/b\u003e Ghosts will move with various algorithms.\u003c/p\u003e\u003cp\u003e\u003cb\u003eFar Future:\u003c/b\u003e Asteroids and Space Invaders\u003c/p\u003e","function_template":"function  [newdir]=pacmat(map)\r\n newdir=randi(4);\r\nend\r\n","test_suite":"%%\r\nfeval(@assignin,'caller','score',2000);\r\n%%\r\nmap=[...\r\n      repmat('a',1,28);\r\n      'accccccccccccaacccccccccccca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acccccccccccccccccccccccccca';\r\n      'acaaaacaacaaaaaaaacaacaaaaca';\r\n      'acaaaacaacaaaaaaaacaacaaaaca';\r\n      'accccccaaccccaaccccaacccccca';\r\n      'aaaaaacaaaaabaabaaaaacaaaaaa';\r\n      'aaaaaacaaaaabaabaaaaacaaaaaa';\r\n      'aaaaaacaabbbbbbbbbbaacaaaaaa';\r\n      'aaaaaacaabaaabbaaabaacaaaaaa';\r\n      'aaaaaacaabalbbbblabaacaaaaaa';\r\n      'bbbbbbcbbbabbbbbbabbbcbbbbbb';\r\n      'aaaaaacaabalbbbblabaacaaaaaa';\r\n      'aaaaaacaabaaaaaaaabaacaaaaaa';\r\n      'aaaaaacaabbbbbbbbbbaacaaaaaa';\r\n      'aaaaaacaabaaaaaaaabaacaaaaaa';\r\n      'aaaaaacaabaaaaaaaabaacaaaaaa';\r\n      'accccccccccccaacccccccccccca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acccaacccccccbdcccccccaaccca';\r\n      'aaacaacaacaaaaaaaacaacaacaaa';\r\n      'aaacaacaacaaaaaaaacaacaacaaa';\r\n      'accccccaaccccaaccccaacccccca';\r\n      'acaaaaaaaaaacaacaaaaaaaaaaca';\r\n      'acaaaaaaaaaacaacaaaaaaaaaaca';\r\n      'acccccccccccccccccccccccccca';\r\n      repmat('a',1,28);];\r\n  \r\n  map=map-'b';\r\n  [nr, nc]=size(map);\r\n  mapdelta=[-1 nr 1 -nr]; % Valid as long as not on an edge\r\n  tunnel=find(map(:,1)==0); % tunnelptr\r\n  tunnel=[tunnel tunnel+nr*(nc-1)]; % Entrance/Exit Tunnel\r\n  [pmr, pmc]=find(map==2); % pi 24 row  pj 15 column of map\r\n   ptrpac=find(map==2);\r\n\r\n lives=1; % Lives\r\n  movepac=0;\r\nwhile lives \u0026\u0026 any(mod(map(:),10)==1) \u0026\u0026 movepac\u003c5000 \u0026\u0026 ~isempty(find(map(:)==2))\r\n   while ~isempty(find(map(:)==2)) \u0026\u0026 movepac\u003c5000\r\n     movepac=movepac+1;\r\n\r\n if isempty(find(map==1,1)),break;end % \r\n [curdir]=pacmat(map);\r\n  if curdir==0,continue;end\r\n\r\n if map(ptrpac+mapdelta(curdir))==-1\r\n     % Do nothing - Ran into a Wall\r\n    elseif map(ptrpac+mapdelta(curdir))\u003e2 % ran into ghost\r\n      map(ptrpac)=0; % remove PAC from the board\r\n      lives=0;\r\n      break; % Lose\r\n    else % legal move\r\n      map(ptrpac)=0; % Eat Dot and clear PAC\r\n      ptrpac=ptrpac+mapdelta(curdir);\r\n      if ptrpac==tunnel(1),ptrpac=tunnel(2)-nr;end\r\n      if ptrpac==tunnel(2),ptrpac=tunnel(1)+nr;end\r\n      map(ptrpac)=2;\r\n    end\r\n  end % PAC Move while\r\n  if isempty(find(map==1,1)),break;end % \r\n   if lives==0,break;end\r\n   lives=lives-1;\r\n end % while alive\r\n\r\nfprintf('moves %i\\n',movepac)\r\n\r\nassert(lives\u003e0)\r\nassert(isempty(find(map==1)))\r\n\r\n\r\nfeval( @assignin,'caller','score',floor(min( 2000,movepac )) );","published":true,"deleted":false,"likes_count":4,"comments_count":4,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":33,"created_at":"2013-01-30T04:55:54.000Z","updated_at":"2026-08-12T16:08:25.000Z","published_at":"2013-01-30T05:48:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Classic PACMAN game brought to Cody.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePACMAT_Easy is the simple case of clearing the board of Yellow Dots while not bumping into the non-moving ghosts.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo aid in development of your routine, a PACMAT.m file that creates a video has been posted at\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_Easy.m?attredirects=0\u0026amp;d=1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePACMAT_Easy.m\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. (Right click, 'save link as'). Using patches (not sprites).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn example video of the first Player\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/pac_s314_motMP4_v004.mp4?attredirects=0\u0026amp;d=1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePACMAT_Easy_Video\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (MP4: Left click and Windows Media Player)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAlfonso Nieto-Castanon's 298\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_Easy_ANC_298.mp4?attredirects=0\u0026amp;d=1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePACMAT Video\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAlfonso employed a Local Optimum Monte-Carlo approach to find a best solution. Solution #8 is the very compact non-apriori PACMAT solver.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Map Definitions: -1=Wall, 0=Empty, 1=Dot, 2=PACMAT, \u0026gt;2=Ghost\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Direction Definitions: 1-Up, 2-Right, 3-Down, 4-Left, 0-No move\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Total # of Moves to Clear the Yellow Dots\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNear Future:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Ghosts will move with various algorithms.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFar Future:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Asteroids and Space 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\"}]}"},{"id":44630,"title":"Guess the number I'm thinking of (Part 1)","description":"In this game you are competing against two other people to guess the number that I'm thinking of.\r\nI randomly choose an integer between one and ten (inclusive). I don't provide any clues about the number.\r\nYour first opponent tries to guess the number. They guess randomly.\r\nYour second opponent tries to guess the number. They also guess randomly.\r\nYou try to guess the number. But you guess strategically.\r\nThe winner is the person who guesses my chosen number, or the person who guesses closest to my chosen number. This represents a \"win\".\r\nIf two contestants are equally close, they may share the win, with such a result being declared a \"draw\". (It is a loss for the remaining contestant.) A draw is worth half as much as a win.\r\nEach person hears the guesses stated by any preceding competitors, so you will be aware of the two prior guesses (provided to you as the vector guessesOfOpponents). Moreover, each guess must be unique.\r\nIf everyone guessed randomly, each person should have an equal chance of winning.\r\nIt might seem that you're at a disadvantage, having the last opportunity to guess. But actually you have the advantage of extra knowledge.\r\nBy guessing strategically, you should be able to achieve a success rate of 45% or more, in which\r\nsuccess rate = (wins + draws/2) / games\r\n\r\nRELATED PROBLEM:  \r\nProblem 52323. Guess the number I'm thinking of (Part 2)","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 484px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 242px; transform-origin: 407px 242px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIn this game you are competing against two other people to guess the number that I'm thinking of.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 160px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 80px; transform-origin: 391px 80px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eI randomly choose an\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003einteger\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e between\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eone\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eten\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e (inclusive). I don't provide any clues about the number.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYour first opponent tries to guess the number. They guess randomly.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYour second opponent tries to guess the number. They also guess randomly.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou try to guess the number. But you guess\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estrategically\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20px; text-align: left; transform-origin: 363px 20px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe winner is the person who guesses my chosen number, or the person who guesses closest to my chosen number. This represents a \"win\".\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20px; text-align: left; transform-origin: 363px 20px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIf two contestants are equally close, they may share the win, with such a result being declared a \"draw\". (It is a loss for the remaining contestant.) A draw is worth half as much as a win.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eEach person hears the guesses stated by any preceding competitors, so you will be aware of the two prior guesses (provided to you as the vector\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eguessesOfOpponents\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e). Moreover, each guess must be unique.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIf everyone guessed randomly, each person should have an equal chance of winning.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIt might seem that you're at a disadvantage, having the last opportunity to guess. But actually you have the advantage of extra knowledge.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eBy guessing strategically, you should be able to\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eachieve a success rate of 45% or more\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, in which\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003esuccess rate = (wins + draws/2) / games\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eRELATED PROBLEM:  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 10px; transform-origin: 391px 10px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10px; text-align: left; transform-origin: 363px 10px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52323\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 52323. Guess the number I'm thinking of (Part 2)\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = myGuess(guessesOfOpponents)\r\n    y = 42;\r\nend","test_suite":"%% Anti-hacking test\r\nassessFunctionAbsence({'rng', 'RandStream'}, 'FileName','myGuess.m')\r\n\r\n%% Ensure unique guesses of integers, which are in-range\r\nfor j = 1 : 1000\r\n    numberToBeGuessed = randi(10);\r\n    gOO = randperm(10, 2);\r\n    mG = myGuess(gOO);\r\n    assert( mG \u003e= 1  \u0026  mG \u003c= 10 , 'Out of requested range.' )\r\n    u = unique( floor([gOO mG]) );\r\n    assert( length(u) == 3 , 'Your guess must not have been already chosen.' )\r\nend;\r\n\r\n%% maxIts: 20000 = Too small; 30000 = Not quite big enough; 35000 = Just big enough (usually!); 50000 = Big enough (usually!); 100000 = Big enough, plus safety margin \u0026 efficiency incentive (but waste of resources)\r\nmaxIts = 100000;    \r\ntic\r\nfor j = 1 : 10\r\n    WDL = [0 0 0];\r\n    for itn = 1 : maxIts\r\n        numberToBeGuessed = randi(10);\r\n        gOO = randperm(10, 2);\r\n        diffs = abs( [gOO myGuess(gOO)] - numberToBeGuessed );\r\n        winningContestant = find( min(diffs)==diffs );\r\n        if any( winningContestant == 3 ),\r\n            if length(winningContestant) == 1,\r\n                % Win\r\n                WDL(1) = WDL(1) + 1;  \r\n            else\r\n                % Draw\r\n                WDL(2) = WDL(2) + 1;  \r\n            end;\r\n        else\r\n            % Loss\r\n            WDL(3) = WDL(3) + 1;  \r\n        end;\r\n    end;\r\n    successRate = (WDL(1) + WDL(2)/2) / maxIts\r\n    assert( successRate \u003e= 0.45 )\r\nend;\r\ntoc","published":true,"deleted":false,"likes_count":13,"comments_count":6,"created_by":64439,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":83,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2018-05-04T14:00:17.000Z","updated_at":"2026-08-18T14:22:47.000Z","published_at":"2018-05-05T12:29:22.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this game you are competing against two other people to guess the number that I'm thinking of.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI randomly choose an\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einteger\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e between\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eone\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eten\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (inclusive). I don't provide any clues about the number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour first opponent tries to guess the number. They guess randomly.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour second opponent tries to guess the number. They also guess randomly.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou try to guess the number. But you guess\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estrategically\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe winner is the person who guesses my chosen number, or the person who guesses closest to my chosen number. This represents a \\\"win\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf two contestants are equally close, they may share the win, with such a result being declared a \\\"draw\\\". (It is a loss for the remaining contestant.) A draw is worth half as much as a win.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach person hears the guesses stated by any preceding competitors, so you will be aware of the two prior guesses (provided to you as the vector\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eguessesOfOpponents\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e). Moreover, each guess must be unique.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf everyone guessed randomly, each person should have an equal chance of winning.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt might seem that you're at a disadvantage, having the last opportunity to guess. But actually you have the advantage of extra knowledge.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBy guessing strategically, you should be able to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eachieve a success rate of 45% or more\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, in which\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esuccess rate = (wins + draws/2) / games\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRELATED PROBLEM:  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52323\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 52323. Guess the number I'm thinking of (Part 2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":196,"title":"love is an n-letter word","description":"Given a list of *N words*, return the *N-letter word* (choosing one letter from each word) with the property of having the least distance between each pair of two consecutive letters (if there are multiple optimal solutions return any one of them).\r\n\r\nExample: s1 = {'abcd','bcde','cdef','defg'}; should return s2 = 'dddd'; (with total letter-distance = 0)\r\n\r\nExample: s1={'aldfejk','czoa','vwy','abcde'}; should return s2='love'; (with total letter-distance = 27: _|'l'-'o'|_=3 + _|'o'-'v'|_=7 + _|'v'-'e'|_=17 ; compare for example to the possible word 'aave' which has a total letter-distance of 38)\r\n\r\n\r\n\r\n","description_html":"\u003cp\u003eGiven a list of \u003cb\u003eN words\u003c/b\u003e, return the \u003cb\u003eN-letter word\u003c/b\u003e (choosing one letter from each word) with the property of having the least distance between each pair of two consecutive letters (if there are multiple optimal solutions return any one of them).\u003c/p\u003e\u003cp\u003eExample: s1 = {'abcd','bcde','cdef','defg'}; should return s2 = 'dddd'; (with total letter-distance = 0)\u003c/p\u003e\u003cp\u003eExample: s1={'aldfejk','czoa','vwy','abcde'}; should return s2='love'; (with total letter-distance = 27: \u003ci\u003e\u003ctt\u003e'l'-'o'\u003c/tt\u003e\u003c/i\u003e=3 + \u003ci\u003e\u003ctt\u003e'o'-'v'\u003c/tt\u003e\u003c/i\u003e=7 + \u003ci\u003e\u003ctt\u003e'v'-'e'\u003c/tt\u003e\u003c/i\u003e=17 ; compare for example to the possible word 'aave' which has a total letter-distance of 38)\u003c/p\u003e","function_template":"function s2 = gobbledigook(s1)\r\n  s2 = '';\r\nend","test_suite":"%%\r\ns1 = {'abcd','bcde','cdef','defg'}; \r\nassert(isequal(gobbledigook(s1),'dddd'))\r\ns2_correct = 'dddd';\r\n%%\r\ns1 = {'aldfejk','czoa','vwy','abcde'}; \r\nassert(isequal(gobbledigook(s1),'love'))\r\ns2_correct = 'love';\r\n%%\r\ns1 = {'some','help','check','viterbi','algorithm'}; \r\nassert(isequal(gobbledigook(s1),'eeeeg'))\r\ns2_correct = 'eeeeg';\r\n%%\r\ns1 = {'ldjfac','deamv','fka','idlw','pqmfjavs'}; \r\nassert(isequal(gobbledigook(s1),'lmklm')|isequal(gobbledigook(s1),'aaadf'))\r\ns2_correct = 'lmklm';\r\ns2_correct = 'aaadf';\r\n%% \r\n% avoids look-up table hack\r\ns1 = cellfun(@(x)char('a'-1+randi(26,1,5)),cell(1,7),'uniformoutput',false);\r\nassert(all(any(bsxfun(@eq,gobbledigook(s1),cell2mat(cellfun(@(x)x',s1,'uniformoutput',false)))))\u0026all(sum(abs(diff(double(gobbledigook(s1)))))\u003c=sum(abs(diff(double(cell2mat(cellfun(@(x)x(randi(numel(x),1,1000))',s1,'uniformoutput',false))),1,2)),2)));","published":true,"deleted":false,"likes_count":6,"comments_count":5,"created_by":43,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":67,"test_suite_updated_at":"2012-03-08T02:36:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-31T08:36:36.000Z","updated_at":"2026-07-15T17:19:22.000Z","published_at":"2012-03-08T03:14:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a list of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN words\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN-letter word\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (choosing one letter from each word) with the property of having the least distance between each pair of two consecutive letters (if there are multiple optimal solutions return any one of them).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: s1 = {'abcd','bcde','cdef','defg'}; should return s2 = 'dddd'; (with total letter-distance = 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: s1={'aldfejk','czoa','vwy','abcde'}; should return s2='love'; (with total letter-distance = 27:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'l'-'o'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e=3 +\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'o'-'v'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e=7 +\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'v'-'e'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e=17 ; compare for example to the possible word 'aave' which has a total letter-distance of 38)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44345,"title":"MATLAB Counter","description":"Write a function f = counter(x0,b) to construct a counter handle f that counts with an initial value x0 and a step size b. \r\n\r\nE.g.,\r\n\r\n  \u003e\u003e f = counter(0,1)  % Initialize a counter f() with initial_count = 0 and step_size = 1\r\n  \u003e\u003e f()\r\n  ans =\r\n       0\r\n  \u003e\u003e f()\r\n  ans =\r\n       1\r\n  \u003e\u003e f()\r\n  ans =\r\n       2\r\n\r\n\r\n","description_html":"\u003cp\u003eWrite a function f = counter(x0,b) to construct a counter handle f that counts with an initial value x0 and a step size b.\u003c/p\u003e\u003cp\u003eE.g.,\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e\u0026gt;\u0026gt; f = counter(0,1)  % Initialize a counter f() with initial_count = 0 and step_size = 1\r\n\u0026gt;\u0026gt; f()\r\nans =\r\n     0\r\n\u0026gt;\u0026gt; f()\r\nans =\r\n     1\r\n\u0026gt;\u0026gt; f()\r\nans =\r\n     2\r\n\u003c/pre\u003e","function_template":"function y = counter(x,b)\r\n  y = x;\r\nend","test_suite":"%%\r\nassessFunctionAbsence({'regexp','regexpi','regexprep','str2num'},'FileName','counter.m')\r\n\r\n%%\r\nf = counter(0,1);\r\nassert(isequal(f(),0))\r\nassert(isequal(f(),1))\r\nassert(isequal(2,f()))\r\nassert(isequal(3,f()))\r\n\r\n%%\r\nf = counter(1,0);\r\nassert(isequal(f(),1))\r\nassert(isequal(f(),1))\r\nassert(isequal(1,f()))\r\nassert(isequal(1,f()))\r\n\r\n%%\r\nf = counter(10,2);\r\nassert(isequal(f(),10))\r\nassert(isequal(f(),12))\r\nassert(isequal(14,f()))\r\nassert(isequal(16,f()))\r\n\r\n%%\r\nf = counter(0,5);\r\ny_correct = [0, 5, 10, 15, 20, 55];\r\nassert(isequal([f() f() f() f() f() f()+f()],y_correct))\r\n\r\n%%\r\nx0 = randi(10);\r\nb = randi(10);\r\nf = counter(x0,b);\r\ny_correct = x0 + (0:1000)*b;\r\nassert(isequal(arrayfun(@(n)f(),0:1000),y_correct))","published":true,"deleted":false,"likes_count":23,"comments_count":9,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":305,"test_suite_updated_at":"2017-10-17T00:19:49.000Z","rescore_all_solutions":false,"group_id":34,"created_at":"2017-09-24T01:58:21.000Z","updated_at":"2026-05-28T04:25:58.000Z","published_at":"2017-10-16T01:45:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function f = counter(x0,b) to construct a counter handle f that counts with an initial value x0 and a step size b.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eE.g.,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e f = counter(0,1)  % Initialize a counter f() with initial_count = 0 and step_size = 1\\n\u003e\u003e f()\\nans =\\n     0\\n\u003e\u003e f()\\nans =\\n     1\\n\u003e\u003e f()\\nans =\\n     2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":81,"title":"Mandelbrot Numbers","description":"The \u003chttp://en.wikipedia.org/wiki/Mandelbrot_set Mandelbrot Set\u003e is built around a simple iterative equation.\r\n\r\n z(1)   = c\r\n z(n+1) = z(n)^2 + c\r\n\r\nFor any complex c, we can continue this iteration until either\r\nabs(z(n+1)) \u003e 2 or n == lim, then return the iteration count n.\r\n\r\n* If c = 0   and lim = 3, then z = [0 0 0] and n = 3.\r\n* If c = 1   and lim = 5, then z = [1 2], and n = length(z) or 2.\r\n* If c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\r\n\r\nFor a matrix of complex numbers C, return a corresponding matrix N such\r\nthat each element of N is the iteration count n for each complex number c\r\nin the matrix C, subject to the iteration count limit of lim.\r\n\r\nIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\r\n\r\nCleve Moler has a whole chapter on the Mandelbrot set in his book Experiments\r\nwith MATLAB: \u003chttp://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf \r\nChapter 10, Mandelbrot Set (PDF)\u003e","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 296.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 148.083px; transform-origin: 407px 148.083px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.5px 8px; transform-origin: 12.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://en.wikipedia.org/wiki/Mandelbrot_set\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMandelbrot Set\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133px 8px; transform-origin: 133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is built around a simple iterative equation.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 44px 8.5px; transform-origin: 44px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e z(1)   = c\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e z(n+1) = z(n)^2 + c\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379.5px 8px; transform-origin: 379.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor any complex c, we can continue this iteration until either abs(z(n+1)) \u0026gt; 2 or n == lim, then return the iteration count n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 142.5px 8px; transform-origin: 142.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 0 and lim = 3, then z = [0 0 0] and n = 3.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 176.5px 8px; transform-origin: 176.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 1 and lim = 5, then z = [1 2], and n = length(z) or 2.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 226.5px 8px; transform-origin: 226.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377px 8px; transform-origin: 377px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a matrix of complex numbers C, return a corresponding matrix N such that each element of N is the iteration count n for each complex number c in the matrix C, subject to the iteration count limit of lim.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 149.5px 8px; transform-origin: 149.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127px 8px; transform-origin: 127px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCleve Moler has a whole chapter on the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/exm/chapters/mandelbrot.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMandelbrot set\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38px 8px; transform-origin: 38px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in his book \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/moler/exm/chapters.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eExperiments with MATLAB\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function N = mandelbrot(C,lim)\r\n  N = ones(size(C));\r\nend","test_suite":"%%\r\nC = 0;\r\nlim = 5;\r\nN_correct = 5;\r\nassert(isequal(mandelbrot(C,lim),N_correct))\r\n\r\n%%\r\nC = [0 0.5; 1 4];\r\nlim = 5;\r\nN_correct = [5 4; 2 1];\r\nassert(isequal(mandelbrot(C,lim),N_correct))\r\n\r\n%%\r\ni = sqrt(-1);\r\nC = [i 1 -2*i -2];\r\nlim = 10;\r\nN_correct = [10 2 1 10];\r\nassert(isequal(mandelbrot(C,lim),N_correct))","published":true,"deleted":false,"likes_count":17,"comments_count":9,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1783,"test_suite_updated_at":"2012-01-26T03:21:20.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:28.000Z","updated_at":"2026-10-20T11:26:19.000Z","published_at":"2012-01-18T01:00:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Mandelbrot_set\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot Set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is built around a simple iterative equation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ z(1)   = c\\n z(n+1) = z(n)^2 + c]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor any complex c, we can continue this iteration until either abs(z(n+1)) \u0026gt; 2 or n == lim, then return the iteration count n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 0 and lim = 3, then z = [0 0 0] and n = 3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 1 and lim = 5, then z = [1 2], and n = length(z) or 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a matrix of complex numbers C, return a corresponding matrix N such that each element of N is the iteration count n for each complex number c in the matrix C, subject to the iteration count limit of lim.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCleve Moler has a whole chapter on the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/exm/chapters/mandelbrot.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in his book \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/moler/exm/chapters.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eExperiments with MATLAB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42580,"title":"Conic equation","description":"A conic of revolution (around the |z| axis) can be defined by the equation\r\n\r\n   s^2 – 2*R*z + (k+1)*z^2 = 0\r\n\r\nwhere |s^2=x^2+y^2|, |R| is the vertex radius of curvature, and |k| is the conic constant: |k\u003c-1| for a hyperbola, |k=-1| for a parabola, |-1\u003ck\u003c0| for a tall ellipse, |k=0| for a sphere, and |k\u003e0| for a short ellipse.\r\n\r\nWrite a function |z=conic(s,R,k)| to calculate height |z| as a function of radius |s| for given |R| and |k|.  Choose the branch of the solution that gives |z=s^2/(2*R)+...| for small values of |s|.  This defines a concave surface for |R\u003e0| and a convex surface for |R\u003c0|.  \r\n\r\nThe trick is to get full machine precision for all values of |s| and |R|.  The test suite will require a relative error less than |4*eps|, where |eps| is the machine precision.\r\n\r\nHint (added 2015/09/03): the straightforward solution is \r\n\r\n   z = (R-sqrt(R^2-(k+1)*s^2))/(k+1), \r\n\r\nbut this does not work if |k=-1|, gives the wrong branch of the solution if |R\u003c0|, and is subject to severe roundoff error if |s^2| is small compared to |R^2|.  It is possible, however, to find a mathematically equivalent form of the solution that solves all three problems at once.\r\n","description_html":"\u003cp\u003eA conic of revolution (around the \u003ctt\u003ez\u003c/tt\u003e axis) can be defined by the equation\u003c/p\u003e\u003cpre\u003e   s^2 – 2*R*z + (k+1)*z^2 = 0\u003c/pre\u003e\u003cp\u003ewhere \u003ctt\u003es^2=x^2+y^2\u003c/tt\u003e, \u003ctt\u003eR\u003c/tt\u003e is the vertex radius of curvature, and \u003ctt\u003ek\u003c/tt\u003e is the conic constant: \u003ctt\u003ek\u0026lt;-1\u003c/tt\u003e for a hyperbola, \u003ctt\u003ek=-1\u003c/tt\u003e for a parabola, \u003ctt\u003e-1\u0026lt;k\u0026lt;0\u003c/tt\u003e for a tall ellipse, \u003ctt\u003ek=0\u003c/tt\u003e for a sphere, and \u003ctt\u003ek\u0026gt;0\u003c/tt\u003e for a short ellipse.\u003c/p\u003e\u003cp\u003eWrite a function \u003ctt\u003ez=conic(s,R,k)\u003c/tt\u003e to calculate height \u003ctt\u003ez\u003c/tt\u003e as a function of radius \u003ctt\u003es\u003c/tt\u003e for given \u003ctt\u003eR\u003c/tt\u003e and \u003ctt\u003ek\u003c/tt\u003e.  Choose the branch of the solution that gives \u003ctt\u003ez=s^2/(2*R)+...\u003c/tt\u003e for small values of \u003ctt\u003es\u003c/tt\u003e.  This defines a concave surface for \u003ctt\u003eR\u0026gt;0\u003c/tt\u003e and a convex surface for \u003ctt\u003eR\u0026lt;0\u003c/tt\u003e.\u003c/p\u003e\u003cp\u003eThe trick is to get full machine precision for all values of \u003ctt\u003es\u003c/tt\u003e and \u003ctt\u003eR\u003c/tt\u003e.  The test suite will require a relative error less than \u003ctt\u003e4*eps\u003c/tt\u003e, where \u003ctt\u003eeps\u003c/tt\u003e is the machine precision.\u003c/p\u003e\u003cp\u003eHint (added 2015/09/03): the straightforward solution is\u003c/p\u003e\u003cpre\u003e   z = (R-sqrt(R^2-(k+1)*s^2))/(k+1), \u003c/pre\u003e\u003cp\u003ebut this does not work if \u003ctt\u003ek=-1\u003c/tt\u003e, gives the wrong branch of the solution if \u003ctt\u003eR\u0026lt;0\u003c/tt\u003e, and is subject to severe roundoff error if \u003ctt\u003es^2\u003c/tt\u003e is small compared to \u003ctt\u003eR^2\u003c/tt\u003e.  It is possible, however, to find a mathematically equivalent form of the solution that solves all three problems at once.\u003c/p\u003e","function_template":"function z=conic(s,R,k)\r\nz=0;\r\nend","test_suite":"%%\r\nR=5;\r\nk=-1;\r\ns=-5:5;\r\nz=[25 16 9 4 1 0 1 4 9 16 25]/10;\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=-5;\r\nk=-1;\r\ns=-5:5;\r\nz=-[25 16 9 4 1 0 1 4 9 16 25]/10;\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=6;\r\nk=0;\r\ns=0:0.125:2;\r\nz=[0 0.001302224649086391 0.005210595859100573 ...\r\n   0.01173021649825800 0.02086962844930099 ...\r\n   0.03264086885999461 0.04705955010467117 ...\r\n   0.06414496470811713 0.08392021690038396 ...\r\n   0.1064123829368584 0.1316527028472488 ...\r\n   0.1596768068881667 0.1905249806888747 ...\r\n   0.2242424739260392 0.2608798583755018 ...\r\n   0.3004934424110011 0.3431457505076198];\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=6800;\r\nk=-2;\r\ns=10.^(-9:9);\r\nz=[7.352941176470588e-23 7.352941176470588e-21 ...\r\n   7.352941176470588e-19 7.352941176470588e-17 ...\r\n   7.352941176470588e-15 7.352941176470588e-13 ...\r\n   7.352941176470548e-11 7.352941176466613e-9 ...\r\n   7.352941176073046e-7 0.00007352941136716365 ...\r\n   0.007352937201052538 0.7352543677216725 ...\r\n   73.13611097583313 5292.973166264779 93430.93334894173 ...\r\n   993223.1197327390 9.993202311999733e6 9.99932002312e7 ...\r\n   9.9999320002312e8];\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=exp(1);\r\nk=pi;\r\ns=10.^(-7:0);\r\nz=[1.839397205857214e-15 1.839397205857469e-13 ...\r\n   1.839397205882986e-11 1.839397208434684e-09 ...\r\n   1.839397463604480e-07 0.00001839422981299153 ...\r\n   0.001841981926630790 0.2212216213343403];\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nt=fileread('conic.m');\r\nassert(isempty(findstr(t,'roots')))\r\nassert(isempty(findstr(t,'fzero')))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":245,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":37,"created_at":"2015-08-26T21:39:35.000Z","updated_at":"2026-05-25T04:09:40.000Z","published_at":"2015-08-26T22:21:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA conic of revolution (around the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e axis) can be defined by the equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   s^2 – 2*R*z + (k+1)*z^2 = 0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es^2=x^2+y^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the vertex radius of curvature, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the conic constant:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u0026lt;-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a hyperbola,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek=-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a parabola,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-1\u0026lt;k\u0026lt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a tall ellipse,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek=0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a sphere, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u0026gt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a short ellipse.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez=conic(s,R,k)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to calculate height\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as a function of radius\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for given\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Choose the branch of the solution that gives\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez=s^2/(2*R)+...\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for small values of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. This defines a concave surface for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u0026gt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and a convex surface for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u0026lt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe trick is to get full machine precision for all values of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The test suite will require a relative error less than\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e4*eps\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eeps\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the machine precision.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint (added 2015/09/03): the straightforward solution is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   z = (R-sqrt(R^2-(k+1)*s^2))/(k+1),]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ebut this does not work if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek=-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, gives the wrong branch of the solution if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u0026lt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and is subject to severe roundoff error if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is small compared to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. It is possible, however, to find a mathematically equivalent form of the solution that solves all three problems at once.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44963,"title":"Mask Generation Function (MGF1) for PKCS #1 Standard utilizing Optimal Asymmetric Encryption Padding for RSA Cryptography","description":"Create Mask Generation Function (MGF1) from PKCS #1 v2.2 standard (B.2.1 page 50) at below link. Input will be character array (mgfSeed) which will need to be converted to octet array using UTF-8 representation. Output must be octet array (uint8) of length, maskLen (input). Hashing must use SHA-1 (160 - 20 byte).\r\n\r\nFor example:\r\n\r\n  mgfSeed = 'I like to swim.';%input\r\n  maskLen = 20;%input\r\n  mask = [170,251,101,210,23,101,10,242,193,163,174,148,104,138,228,245,52,234,0,195];%output\r\n\r\n\r\n\u003chttps://www.emc.com/collateral/white-papers/h11300-pkcs-1v2-2-rsa-cryptography-standard-wp.pdf\u003e","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 194px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 97px; transform-origin: 407px 97px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCreate Mask Generation Function (MGF1) from PKCS #1 v2.2 standard (B.2.1) at below link. Input will be character array (mgfSeed) which will need to be converted to octet array using UTF-8 representation. Output must be octet array (uint8) of length, maskLen (input). Hashing must use SHA-1 (160 - 20 byte).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 60px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 30px; transform-origin: 404px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003emgfSeed = \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); \"\u003e'I like to swim.'\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e;\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration: none; text-decoration-color: rgb(2, 128, 9); \"\u003e%input\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003emaskLen = 20;\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration: none; text-decoration-color: rgb(2, 128, 9); \"\u003e%input\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003emask = [170,251,101,210,23,101,10,242,193,163,174,148,104,138,228,245,52,234,0,195];\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration: none; text-decoration-color: rgb(2, 128, 9); \"\u003e%output\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSee: https://www.foo.be/docs/opensst/ref/pkcs/pkcs-1/pkcs-1v2-1d1.pdf\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function mask = mgf(mgfSeed,maskLen)\r\n    mask = []%octet array of length maskLen\r\nend","test_suite":"%%\r\nmgfSeed = 'I like to swim.';\r\nmaskLen = 20;\r\nmask = [170,251,101,210,23,101,10,242,193,163,174,148,104,138,228,245,52,234,0,195];\r\nassert(isequal(mgf(mgfSeed,maskLen),mask))\r\n%%\r\nmgfSeed = 'People who succeed have momentum. The more they succeed, the more they want to succeed and the more they find a way to succeed. Similarly, when someone is failing, the tendency is to get on a downward spiral that can even become a self-fulfilling prophecy.';\r\nmaskLen = 825;\r\nmask = [40    55   251    83   143   211    49    16    87    56   109   116    17   188    72    54   231    67   125   182   223    53   149    36   246   233    71   113   113    29   176    61    74    77   205   167   179    99   172   172   212   249    53   148    13    89   253     3    85     0   155   181    94    15     8   122   120    92    29   229   229    46   192   162   252   119   243    94    52    12   133    98   161   249   152    68    69    22 156   155   229   132    30   163   102    90   217   160    36    53   185   128    74   224   105   214   134    90   188   101    98   220    43   162   251   183    72    54   219     4    44   185   199   193    31    42   129   112    74    25    81   133    70   156    38   225   243    24    50   132    79   130    42    72   145   158   105   253   190    62    73   107    95   133    78   238   214    39    88   245    40    46   166   201   173   209   234   194     3   117   226    32   176    12   139    83   211    67   101    99   174   126   103   130    83    56   157    52    76    21   189    99   217    43   150    92   219   148   173   138   184   183   203    62   231   125    42    79    29   248    30    26   127    50     9    31   219   212   160   157   243    15    52   217     7   144    43   241    70    98   247   231   174   111    96    91   108    59   164   146    77   180   212   155   165    18   150   198   100   233   255   129    44   170   150   243   244   126   203   255   231    28    94    77    58   198   147    84   212   248    36    34   107   210    77    79    80   224    24   126    88   125   255    11   124   227    44   253   242   234    59   176   108   146   170   132    20   128   230   141   187    81   139    26   119    47   159     8   182    40    94   213   107   223    21   187    35     1    40   145   154    92   218   252    46   201   203    65    48    94   118   110     5   158   212    19   129     9    59   124    19   190   201    55   141   124   210    85   240    34   150    81   154    11     3   116   204    37    73    39   169   234    50   241   131    94     9   133     0   209   190   171   206    93   165   145   142   117   230    34   245   223   205   153   227   202     3   218    56   163   203   137    46   114    78   248   196   136    19   177   126    95   231   213   251   130    39    57    59   228   251    73    48     9   109    11   172   152   223   120   153   108   233    76   117   219     8     6   124    44     7   249   116    43   198    98    55   235    52    47   146   239    76   142    88    19    64   169   209   206   255   101    91   197    36   180   253    52    54    63   198    63   113    58    43   229   141    59     4   147    34   200     7   184   108   176   153    95    94    18   235   178   160    51    63   154   227    39   231    71   246   109    13   199   185   220   180    50   146    85   194   176   175   159   103   177    47   149   252   182    33   224   226     1   232   167    94    93   202    55    60   201   228   107   135   142    22   165   168   124   219   216    34   230   174   179    66    67    91    92   186    30    48     9   177   192   254   190   236    52    84   114   255     3    81   150   112   131    49   157    48   243   218    11   132    40    13    68   214   159    36   109   152   219    32   219   193   182    69    37   104   217   115    54   158    79    90     3   223   116   127     8    28   233   223   194    30   241   180    45   209    77   180   184    52   132   164    49   206    50    57   149   118   105    44    25   212   141   253   150    45   244    73   203    10   137   161   118    49   165   248   105   215    58    90    67   180    78    22   135   102   173   139    62    31    63    82   187    78    47     2   176   144    83    22   143    31   155     8   160    12   252   164    52   159   102   113    95   132    49   168   194   137    32   131   189   139    77   143   248    36    30   154   239   163   149    86     9   178   122     6   248    25   208   211   142    59    23    72    43   158   195   244   232   229   245   148    49   163    28    81    93   106    33   239   249    26   220    73    65   112   249   254   251    91   106   204   113    10    59    34   114   189   185   188   181   100   185    22   188   221   187   109   170    35    57   181   234   157   230   206   169    97   140    51   170   128   215   188    14    50   190   167    41   173    19    10    98   165    12    77    49    21    33   147    93    84   163   106   151   234    76   252    91   165   248   223   136    85   124   174    90   188   130   174    83    92   181   134    65    91   105    15   103    91    15    27   201   162    58    84   164    33   137    63     0    84     0    78   180    31   218    47    84    43    13    35   122   117   205    59    81   146    97    14];\r\nassert(isequal(mgf(mgfSeed,maskLen),mask))\r\n%%\r\nmgfSeed = 'First, have a definite, clear practical ideal; a goal, an objective. Second, have the necessary means to achieve your ends; wisdom, money, materials, and methods.';\r\nmaskLen = 300;\r\nmask = [96   185   223   209   149    51   224   128   249   139    57   249   190    69   199   132    37    24    75   127    98    59   231   206    13    83    79   111   181   220   204   120    27   178   155   116   155    11   157   112    10   195   106     4   127   146   101   112   197    29    54    45    14    78    16   100     1   111   156    44   138   141   219   101   171     1   126   254    60    82   214    63    13    94   227   238    64   173    93   142     3   224    63    76     8   190   105     8    77   113   250   243   249    82    56   124   129   116   121   131   207   116    80   185    72   184   244   232   236   127    37   195   236   163   176   245    65    48   169   131    19    36   208   178   184   150   188    50   221    83   132   241    73   205    23     9    41    74    65   251    10    21   133   150   101    15    42   153   164   197   136    19   113   134   153   247    10   161   221   184   195   215   253   149   223    83   180   148   198     4    53   112   114    39    18   132   254   170   130    61     6   158   224   166    76   187   190   128    14   251   158   218   192    68    46   210   199   231   120    57   212    10   107     2    50    37   110    30    87    48     2   134    81   165   107    95   250   206    98    26    45   102   173    46    85   103   137     4   140   154   236   142   125   211    28   164    94    41     8    70   215    10    13   140   139    97   205    60   212   205    35   175   235   158    88   165    40    41   187   215    72   172    97   159   119    79    80    31   128   121   108    94   219   216    77   209   184   244    90   238   182   207   244    52   248     6   220   175   117   122   236   228   219    42    49   196   186    12    19    95];\r\nassert(isequal(mgf(mgfSeed,maskLen),mask))","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2019-09-06T22:10:21.000Z","updated_at":"2026-05-25T02:42:38.000Z","published_at":"2019-09-06T22:31:17.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate Mask Generation Function (MGF1) from PKCS #1 v2.2 standard (B.2.1) at below link. Input will be character array (mgfSeed) which will need to be converted to octet array using UTF-8 representation. Output must be octet array (uint8) of length, maskLen (input). Hashing must use SHA-1 (160 - 20 byte).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[mgfSeed = 'I like to swim.';%input\\nmaskLen = 20;%input\\nmask = [170,251,101,210,23,101,10,242,193,163,174,148,104,138,228,245,52,234,0,195];%output]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee: https://www.foo.be/docs/opensst/ref/pkcs/pkcs-1/pkcs-1v2-1d1.pdf\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44765,"title":"Lights Out 11 - 5x5, with wrapping, x moves","description":"\u003chttps://en.wikipedia.org/wiki/Lights_Out_(game) Lights Out\u003e is a logic game wherein all lights need to be turned off to complete each board. See \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44751-lights-out-1-5x5-3-moves the first problem in the series\u003e for an introduction.\r\n\r\nThis problem contains boards that each require any number of moves to solve. However, now wrapping of the lights occurs. For example, if \r\n\r\n board = [1 0 0 0 1  \r\n          1 1 1 0 1  \r\n          0 1 1 1 0  \r\n          1 1 1 0 0  \r\n          0 0 0 1 1]\r\n\r\nthe answer is:\r\n\r\n moves = [2 4 13 25]\r\n\r\nPrev.: \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44764 5x5, wrapping, 6 moves\u003e — \r\nNext: \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44766 5x5, 3 stages, \u003c7 moves\u003e","description_html":"\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Lights_Out_(game)\"\u003eLights Out\u003c/a\u003e is a logic game wherein all lights need to be turned off to complete each board. See \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44751-lights-out-1-5x5-3-moves\"\u003ethe first problem in the series\u003c/a\u003e for an introduction.\u003c/p\u003e\u003cp\u003eThis problem contains boards that each require any number of moves to solve. However, now wrapping of the lights occurs. For example, if\u003c/p\u003e\u003cpre\u003e board = [1 0 0 0 1  \r\n          1 1 1 0 1  \r\n          0 1 1 1 0  \r\n          1 1 1 0 0  \r\n          0 0 0 1 1]\u003c/pre\u003e\u003cp\u003ethe answer is:\u003c/p\u003e\u003cpre\u003e moves = [2 4 13 25]\u003c/pre\u003e\u003cp\u003ePrev.: \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44764\"\u003e5x5, wrapping, 6 moves\u003c/a\u003e — \r\nNext: \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44766\"\u003e5x5, 3 stages, \u0026lt;7 moves\u003c/a\u003e\u003c/p\u003e","function_template":"function moves = lights_out_11(board) % 5x5 board, with wrapping, any number of moves\r\n moves = board;\r\nend","test_suite":"%% \r\n board = [1 0 0 0 1  \r\n          1 1 1 0 1  \r\n          0 1 1 1 0  \r\n          1 1 1 0 0  \r\n          0 0 0 1 1];\r\nmoves = lights_out_11(board); % [2 4 13 25]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1);\r\nb1(1,5) = 1; b1(5,1) = 1; b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b2; b2,b1,b2,b3,b3; b3,b2,b1,b2,b3; b3,b3,b2,b1,b2; b2,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\n\r\n%% \r\n board = [1 1 0 1 1  \r\n          1 0 0 0 1  \r\n          0 0 0 0 0  \r\n          1 0 0 0 1  \r\n          1 1 0 1 1];\r\nmoves = lights_out_11(board); % [1 5 21 25]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1);\r\nb1(1,5) = 1; b1(5,1) = 1; b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b2; b2,b1,b2,b3,b3; b3,b2,b1,b2,b3; b3,b3,b2,b1,b2; b2,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\n\r\n%% \r\n board = [0 1 0 1 0  \r\n          1 0 1 0 1  \r\n          0 1 0 1 0  \r\n          1 0 1 0 1  \r\n          0 1 0 1 0];\r\nmoves = lights_out_11(board); % [2 6 8 12 14 18 20 24]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1);\r\nb1(1,5) = 1; b1(5,1) = 1; b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b2; b2,b1,b2,b3,b3; b3,b2,b1,b2,b3; b3,b3,b2,b1,b2; b2,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\n\r\n%% \r\n board = [1 1 0 0 0  \r\n          0 1 0 1 1  \r\n          0 0 0 0 1  \r\n          0 0 0 1 1  \r\n          1 0 0 1 1];\r\nmoves = lights_out_11(board); % [3 7 17 21 23:25]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1);\r\nb1(1,5) = 1; b1(5,1) = 1; b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b2; b2,b1,b2,b3,b3; b3,b2,b1,b2,b3; b3,b3,b2,b1,b2; b2,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\n\r\n%% \r\n board = [0 1 1 1 0  \r\n          1 1 0 1 1  \r\n          1 0 1 0 1  \r\n          1 1 0 1 1  \r\n          0 1 1 1 0];\r\nmoves = lights_out_11(board); % [7:9 12:14 17:19]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1);\r\nb1(1,5) = 1; b1(5,1) = 1; b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b2; b2,b1,b2,b3,b3; b3,b2,b1,b2,b3; b3,b3,b2,b1,b2; b2,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\n\r\n%% \r\n board = [0 1 1 1 0  \r\n          0 1 1 1 0  \r\n          0 1 1 1 0  \r\n          0 1 1 1 0  \r\n          0 1 1 1 0];\r\nmoves = lights_out_11(board); % [11:15]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1);\r\nb1(1,5) = 1; b1(5,1) = 1; b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b2; b2,b1,b2,b3,b3; b3,b2,b1,b2,b3; b3,b3,b2,b1,b2; b2,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\n\r\n%% \r\n board = [1 1 1 0 0  \r\n          0 0 1 0 0  \r\n          1 1 1 1 1  \r\n          1 0 0 1 0  \r\n          1 1 0 1 0];\r\nmoves = lights_out_11(board); % [9 11 14 21 23 25]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1);\r\nb1(1,5) = 1; b1(5,1) = 1; b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b2; b2,b1,b2,b3,b3; b3,b2,b1,b2,b3; b3,b3,b2,b1,b2; b2,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\n\r\n%% \r\n board = [1 1 0 1 1  \r\n          1 1 0 1 1  \r\n          0 0 1 0 0  \r\n          1 1 0 1 1  \r\n          1 1 0 1 1];\r\nmoves = lights_out_11(board); % on your own\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1);\r\nb1(1,5) = 1; b1(5,1) = 1; b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b2; b2,b1,b2,b3,b3; b3,b2,b1,b2,b3; b3,b3,b2,b1,b2; b2,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\n\r\n%% \r\n board = [0 0 1 0 1  \r\n          0 0 1 0 1  \r\n          0 0 1 0 1  \r\n          0 0 1 0 1  \r\n          0 0 1 0 1];\r\nmoves = lights_out_11(board);\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1);\r\nb1(1,5) = 1; b1(5,1) = 1; b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b2; b2,b1,b2,b3,b3; b3,b2,b1,b2,b3; b3,b3,b2,b1,b2; b2,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\n\r\n%% \r\n board = [1 0 0 0 1  \r\n          0 1 1 1 0  \r\n          0 1 1 1 0  \r\n          0 1 1 1 0  \r\n          1 0 0 0 1];\r\nmoves = lights_out_11(board);\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1);\r\nb1(1,5) = 1; b1(5,1) = 1; b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b2; b2,b1,b2,b3,b3; b3,b2,b1,b2,b3; b3,b3,b2,b1,b2; b2,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":624,"created_at":"2018-10-31T16:37:46.000Z","updated_at":"2026-05-25T02:30:59.000Z","published_at":"2019-05-02T12:20:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Lights_Out_(game)\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLights Out\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a logic game wherein all lights need to be turned off to complete each board. See\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44751-lights-out-1-5x5-3-moves\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ethe first problem in the series\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for an introduction.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem contains boards that each require any number of moves to solve. However, now wrapping of the lights occurs. For example, if\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ board = [1 0 0 0 1  \\n          1 1 1 0 1  \\n          0 1 1 1 0  \\n          1 1 1 0 0  \\n          0 0 0 1 1]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe answer is:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ moves = [2 4 13 25]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrev.:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44764\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e5x5, wrapping, 6 moves\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e — Next:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44766\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e5x5, 3 stages, \u0026lt;7 moves\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44263,"title":"Multivariate polynomials - emulate symbolic form","description":"In \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44262-multivariate-polynomials-overload-multiplication Problem 44262\u003e I asked you to create a class |mPoly| with overloaded multiplication, so a product of two polynomials can be expressed in the form |p = p1*p2|. However, the method of constructing these polynomials is still somewhat unintuitive. In the \u003chttps://www.mathworks.com/products/symbolic.html Symbolic Math Toolbox\u003e, one can simply define some variables,\r\n\r\n  syms x y z\r\n\r\nand then create a polynomial:\r\n\r\n  p = 2*x*y + 3*x^5*z;\r\n\r\nWe would like to do something like that here. As a start, create a class |mPolySym| with properties |exponents| and |coefficients|, and |varnames|,  where the first two properties are the same as in previous problems and |varnames| is a \u003chttps://www.mathworks.com/help/matlab/characters-and-strings.html string array\u003e. The constructor should accept a numeric, char or string input, e.g.,\r\n\r\n  x = mPolySym('x')\r\n\r\n  x = \r\n\r\n  mPolySym with properties:\r\n\r\n        varnames: \"x\"\r\n       exponents: 1\r\n    coefficients: 1\r\n\r\n  r = mPolySym(pi)\r\n\r\n  r = \r\n\r\n  mPolySym with properties:\r\n\r\n        varnames: [0×0 string]\r\n       exponents: 1\r\n    coefficients: 3.1416\r\n\r\nAlso modify the method |mtimes| from the previous problem so it can multiply polynomials with different variable names.","description_html":"\u003cp\u003eIn \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44262-multivariate-polynomials-overload-multiplication\"\u003eProblem 44262\u003c/a\u003e I asked you to create a class \u003ctt\u003emPoly\u003c/tt\u003e with overloaded multiplication, so a product of two polynomials can be expressed in the form \u003ctt\u003ep = p1*p2\u003c/tt\u003e. However, the method of constructing these polynomials is still somewhat unintuitive. In the \u003ca href = \"https://www.mathworks.com/products/symbolic.html\"\u003eSymbolic Math Toolbox\u003c/a\u003e, one can simply define some variables,\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003esyms x y z\r\n\u003c/pre\u003e\u003cp\u003eand then create a polynomial:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ep = 2*x*y + 3*x^5*z;\r\n\u003c/pre\u003e\u003cp\u003eWe would like to do something like that here. As a start, create a class \u003ctt\u003emPolySym\u003c/tt\u003e with properties \u003ctt\u003eexponents\u003c/tt\u003e and \u003ctt\u003ecoefficients\u003c/tt\u003e, and \u003ctt\u003evarnames\u003c/tt\u003e,  where the first two properties are the same as in previous problems and \u003ctt\u003evarnames\u003c/tt\u003e is a \u003ca href = \"https://www.mathworks.com/help/matlab/characters-and-strings.html\"\u003estring array\u003c/a\u003e. The constructor should accept a numeric, char or string input, e.g.,\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ex = mPolySym('x')\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ex = \r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003emPolySym with properties:\r\n\u003c/pre\u003e\u003cpre\u003e        varnames: \"x\"\r\n       exponents: 1\r\n    coefficients: 1\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003er = mPolySym(pi)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003er = \r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003emPolySym with properties:\r\n\u003c/pre\u003e\u003cpre\u003e        varnames: [0×0 string]\r\n       exponents: 1\r\n    coefficients: 3.1416\u003c/pre\u003e\u003cp\u003eAlso modify the method \u003ctt\u003emtimes\u003c/tt\u003e from the previous problem so it can multiply polynomials with different variable names.\u003c/p\u003e","function_template":"classdef mPolySym\r\n    properties\r\n        varnames\r\n        exponents\r\n        coefficients\r\n    end\r\n    \r\n    methods\r\n        function p = mPolySym(s)\r\n        end\r\n        \r\n        function p = mtimes(p1,p2)\r\n        end            \r\n    end\r\n    \r\nend\r\n\r\n","test_suite":"%% Test mPolySym\r\nfiletext = fileread('mPolySym.m');\r\nassert(~contains(filetext,'regexp'))\r\n\r\n\r\n%%\r\nr = randi(1000);\r\nx = mPolySym(r);\r\nassert(isempty(x.varnames))\r\nassert(isequal(x.exponents,0))\r\nassert(isequal(x.coefficients,r))\r\n\r\n%%\r\nr = randi(1000);\r\nx = mPolySym('x');\r\ny = r*x;\r\nassert(isequal(y.varnames,\"x\"))\r\nassert(isequal(y.exponents,1))\r\nassert(isequal(y.coefficients,r))\r\nassert(isequal(r*x,x*r))\r\n\r\n%%\r\nx = mPolySym('x');\r\ny = mPolySym(\"y\");\r\nz = mPolySym('z');\r\nw = x*y*z;\r\nassert(isequal(w.varnames,[\"x\" \"y\" \"z\"]))\r\nassert(isequal(w.exponents,[1 1 1]))\r\nassert(isequal(w.coefficients,1))\r\n\r\n%%\r\nm = randi(5);\r\nn = randi(4);\r\nx = mPolySym(\"x\");\r\ny = mPolySym(\"y\");\r\np = [repmat(x,1,m) repmat(y,1,n)];\r\np = p(randperm(length(p)));\r\nr = randi(1000);\r\np_prod = r;\r\nfor ii=1:length(p)\r\n    p_prod = p_prod*p(ii);\r\nend\r\ns = randi(1000);\r\np_prod = p_prod*s;\r\nassert(isequal(p_prod.varnames,[\"x\" \"y\"]))\r\nassert(isequal(p_prod.exponents,[m n]))\r\nassert(isequal(p_prod.coefficients,r*s))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":1011,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-07-14T23:13:17.000Z","updated_at":"2026-05-25T00:58:31.000Z","published_at":"2017-07-14T23:13:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44262-multivariate-polynomials-overload-multiplication\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 44262\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e I asked you to create a class\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emPoly\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with overloaded multiplication, so a product of two polynomials can be expressed in the form\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = p1*p2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. However, the method of constructing these polynomials is still somewhat unintuitive. In the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/products/symbolic.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSymbolic Math Toolbox\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, one can simply define some variables,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[syms x y z]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand then create a polynomial:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[p = 2*x*y + 3*x^5*z;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe would like to do something like that here. As a start, create a class\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emPolySym\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with properties\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexponents\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecoefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003evarnames\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where the first two properties are the same as in previous problems and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003evarnames\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/characters-and-strings.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003estring array\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The constructor should accept a numeric, char or string input, e.g.,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x = mPolySym('x')\\n\\nx = \\n\\nmPolySym with properties:\\n\\n        varnames: \\\"x\\\"\\n       exponents: 1\\n    coefficients: 1\\n\\nr = mPolySym(pi)\\n\\nr = \\n\\nmPolySym with properties:\\n\\n        varnames: [0×0 string]\\n       exponents: 1\\n    coefficients: 3.1416]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAlso modify the method\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emtimes\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from the previous problem so it can multiply polynomials with different variable names.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2511,"title":" BLOCK x3 (Version 4) ","description":"Always in this series ( \u003chttp://www.mathworks.com/matlabcentral/cody/problems/2451-block-x3-version-1/ 2451\u003e, \u003chttp://www.mathworks.com/matlabcentral/cody/problems/2484-block-x3-version-3/ 2484\u003e, and \u003chttp://www.mathworks.com/matlabcentral/cody/problems/2478-block-x3-version-2 2478\u003e ).\r\n\r\nNow we are in color (1 for red  and 2 for white).\r\nYour task is always to count the  *minimum number* of movements required to align the 3 blocks in each colors (vertically or horizontally).\r\n\r\n\r\n\r\n\u003c\u003chttp://4.bp.blogspot.com/-iveYgRwOmLs/Udk9ZctxnUI/AAAAAAAA3Uw/Z9XNHw6f-f4/s400/pack+2+level+2-1.png\u003e\u003e\r\n\r\n* [0 0 0 0 0 0 0;\r\n*  0 0 1 2 0 0 0;\r\n*  0 0 0 0 0 0 0;\r\n*  0 0 1 2 0 0 0;\r\n*  0 0 1 2 0 0 0;\r\n*  0 0 0 0 0 0 0;\r\n*  0 0 0 0 0 0 0]\r\n\r\nIn this example you can move down the first two blocks ( *in two moves* ).\r\n\r\n\r\nNote that blocks can be *swapped* . \r\n\r\n\r\nIn this second example :\r\n\r\n\u003c\u003chttp://1.bp.blogspot.com/-XJP6Mn4X9Ws/Udk9bHEKx_I/AAAAAAAA3Vo/V_Ar3oF9gYw/s400/pack+2+level+2-7.png\u003e\u003e\r\n\r\n* [0 0 0 0 0 0 0;\r\n*  0 0 0 0 0 0 0;\r\n*  0 0 1 2 0 0 0;\r\n*  0 0 2 1 0 0 0;\r\n*  0 0 1 2 0 0 0;\r\n*  0 0 0 0 0 0 0;\r\n*  0 0 0 0 0 0 0]\r\n\r\nHere you win in only *one move* by swapping the two central blocks.\r\n\r\nGood luck !","description_html":"\u003cp\u003eAlways in this series ( \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/2451-block-x3-version-1/\"\u003e2451\u003c/a\u003e, \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/2484-block-x3-version-3/\"\u003e2484\u003c/a\u003e, and \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/2478-block-x3-version-2\"\u003e2478\u003c/a\u003e ).\u003c/p\u003e\u003cp\u003eNow we are in color (1 for red  and 2 for white).\r\nYour task is always to count the  \u003cb\u003eminimum number\u003c/b\u003e of movements required to align the 3 blocks in each colors (vertically or horizontally).\u003c/p\u003e\u003cimg src = \"http://4.bp.blogspot.com/-iveYgRwOmLs/Udk9ZctxnUI/AAAAAAAA3Uw/Z9XNHw6f-f4/s400/pack+2+level+2-1.png\"\u003e\u003cul\u003e\u003cli\u003e[0 0 0 0 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 1 2 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 0 0 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 1 2 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 1 2 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 0 0 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 0 0 0 0 0]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eIn this example you can move down the first two blocks ( \u003cb\u003ein two moves\u003c/b\u003e ).\u003c/p\u003e\u003cp\u003eNote that blocks can be \u003cb\u003eswapped\u003c/b\u003e .\u003c/p\u003e\u003cp\u003eIn this second example :\u003c/p\u003e\u003cimg src = \"http://1.bp.blogspot.com/-XJP6Mn4X9Ws/Udk9bHEKx_I/AAAAAAAA3Vo/V_Ar3oF9gYw/s400/pack+2+level+2-7.png\"\u003e\u003cul\u003e\u003cli\u003e[0 0 0 0 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 0 0 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 1 2 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 2 1 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 1 2 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 0 0 0 0 0;\u003c/li\u003e\u003cli\u003e0 0 0 0 0 0 0]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eHere you win in only \u003cb\u003eone move\u003c/b\u003e by swapping the two central blocks.\u003c/p\u003e\u003cp\u003eGood luck !\u003c/p\u003e","function_template":"function y = block3_4(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [0 0 0 0 0 0 0;0 0 0 0 0 0 0;0 0 1 2 0 0 0;0 0 0 0 0 0 0;0 0 1 2 0 0 0;0 0 1 2 0 0 0;0 0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(block3_4(x),y_correct))\r\n\r\n\r\n%%\r\nx = [0 0 0 0 0 0 0;0 0 0 0 0 0 0;0 0 0 2 1 0 0;0 0 0 1 2 0 0;0 0 0 2 1 0 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0];\r\ny_correct = 1;\r\nassert(isequal(block3_4(x),y_correct))\r\n\r\n\r\n%%\r\nx = [0 0 0 0 0 0 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0;0 0 2 1 2 0 0;0 0 1 2 1 0 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0];\r\ny_correct = 1;\r\nassert(isequal(block3_4(x),y_correct))\r\n\r\n\r\n%%\r\nx = [0 0 0 0 0 0 0;0 0 0 0 0 0 0;0 0 1 0 1 1 0;0 0 2 2 0 2 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(block3_4(x),y_correct))\r\n\r\n\r\n%%\r\nx = [0 0 0 0 0 0 0;0 0 0 0 0 0 0;0 0 1 1 2 0 0;0 0 2 2 1 0 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0];\r\ny_correct = 1;\r\nassert(isequal(block3_4(x),y_correct))\r\n\r\n%%\r\nx = [0 0 0 0 0 0 0;0 0 0 0 0 0 0;0 0 1 1 0 0 0;0 0 2 2 0 0 0;0 0 2 1 0 0 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(block3_4(x),y_correct))\r\n\r\n%%\r\nx = [0 0 0 0 0 0 0;0 0 0 1 0 0 0;0 0 2 0 1 0 0;0 0 1 0 2 0 0;0 0 0 2 0 0 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0];\r\ny_correct = 3;\r\nassert(isequal(block3_4(x),y_correct))\r\n\r\n%%\r\nx = [0 0 0 0 0 0 0;0 0 0 1 0 0 0;0 0 1 2 1 0 0;0 0 2 0 2 0 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0;0 0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(block3_4(x),y_correct))\r\n\r\n%%\r\nx = [0 0 0 0 0 0 0;0 0 0 1 0 0 0;0 0 0 1 0 0 0;0 0 1 2 0 0 0;0 0 2 0 0 0 0;0 0 2 0 0 0 0;0 0 0 0 0 0 0];\r\ny_correct = 1;\r\nassert(isequal(block3_4(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":5390,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-08-15T07:15:35.000Z","updated_at":"2026-05-25T00:45:42.000Z","published_at":"2014-08-15T07:17:45.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.png\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/media/image2.png\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAlways in this series (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/2451-block-x3-version-1/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e2451\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/2484-block-x3-version-3/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e2484\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/2478-block-x3-version-2\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e2478\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNow we are in color (1 for red and 2 for white). Your task is always to count the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eminimum number\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of movements required to align the 3 blocks in each colors (vertically or horizontally).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[0 0 0 0 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 1 2 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 0 0 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 1 2 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 1 2 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 0 0 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 0 0 0 0 0]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this example you can move down the first two blocks (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ein two moves\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote that blocks can be\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eswapped\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this second example :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[0 0 0 0 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 0 0 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 1 2 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 2 1 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 1 2 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 0 0 0 0 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 0 0 0 0 0 0]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere you win in only\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eone move\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e by swapping the two central blocks.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood luck 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\"},{\"partUri\":\"/media/image2.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\"}]}"},{"id":2451,"title":"BLOCK x3 (Version 1)","description":"\r\n\u003chttps://play.google.com/store/apps/details?id=com.noodlecake.blockblock BLOCK x3\u003e is a simple, fun and relaxing puzzle game.\r\n\r\nThe basics are easy. Solve the puzzles by getting *3 blocks* in a row or column. \r\n\r\nThe puzzle is coded a 6x6 matrix and the 3 blocks are indicated by 1 (and 0 for free space).\r\n\r\nIn this example :\r\n\r\n\u003c\u003chttp://1.bp.blogspot.com/-GbZ-AMjylSs/Udk6kRyp4uI/AAAAAAAA3Pk/3jdWrVSqQpc/s400/pack+1+level+1-1.png\u003e\u003e\r\n \r\n \r\n\r\n* [0 0 0 0 0 0\r\n* \r\n* 0 0 1 0 0 0\r\n* \r\n* 0 0 1 0 0 0\r\n* \r\n* 0 0 0 0 0 0\r\n* \r\n* 0 0 1 0 0 0\r\n* \r\n* 0 0 0 0 0 0]\r\n\r\nYou line up 3 blocks in one move by dragging the last block to the top (you can move a block in the free space only horizontally or vertically.)\r\n\r\n\r\n\r\nThe goal in this first problem is to give the *smallest number* of moves to solve the puzzle.\r\n\r\n\r\n\r\n","description_html":"\u003cp\u003e\u003ca href = \"https://play.google.com/store/apps/details?id=com.noodlecake.blockblock\"\u003eBLOCK x3\u003c/a\u003e is a simple, fun and relaxing puzzle game.\u003c/p\u003e\u003cp\u003eThe basics are easy. Solve the puzzles by getting \u003cb\u003e3 blocks\u003c/b\u003e in a row or column.\u003c/p\u003e\u003cp\u003eThe puzzle is coded a 6x6 matrix and the 3 blocks are indicated by 1 (and 0 for free space).\u003c/p\u003e\u003cp\u003eIn this example :\u003c/p\u003e\u003cimg src = \"http://1.bp.blogspot.com/-GbZ-AMjylSs/Udk6kRyp4uI/AAAAAAAA3Pk/3jdWrVSqQpc/s400/pack+1+level+1-1.png\"\u003e\u003cul\u003e\u003cli\u003e[0 0 0 0 0 0\u003c/li\u003e\u003cli\u003e\u003c/li\u003e\u003cli\u003e0 0 1 0 0 0\u003c/li\u003e\u003cli\u003e\u003c/li\u003e\u003cli\u003e0 0 1 0 0 0\u003c/li\u003e\u003cli\u003e\u003c/li\u003e\u003cli\u003e0 0 0 0 0 0\u003c/li\u003e\u003cli\u003e\u003c/li\u003e\u003cli\u003e0 0 1 0 0 0\u003c/li\u003e\u003cli\u003e\u003c/li\u003e\u003cli\u003e0 0 0 0 0 0]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eYou line up 3 blocks in one move by dragging the last block to the top (you can move a block in the free space only horizontally or vertically.)\u003c/p\u003e\u003cp\u003eThe goal in this first problem is to give the \u003cb\u003esmallest number\u003c/b\u003e of moves to solve the puzzle.\u003c/p\u003e","function_template":"function y = block3(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [0 0 0 0 0 0;0 0 0 0 0 0;0 0 1 0 0 0;0 0 1 0 0 0;0 0 0 1 0 0;0 0 0 0 0 0];\r\ny_correct = 1;\r\nassert(isequal(block3(x),y_correct))\r\n%%\r\nx = [0 0 0 0 0 0;0 0 0 0 0 0;0 0 1 0 0 0;0 1 0 0 0 0;0 0 1 0 0 0;0 0 0 0 0 0];\r\ny_correct = 1;\r\nassert(isequal(block3(x),y_correct))\r\n%%\r\nx = [0 0 0 0 0 0;0 0 0 0 0 0;0 0 1 0 0 0;0 0 0 1 0 0;0 0 0 0 1 0;0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(block3(x),y_correct))\r\n%%\r\nx = [0 0 0 0 0 0;0 0 1 0 0 0;0 0 0 0 0 0;0 0 1 0 0 0;0 0 0 0 0 0;0 0 1 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(block3(x),y_correct))\r\n%%\r\nx = [0 0 0 0 0 0;0 0 0 0 0 0;0 1 0 1 1 0;0 0 0 0 0 0;0 0 0 0 0 0;0 0 0 0 0 0];\r\ny_correct = 1;\r\nassert(isequal(block3(x),y_correct))\r\n%%\r\nx = [0 0 0 0 0 0;0 0 0 0 0 0;0 0 0 1 1 0;0 0 0 0 0 0;0 0 1 0 0 0;0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(block3(x),y_correct))\r\n%%\r\nx = [0 0 0 0 0 0;0 0 0 0 0 0;0 0 0 1 1 0;0 0 0 1 0 0;0 0 0 0 0 0;0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(block3(x),y_correct))\r\n%%\r\nx = [0 0 0 0 0 0;0 0 0 0 0 0;0 0 0 1 0 0;0 0 0 1 1 0;0 0 0 0 0 0;0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(block3(x),y_correct))\r\n%%\r\nx = [0 0 0 0 0 0;0 0 1 0 1 0;0 0 0 0 0 0;0 0 0 0 0 0;0 0 0 1 0 0;0 0 0 0 0 0];\r\ny_correct = 3;\r\nassert(isequal(block3(x),y_correct))\r\n%%\r\nx = [0 0 0 0 0 0;0 0 1 0 1 0;0 0 1 0 0 0;0 0 0 0 0 0;0 0 0 0 0 0;0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(block3(x),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":5390,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2014-07-20T00:15:18.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-07-19T23:58:55.000Z","updated_at":"2026-05-25T00:43:28.000Z","published_at":"2014-07-20T00:15:18.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.png\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://play.google.com/store/apps/details?id=com.noodlecake.blockblock\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eBLOCK x3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a simple, fun and relaxing puzzle game.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe basics are easy. 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\"}]}"},{"id":2478,"title":"BLOCK x3 (Version 2)","description":"An extension to problem 2451 ( \u003chttps://www.mathworks.com/matlabcentral/cody/problems/2451-block-x3-version-1\u003e ).\r\n\r\nIt is based on an android game - BLOCK x3. The objective is to align the 1's in the matrix using minimum movements. The valid movements are  horizontal and vertical (by one step). A zero (0) indicates an empty space. Your task is to count minimum number of movements required to align the three 1's vertically or horizontally.\r\n\r\nNew challenge in this problem : There are some static elements which can not be moved and can not be included in the alignment. These elements are indicated by 2. This makes the problem a bit challenging.\r\n\r\nExample:\r\n\r\n\r\n  Input =[0 0 0 0 0 0 0 0;\r\n          0 0 1 0 1 0 0 0;\r\n          0 0 0 2 1 0 0 0;\r\n          0 0 0 0 0 0 0 0]\r\n  \r\n  Output = 2;\r\n","description_html":"\u003cp\u003eAn extension to problem 2451 ( \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/2451-block-x3-version-1\"\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/2451-block-x3-version-1\u003c/a\u003e ).\u003c/p\u003e\u003cp\u003eIt is based on an android game - BLOCK x3. The objective is to align the 1's in the matrix using minimum movements. The valid movements are  horizontal and vertical (by one step). A zero (0) indicates an empty space. Your task is to count minimum number of movements required to align the three 1's vertically or horizontally.\u003c/p\u003e\u003cp\u003eNew challenge in this problem : There are some static elements which can not be moved and can not be included in the alignment. These elements are indicated by 2. This makes the problem a bit challenging.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eInput =[0 0 0 0 0 0 0 0;\r\n        0 0 1 0 1 0 0 0;\r\n        0 0 0 2 1 0 0 0;\r\n        0 0 0 0 0 0 0 0]\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eOutput = 2;\r\n\u003c/pre\u003e","function_template":"function y = blockx3_2(x)\r\n\r\nend","test_suite":"%%\r\n\r\nx =  [0 0 0 0 0 0 0 0;\r\n      0 0 1 0 1 0 0 0;\r\n      0 0 0 2 1 0 0 0;\r\n      0 0 0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(blockx3_2(x),y_correct));\r\n\r\n\r\n%%\r\nx =  [0 0 0 0 0 0 0 0;\r\n      0 0 1 0 1 0 0 0;\r\n      0 0 0 2 0 0 0 0;\r\n      0 0 1 0 0 0 0 0];\r\ny_correct = 3;\r\nassert(isequal(blockx3_2(x),y_correct))\r\n\r\n%%\r\nx =  [1 1 0 0 0 0 0 0;\r\n      1 2 0 0 0 0 0 0;\r\n      0 0 0 0 0 0 0 0;\r\n      0 0 0 0 0 0 0 0];\r\ny_correct = 3;\r\nassert(isequal(blockx3_2(x),y_correct))\r\n\r\n%%\r\nx =  [0 0 0 1 0 0 0 0;\r\n      0 0 1 2 1 0 0 0;\r\n      0 0 0 0 0 0 0 0;\r\n      0 0 0 0 0 0 0 0];\r\ny_correct = 2;\r\nassert(isequal(blockx3_2(x),y_correct))\r\n\r\n\r\n%%\r\nx =  [0 0 0 1 0 0 0 0;\r\n      0 0 1 2 0 0 0 0;\r\n      0 0 1 0 0 0 0 0;\r\n      0 0 0 0 0 0 0 0]\r\ny_correct = 1;\r\nassert(isequal(blockx3_2(x),y_correct))\r\n\r\n\r\n%%\r\nx =  [0 0 0 1 0 0 0 0;\r\n      0 0 1 2 0 0 0 0;\r\n      0 0 0 0 0 0 0 1;\r\n      0 0 0 0 0 0 0 0]\r\ny_correct = 6;\r\nassert(isequal(blockx3_2(x),y_correct))\r\n\r\n\r\n%%\r\nx =  [0 0 0 1 0 0 0 0;\r\n      0 0 0 2 0 0 0 0;\r\n      0 0 0 1 0 0 0 0;\r\n      0 0 0 1 0 0 0 0]\r\ny_correct = 4;\r\nassert(isequal(blockx3_2(x),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":17203,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2014-08-03T08:43:51.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-08-03T08:31:00.000Z","updated_at":"2026-05-25T00:44:08.000Z","published_at":"2014-08-03T08:31:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn extension to problem 2451 (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/2451-block-x3-version-1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/2451-block-x3-version-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt; ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt is based on an android game - BLOCK x3. The objective is to align the 1's in the matrix using minimum movements. The valid movements are horizontal and vertical (by one step). A zero (0) indicates an empty space. Your task is to count minimum number of movements required to align the three 1's vertically or horizontally.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNew challenge in this problem : There are some static elements which can not be moved and can not be included in the alignment. These elements are indicated by 2. This makes the problem a bit challenging.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Input =[0 0 0 0 0 0 0 0;\\n        0 0 1 0 1 0 0 0;\\n        0 0 0 2 1 0 0 0;\\n        0 0 0 0 0 0 0 0]\\n\\nOutput = 2;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60746,"title":"List Ormiston prime pairs","description":"The numbers 1913 and 1931 form the first Ormiston prime pair. The numbers are consecutive primes, and they are anagrams of each other—that is, the digits of one number can be arranged to give the second number. 347 and 743 are not an Ormiston prime pair: they are anagrams of each other, but they are not consecutive primes. \r\nWrite a function that produces the nth Ormiston prime pair.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe numbers 1913 and 1931 form the first Ormiston prime pair. The numbers are consecutive primes, and they are anagrams of each other—that is, the digits of one number can be arranged to give the second number. 347 and 743 are not an Ormiston prime pair: they are anagrams of each other, but they are not consecutive primes. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that produces the nth Ormiston prime pair.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = OrmistonPrimePair(n)\r\n  p = primes(n); \r\n  y = isequal(sort(p(n)),sort(p(n+1)));\r\nend","test_suite":"%%\r\nn = 1;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [1913 1931];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 18;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [55313 55331];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 54;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [131413 131431];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 126;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [343337 343373];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 180;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [481513 481531];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1080;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [2744279 2744297];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1818;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [4696613 4696631];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 5436;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [14589013 14589031];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 7290;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [19592813 19592831];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 10800;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [29470879 29470897];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 17496;\r\ny = OrmistonPrimePair(n);\r\ny_correct = [48654979 48654997];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 11111;\r\ny = OrmistonPrimePair(n);\r\nsmf_correct = 81182;\r\nsmf = sum([max(factor(y(1)+1)) max(factor(y(2)+1))]);\r\nassert(isequal(smf,smf_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2024-10-09T05:13:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-10-09T05:13:08.000Z","updated_at":"2026-06-06T01:40:24.000Z","published_at":"2024-10-09T05:13:23.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe numbers 1913 and 1931 form the first Ormiston prime pair. The numbers are consecutive primes, and they are anagrams of each other—that is, the digits of one number can be arranged to give the second number. 347 and 743 are not an Ormiston prime pair: they are anagrams of each other, but they are not consecutive primes. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that produces the nth Ormiston prime pair.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61292,"title":"The Singularity - Event Horizon (Absolute Zero)","description":"Inspired by Problem61291\r\nMô tả:\r\nBầy đàn gồm M agents phải di chuyển xuyên qua không gian 5D Hyper-Torus ( kích thước mỗi chiều L = 100 ) từ Node 1 đến Target Node. Để sống sót, thuật toán của bạn phải tuân thủ nghiêm ngặt các định luật vật lí sau:\r\n1. Hình học Torus 5D: Khoảng cách giữa 2 điểm là khoảng cách Chebyshev trên mặt Torus:\r\n        d = max(min( | x_i - y_i |,100 - | x_i - y_i | )) cho i = 1..5.\r\n2. Động lực học Pulse: Chi phí năng lượng tại thời điểm cập bến t bị nhân bởi hệ số \r\n        Pulse(t) = 1 + 2 sin^2(pi*t/2). Lưu ý: V_{swarm} = 20.\r\n3. Kẻ săn mồi ( Dynamic Predator ): Predator xuất phát từ pred_start với V_p = 15. Nếu tại bất kì node trung gian nào, Predator có thể đến trước hoặc cùng lúc với bầy đàn ( t_p \u003c= t_s ), bầy đàn sẽ bị tiêu diệt ( Energy = -1 ).\r\n4. Cấm quay đầu ( No-Revisit Rule ): Để tránh việc \"câu giờ\" đợi nhịp Pulse thấp, bầy đàn không được phép đi qua 1 node quá một lần trong cùng 1 hành trình.\r\n5. Hệ số bão hòa \u0026 Thuế Entropy: *Sat  = M + 0.125 x M x ( M - 1 ).\r\n6. Cộng hưởng Spin: Nếu tọa độ thứ 5(ω) của node đến gần sát một số nguyên ( sai số \u003c 0.05 ), một hình phạt Spin = 50 x (step + 1) sẽ được cộng vào chi phí","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 405px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 202.5px; transform-origin: 468.5px 202.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInspired by \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://ww2.mathworks.cn/matlabcentral/cody/groups/97667/problems/61291\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); \"\u003e\u003cspan style=\"\"\u003eProblem61291\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eMô tả:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBầy đàn gồm \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e agents phải di chuyển xuyên qua không gian 5D Hyper-Torus ( kích thước mỗi chiều \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 100 ) từ Node 1 đến Target Node. Để sống sót, thuật toán của bạn phải tuân thủ nghiêm ngặt các định luật vật lí sau:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHình học Torus 5D\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Khoảng cách giữa 2 điểm là khoảng cách Chebyshev trên mặt Torus:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        d = max(min( | x_i - y_i |,100 - | x_i - y_i | )) cho i = 1..5.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eĐộng lực học Pulse\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Chi phí năng lượng tại thời điểm cập bến \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003et\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e bị nhân bởi hệ số \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        Pulse(t) = 1 + 2 sin^2(pi*t/2). Lưu ý: V_{swarm} = 20.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eKẻ săn mồi ( Dynamic Predator ):\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Predator xuất phát từ pred_start với V_p = 15. Nếu tại bất kì node trung gian nào, Predator có thể đến trước hoặc cùng lúc với bầy đàn ( t_p \u0026lt;= t_s ), bầy đàn sẽ bị tiêu diệt ( Energy = -1 ).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCấm quay đầu ( No-Revisit Rule ):\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Để tránh việc \"câu giờ\" đợi nhịp Pulse thấp, bầy đàn không được phép đi qua 1 node quá một lần trong cùng 1 hành trình.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e5. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHệ số bão hòa \u0026amp; Thuế Entropy\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: *Sat  = \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e + 0.125 x M x ( M - 1 ).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e6. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCộng hưởng Spin\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Nếu tọa độ thứ 5(ω) của node đến gần sát một số nguyên ( sai số \u0026lt; 0.05 ), một hình phạt Spin = 50 x (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e + 1) sẽ được cộng vào chi phí\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [max_energy, best_path] = solve_event_horizon_v3(nodes, pred_start, params)\r\n    V_p = 15;%\r\nend","test_suite":"%% PHASE 1: THE PULSE TIMING TRAP\r\nclear n p;\r\np.M = 1; p.target = 2; p.ATP_total = 2000;\r\nn(1).coord = [0,0,0,0,0.5]; n(1).res = 1;\r\nn(2).coord = [30,0,0,0,0.5]; n(2).res = 10; \r\nn(3).coord = [10,0,0,0,0.5]; n(3).res = 0.1;\r\n[e1, s1] = solve_event_horizon_v3(n, 0, p);\r\nassert(~isempty(s1) \u0026\u0026 length(s1{1}) == 3, 'FAILED T1: Phải đi vòng qua Node 3 để khớp t=2.0s.');\r\n\r\n%% PHASE 2: HYPER-TORUS WRAP-AROUND \r\nclear n p; p.M = 1; p.ATP_total = 2000; p.target = 2;\r\nbase.res = 1; base.coord = [0,0,0,0,0.5];\r\n\r\n% Test 2: Chiều 1\r\nn2 = repmat(base, 1, 2); n2(2).coord(1) = 90;\r\n[e2, ~] = solve_event_horizon_v3(n2, 0, p);\r\nassert(abs(e2 - 1980) \u003c 1e-3, 'FAILED T2: Lỗi Torus chiều 1');\r\n\r\n% Test 3: Chiều 5\r\nn3 = repmat(base, 1, 2); n3(2).coord(5) = 95.5; \r\n[e3, ~] = solve_event_horizon_v3(n3, 0, p);\r\nassert(e3 \u003e 1990, 'FAILED T3: Lỗi Torus chiều 5');\r\n\r\n%% PHASE 4: PREDATOR INTERCEPT \r\nclear n p; p.M = 1; p.ATP_total = 5000; p.target = 2;\r\nn(1).coord = [0,0,0,0,0.5]; n(1).res = 1;\r\nn(2).coord = [40,0,0,0,0.5]; n(2).res = 1; \r\n\r\nn(3).coord = [0,20,0,0,0.5]; n(3).res = 0.1; \r\n\r\nn(4).coord = [0,60,0,0,0.5]; \r\n\r\n[e7, s7] = solve_event_horizon_v3(n, 4, p);\r\n\r\nassert(~isempty(s7) \u0026\u0026 e7 \u003e 0, 'FAILED T7: Vẫn không tìm thấy đường an toàn');\r\n\r\n%% TEST 20: THE OMEGA LABYRINTH (Bản Chuẩn Hóa 100%)\r\nclear n p;\r\n% 1. Cấu hình cố định để Solver và Testcase đồng bộ\r\np.M = 10; \r\np.target = 5; \r\np.ATP_total = 10000;\r\nV_s = 20; \r\nV_p = 15; % Hằng số Predator\r\n\r\n% 2. Tạo 5 Nodes với tọa độ NẰM TRONG KHOẢNG [0, 100]\r\n% Node 1: Xuất phát\r\nn(1).coord = [10, 10, 10, 10, 0.5]; n(1).res = 1;\r\n% Node 2: Predator (Kẻ săn mồi đứng đây)\r\nn(2).coord = [30, 10, 10, 10, 0.5]; n(2).res = 1;\r\n% Node 3: Node trung gian (Đường vòng an toàn)\r\nn(3).coord = [10, 50, 10, 10, 0.5]; n(3).res = 0.5;\r\n% Node 4: Node rác\r\nn(4).coord = [80, 80, 80, 80, 0.5]; n(4).res = 1;\r\n% Node 5: Đích\r\nn(5).coord = [50, 50, 10, 10, 0.5]; n(5).res = 0.5;\r\n\r\n% 3. Chạy Solver\r\n[user_e, user_path] = solve_event_horizon_v3(n, 2, p);\r\n\r\n% 4. CHẶN LỖI CRASH (Nếu Solver trả về rỗng)\r\nassert(~isempty(user_path) \u0026\u0026 ~isempty(user_path{1}), 'Solver không tìm thấy bất kỳ con đường nào!');\r\n\r\n% 5. KIỂM TRA LOGIC SINH TỒN\r\npath = user_path{1};\r\nt_run = 0; is_captured = false;\r\nSat = p.M + 0.125 * p.M * (p.M - 1);\r\ne_val = p.ATP_total;\r\n\r\nfor k = 1:length(path)-1\r\n    u = path(k); v = path(k+1);\r\n    df = abs(n(u).coord - n(v).coord);\r\n    % Chuẩn hóa khoảng cách Torus chuẩn 100%\r\n    d = max(min(df, 100 - df));\r\n    \r\n    t_run = t_run + d/V_s;\r\n    \r\n    % Kiểm tra Predator (Node 2) có bắt được tại Node v không\r\n    df_p = abs(n(2).coord - n(v).coord);\r\n    dp = max(min(df_p, 100 - df_p));\r\n    \r\n    if dp/V_p \u003c= t_run + 1e-9\r\n        is_captured = true; break;\r\n    end\r\n    \r\n    % Tính năng lượng để đối chiếu\r\n    pulse = 1 + 2 * (sin(t_run * pi / 2)^2);\r\n    cost = (d * n(v).res * Sat * pulse) * (1.15^(k-1));\r\n    if abs(n(v).coord(5) - round(n(v).coord(5))) \u003c 0.05\r\n        cost = cost + 50 * k;\r\n    end\r\n    e_val = e_val - cost;\r\nend\r\n\r\n% ASSERTION CUỐI CÙNG\r\nassert(~is_captured, 'Omega Phase: Swarm captured! Code của bạn đang phớt lờ Predator.');\r\nassert(abs(user_e - e_val) \u003c 1e-5, 'Omega Phase: Năng lượng tính toán không khớp!');\r\n%% PHASE 5: SPIN SENSITIVITY \r\nclear n p; p.M = 20; p.target = 2; p.ATP_total = 10000;\r\nn(1).coord = [0,0,0,0,0.5]; n(2).coord = [10,0,0,0,1.02]; n(2).res = 1; \r\n[e12, ~] = solve_event_horizon_v3(n, 0, p);\r\nassert(abs(e12 - 8600) \u003c 1e-4, 'FAILED T12: Spin Penalty không kích hoạt đúng ngưỡng.');\r\n\r\nn(2).coord(5) = 1.06;\r\n[e13, ~] = solve_event_horizon_v3(n, 0, p);\r\nassert(abs(e13 - 8650) \u003c 1e-4, 'FAILED T13: Spin Penalty kích hoạt sai mục tiêu.');","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":5076265,"edited_by":5076265,"edited_at":"2026-03-23T17:47:36.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2026-03-23T17:47:36.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-22T19:51:08.000Z","updated_at":"2026-06-06T20:25:40.000Z","published_at":"2026-03-22T19:51:08.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInspired by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://ww2.mathworks.cn/matlabcentral/cody/groups/97667/problems/61291\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem61291\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMô tả:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBầy đàn gồm \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e agents phải di chuyển xuyên qua không gian 5D Hyper-Torus ( kích thước mỗi chiều \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 100 ) từ Node 1 đến Target Node. Để sống sót, thuật toán của bạn phải tuân thủ nghiêm ngặt các định luật vật lí sau:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHình học Torus 5D\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Khoảng cách giữa 2 điểm là khoảng cách Chebyshev trên mặt Torus:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        d = max(min( | x_i - y_i |,100 - | x_i - y_i | )) cho i = 1..5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eĐộng lực học Pulse\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Chi phí năng lượng tại thời điểm cập bến \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e bị nhân bởi hệ số \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        Pulse(t) = 1 + 2 sin^2(pi*t/2). Lưu ý: V_{swarm} = 20.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eKẻ săn mồi ( Dynamic Predator ):\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Predator xuất phát từ pred_start với V_p = 15. Nếu tại bất kì node trung gian nào, Predator có thể đến trước hoặc cùng lúc với bầy đàn ( t_p \u0026lt;= t_s ), bầy đàn sẽ bị tiêu diệt ( Energy = -1 ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e4. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCấm quay đầu ( No-Revisit Rule ):\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Để tránh việc \\\"câu giờ\\\" đợi nhịp Pulse thấp, bầy đàn không được phép đi qua 1 node quá một lần trong cùng 1 hành trình.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e5. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHệ số bão hòa \u0026amp; Thuế Entropy\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: *Sat  = \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e + 0.125 x M x ( M - 1 ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e6. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCộng hưởng Spin\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Nếu tọa độ thứ 5(ω) của node đến gần sát một số nguyên ( sai số \u0026lt; 0.05 ), một hình phạt Spin = 50 x (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e + 1) sẽ được cộng vào chi phí\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61046,"title":"Decipher Message Using Prime of Primitive Root of Two Sequence Key","description":"Provided a message with all characters \u003c= 255 (ascii) as an input, decode the padded message (removing the random character pad), XORing input converted to binary vector (8 bits each) with the inputted prime having primitive root of two as the key. The key is the repeated sequence of 2^x modulo prime key input starting from x=0 until the cycle repeats (unpadded zero binary represented vector of the repeated sequence). After XORing, remove the padded front and return the character array as output.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 105px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 52.5px; transform-origin: 408px 52.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 52.5px; text-align: left; transform-origin: 385px 52.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eProvided a message with all characters \u0026lt;= 255 (ascii) as an input, decode the padded message (removing the random character pad), XORing input converted to binary vector (8 bits each) with the inputted prime having primitive root of two as the key. The key is the repeated sequence of 2^x modulo prime key input starting from x=0 until the cycle repeats (unpadded zero binary represented vector of the repeated sequence). After XORing, remove the padded front and return the character array as output.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function d = deCipher(x,key)\r\n  d=xor(x,key);\r\nend\r\n","test_suite":"%%\r\nx=[39   212    74    83   164    14     3   175    39   212    74    83   164    14     3   175    39   212    74    83   164   14     3   175    39   212    74    83   164    14     3   175    39   212    74    83   164    14     3   175    39   212   74    83   164    14     3   175    39   212    74    83   164    14     3   175    39   212    74    83   164    14     3   19   242    77   208   208    52   219   130    53   242    82   200   207    60   218];\r\nassert(isequal(deCipher(x,19),'I love to swim!'));\r\n%%\r\nx=double('şl‘……‘ŒŒœŚøùè©ădurŢŠª«Ădõ³f ÈijĨĻ™isœ´Ŕ~ê‚ĪŢŞjhĻľŒĒďċĈÓ»ŃÃÜĮîĜŐËīōï´ÖŜąđo‹tŚļŸ‰Ķ¦ĺąˆ®ŝšŊň˜Ç´ļōďƅł¶ÕľŐĔşºśŔ“dk’ĢŠŏĽžá³ÐqfʯĬŕĔăĢċĠŋÆÄĮōĈėĠŽĠ')-100;\r\nassert(isequal(deCipher(x,797),'abcdefghijklmnopqrstuvwxyz !@#$%^\u0026*()_+ 0123456789 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!@#$%^\u0026*()_+ 0123456789 ABCDEFGHIJKLMNOPQRSTUVWXYZ';\r\ny=repmat(y,1,100);\r\nrng(2718);\r\ny=y(randperm(length(y)));\r\nassert(isequal(deCipher(x,16067),y));\r\n%%\r\nx=double('“ŀŝřřŝŠšŁţšőšĖþ¸xĤŒ‘ÇãŖ±äÿĨÚİIJŐÉÝz¦vgy•üňłŃijŐÑî‡kv¾äŅ߶Ħu…ðjĺ½igÄÀŞŜřÞÁ£ŋùdfä©kŇðoꊠ¸ÓĤ«ċ•jâ¯ċpg·Đ¦Õŀ}qĻĻg«ŸlÉĉŞÒġ•ÔÆķ¯»™èÁĜŀ¿ĻęÎ{möġæĽ½ÐĤ°ÉÈĔØœđÀġh‡āĠřu˂ċĜÊĂÕĨęâş×ř¼‹­É¯µĦϦøÓĨăøÌ|¿×ÎÔåá×´Òœİfý–™kĬµijş©×Ţç|īdºĩ€¤ıŖÇýqʂèívĜŔij¼˜ĎĂŝÐřšļnzČmŊãÂĺŅŒûįçıċkõĨ÷ĆÒףĦd…‹ċĮàÿĈĹňÙŐIJÒĊ탂ú›ĭðā‹ôȵ')-100;\r\ny='Men go abroad to wonder at the heights of mountains, at the huge waves of the sea, at the long courses of the rivers, at the vast compass of the ocean, at the circular motions of the stars, and they pass by themselves without wondering.';\r\nassert(isequal(deCipher(x,16067),y));\r\n%%\r\nx=double('˜īņŒŒņ³ÓdÓÅℐjīĭÃÚŔŘśÏĻ|f}Ŏu´ÇŕōæĵòöĬĝoÑ®²vÝř»ěíijĥvÍŌæ󼍑ò¶ĬqipˆÄwŜšğ’¥Ôŗ÷ovĀ{·Ň÷²ŅŒÎéªw‚ŗš²Øqśxr®ď¹”ĩiuóöe«ÖwÇńēÌĠ£ÝÆıÂeœúrśļ‚Īė“«lüĎįā|Ðì½Ý…ŜáĄď¾Œ«žåąŎyÄ¿ĐޖæàåŚÇŠÅŝ¡n½iñĔnê‹Ŀāó µ° ÔÅ÷’ËfÄŋüwùݙ£ħ¹ľęž‘ņĻ¤óu‚ħ‚òʼnÞðÖîí¿ĜŜĀl˜ğĿţ½ĚœĦ¯iĒµĒÕ¦ĿğţŃľöìśzûĽľėã¢İĨuПĈêÏłĘĀŋÙņħÓŗò´­ùšħòij“ñœowĽāÜĥĐÏā½ĸĈđ®Ńšô{‘řăğğôĶŇñeíp‡ģĭą—«°')-100;\r\ny='No man can be judged a criminal until he is found guilty; nor can society take from him the public protection until it has been proved that he has violated the conditions on which it was granted. What right, then, but that of power, can authorize the punishment of a citizen so long as there remains any doubt of his guilt?';\r\nassert(isequal(deCipher(x,16067),y));\r\n%%\r\nx=double('ÆõĘĜĜĘĕĔôĖĔĄĔţĻ}½ñćĒ–ģdıĺíŸå籌˜¿sò¼àĹč÷öæą„īÒ®Ã{ıКºŜ»ŽĦ­Ń·ijˆá¥ğţĝÅ¥ÞŇĺ²kï¼·Ŏā½Ņ…uÍĺy¾uĊšjʬċrn¶ċ¼”Ľ|uôĻuÀŸtÆĒġŠčœÕÆĻ©e†ö~ĉŃsĩČÇ¿gĻčłúºœø´Ì…ŗØœĔÂŝ«ŒëąŘ¸ÄºčĎÊāàåŕÇĖÏţÂØz„³iúĚ³ĵ„ŀÿīÏ´µãӄìÓ×´Òŝí|ø—™rĨªòń~á')-100;\r\ny='When one door closes, another opens; but we often look so long and so regretfully upon the closed door that we do not see the one which has opened for us.';\r\nassert(isequal(deCipher(x,16067),y));\r\n%%\r\nx=double('Ŋy”  ”™˜xš˜ˆ˜ß·āŁm‹ňĎĚŸè­¶qģik‰ĐĔŃïĿĮŀŜµ‘{zj‰Ĉ§ŎIJĿ÷­ŒĖĶÿoÌÔĺÕĽ»µ¦†ÅwŘŕĠÄÁÎŇľkyĩ§³ŋļ²Ą¡ ¸Ôݾv·ĈŽ³Ö©ċvg¯ċzÄĴ|rûö¦¸ØÀÏĖęÏŌ‰ØŸı¨ªÔçyĚIJ¿Ļęβ¾÷ėĤł°œðµÊÈĔÏœĒÂōs‰êčĊd߂ğģ£çÛĪęÜŞÈňn„q„n¦ñČ³ç…ŃÿíÌ|¯ØÌÙð΄zÒşòƒùÛà€éxŝšp¡Îŗİ}óf}êuÁĽō“ð{‹kįóxĚŞô¼£ćĴĎeĔŚŀrkēiĄÐ¹ĻĉřöòòæśyûĩĩčŚíŀd¢‘ņĮÉôĔĿ')-100;\r\ny='What is ominous is the ease with which some people go from saying that they don''t like something to saying that the government should forbid it. When you go down that road, don''t expect freedom to survive very long.';\r\nassert(isequal(deCipher(x,16067),y));\r\n%%\r\nx=[{'ī˜Ďė¨ŒŇ³ī˜Ďė¨ŒŇ³ī˜Ďė¨ŒŇ³ī˜Ďė¨ŒŇ³ī˜Ďė¨ŒŇ³ī˜Ďė¨ŒŇ³ī˜Ďė¨ŒŇ³ī˜Ďė¨Ğ'} ...\r\n    {'pţÅÜw'}    {'âñwnš»¾Śâñwnš»¾Śâñwnš»¾Śâñwnš»¾Śâñwnš»¾Śâñwnš»¾Śâñwnš»¾ŚâñwnšĜ'}...\r\n    {'Ł’ĔčÂŘŝ¹Ł’ĔčÂŘŝ¹Ł’ĔčÂŘŝ¹Ł’Ĕņ'}    {' ijµ¬ģy|Ę ijµ¬ģy|Ę ijµ¬ģy|Ę ijµ¬ģy|Ę ijµ¬ģy|Ę ijµ¬ģy|Ę ijµ¬ģy|Ę ijµ¬ģyė'} ...\r\n    {'Ƶijĺ…ïêŽĆµijĺ…ïêŽĆµijń'}    {'‰ĺ¬µĊpeđ‰ĺ¬µĊpeđ‰ĺ¬µĊpeđ‰ĺ¬µĊpeđ‰ĺ¬µĊpeđ‰ĺ¬µĊpeđ‰ĺ¬µz'}  ...\r\n    {'âñwnš»¾Śâñwnš»¾Śâñwnš»¾Śâñwnš»¾Śâñwnš»¾Śâñś'}    {'²ġ‡œ'}    {'oŜÊã솓çoŜÊã솓çoŜÊã솓çoŜÊã솓çoŜÊã솓çoŜÊã솓çoŜÊãìĕ'} ...\r\n    {'üÏřŐ~'}  {'Øë}dśÁ´ŠĂ'}    {'ÿÌŚœ|ĖģwÿÌŚœ|ĖģwÿÌŚœ|Ě'}    {'îÝŋŢmćĒfîÝŋŢmćĒfĀ'}   ...\r\n    {'Ĉ»ĭĴ‹ñäĈ»ĭĴ‹ñäĈ»ĭĴ‹ñäĈ»ĭĴ‹ñäĈ»ĭĴ‹ñäĈ»ĭĴ‹ñäy'}    {'ĿŒĚē¼Ŗţ·ĿŒĚē¼Ŗţn'} ...\r\n    {'Øë}dśÁ´ŠØë}dśÁ´ŠØë}dśÁ´ŠØë}dśÁ´ŠØë}dśÁ´ŠØë}dśÁ´ŠØë}ś'}    {'ßìzsŜ¶ÃŗßìzsŜ¶ÃŗßìzsŜ¶ÃŗßìzsŜ¶ÃŗßìzŘ'} ...\r\n    {'ªę–ĩÓÆIJªę–ĩÓÆIJªę–ĩÓÆIJªę–ĩÓÆIJªę–ĩÓÆIJªÖ'}    {'ņuóúÅē'}    {'ÝîxqŞ´ÁŕÝîxqŞ´ÁŕÝîxqŞ´ÁŕÝîxqŞ´ÁŕÝîxŗ'} ...\r\n    {'dŗÑØ獈ìdŗÑØ獈ìdŗÑØ獈ìdŗÑØ獈ìdŗÑØ獈ìdŗÑØ獈ìdŗÑØ獈ìdŗÑØ獈p'}    {'vŅãÊõŸšþvŅãÊõŸšþvŅãÊõŸšþvŅãÊõŸšþvŅãÊõŸšþvŅãÊõŸšþvŅãÊõŸšþvŅãÊj'}  ...\r\n    {'xŋÝÄû¡”ĀxŋÝÄû¡”ĀxŋÝÄû¡”ĀxŋÝÄû¡”ĀxŋÝÄû¡”ĀxŋÝÄû¡”ĀxŋÝŢ'}    {'ñâńŝrĈčiñâńŝrĈē'}    {'ńwñøÇĭĨÌńwñøÇĭĨÌńwñøÇĭĨÌńwñøÇĭĨÌńwñøÇĭĨÌńwñøÇĭĨÌńwñøÇĭĨÌńwñøÇĭĐ'}];\r\ny='ABCDEFGHIJKLMNOPQRSTUVWXYZ';\r\nfor k=1:26\r\n  assert(isequal(deCipher(double(x{k})-100,19),y(k)));\r\nend\r\n%%\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":145982,"edited_by":145982,"edited_at":"2025-10-23T11:07:00.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2025-10-23T01:21:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-10-22T22:43:16.000Z","updated_at":"2026-06-06T06:03:32.000Z","published_at":"2025-10-23T01:21:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProvided a message with all characters \u0026lt;= 255 (ascii) as an input, decode the padded message (removing the random character pad), XORing input converted to binary vector (8 bits each) with the inputted prime having primitive root of two as the key. The key is the repeated sequence of 2^x modulo prime key input starting from x=0 until the cycle repeats (unpadded zero binary represented vector of the repeated sequence). After XORing, remove the padded front and return the character array as output.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59079,"title":"The Hacker Parole Problem","description":"The hacker parole problem\r\n\r\n100 hackers have been imprisoned, but have been given a way to get parole.\r\nEach of the 100 prisoners has been given a number.  There is also a room with 100 numbered boxes.  Each box contains a number.  Each prisoner goes into the room and has 50 tries to find their number in a box.\r\nIf all 100 prisoners can find their number within 50 tries, then they all get parole.  But, if one prisoner cannot find their number within 50 tries all the hackers go back to prison for another year.\r\nThe hackers meet and devise an algorithm that has better than a 30 percent chance of going free that year.\r\nThe hacker's solution\r\nIt is obvious that having each prisoner randomly open boxes will fail.  Each prisoner has a 0.5 chance of finding their number and so the chance that all 100 are able to do it is 0.5^100.  Essentially giving a 0 probablility.\r\nThe hacker solution is to have each prisoner go into the room and use their number to find a box.  They open the box, and if their number is in it they are done.  If their number is not in it, then they use the number in the box to choose another box.  They continue following the numbers and opening boxes until they find the box with their number on it.\r\nThis solution will free all the prisoners over 30% of the time.  This is because the random numbers in boxes form loops.  For example if we have five boxes and five number we might see this set of numbers stored in boxes.\r\n\r\nThe hacker holding number 3 would open box 3 and find a 4.  Then the hacker would open box 4 and find a 1.  Then the hacker would open box 1 and find a 3. \r\n\r\nThis solution works because numbers stored this way always form at least one loop.  In this case we have the following loops:\r\n\r\n3 -\u003e 4 -\u003e 1 -\u003e 3\r\n5 -\u003e 2 -\u003e 5\r\n\r\nThe hackers know that they will get their freedom if the longest loop among the 100 boxes is 50 boxes or shorter.  This happens 30% of the time, thus they get their freedom 30% of the time.\r\nTesting the solution\r\nWe want to test the hacker's algorithm by running 10,000 trials and seeing how often the hackers won their freedom.  Math says that the number should be greater than or equal to 3000 times in 10,000 trials.\r\nYour assignment is to write a function named runTrial() that takes a vector of boxes in the room and runs a trial of the hacker's algorithm. It returns whether the hackers found the number after looking at only half the boxes. The boxes are a vector that contains randomized numbers from 1:numBoxes.\r\nThe testbench will run your trial 10000 times and capture the number of times the hackers won their freedom. That number should be above 3000.\r\nThe function looks like this:\r\nfunction foundAll = runTrial(boxes)\r\n        %%  Insert your code here. I solved this problem in 11 lines inside the function\r\nend","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1078.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 539.3px; transform-origin: 408px 539.3px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10px; text-align: left; transform-origin: 384px 10px; white-space-collapse: preserve; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe hacker parole problem\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e100 hackers have been imprisoned, but have been given a way to get parole.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach of the 100 prisoners has been given a number.  There is also a room with 100 numbered boxes.  Each box contains a number.  Each prisoner goes into the room and has 50 tries to find their number in a box.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf all 100 prisoners can find their number within 50 tries, then they all get parole.  But, if one prisoner cannot find their number within 50 tries all the hackers go back to prison for another year.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe hackers meet and devise an algorithm that has better than a 30 percent chance of going free that year.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 20px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 20px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10px; text-align: left; transform-origin: 384px 10px; white-space-collapse: preserve; margin-left: 4px; margin-top: 20px; margin-bottom: 5px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe hacker's solution\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIt is obvious that having each prisoner randomly open boxes will fail.  Each prisoner has a 0.5 chance of finding their number and so the chance that all 100 are able to do it is 0.5^100.  Essentially giving a 0 probablility.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe hacker solution is to have each prisoner go into the room and use their number to find a box.  They open the box, and if their number is in it they are done.  If their number is not in it, then they use the number in the box to choose another box.  They continue following the numbers and opening boxes until they find the box with their number on it.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis solution will free all the prisoners over 30% of the time.  This is because the random numbers in boxes form loops.  For example if we have five boxes and five number we might see this set of numbers stored in boxes.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 22.3px; text-align: left; transform-origin: 384px 22.3px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"114\" height=\"44.5\" style=\"width: 114px; height: 44.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe hacker holding number 3 would open box 3 and find a 4.  Then the hacker would open box 4 and find a 1.  Then the hacker would open box 1 and find a 3. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis solution works because numbers stored this way always form at least one loop.  In this case we have the following loops:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3 -\u0026gt; 4 -\u0026gt; 1 -\u0026gt; 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e5 -\u0026gt; 2 -\u0026gt; 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe hackers know that they will get their freedom if the longest loop among the 100 boxes is 50 boxes or shorter.  This happens 30% of the time, thus they get their freedom 30% of the time.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 20px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 20px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10px; text-align: left; transform-origin: 384px 10px; white-space-collapse: preserve; margin-left: 4px; margin-top: 20px; margin-bottom: 5px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTesting the solution\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe want to test the hacker's algorithm by running 10,000 trials and seeing how often the hackers won their freedom.  Math says that the number should be greater than or equal to 3000 times in 10,000 trials.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour assignment is to write a function named \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003erunTrial()\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that takes a vector of boxes in the room and runs a trial of the hacker's algorithm. It returns whether the hackers found the number after looking at only half the boxes. The boxes are a vector that contains randomized numbers from 1:numBoxes.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe testbench will run your trial 10000 times and capture the number of times the hackers won their freedom. That number should be above 3000.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe function looks like this:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 54px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 404px 27px; transform-origin: 404px 27px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 9px; text-wrap-mode: nowrap; transform-origin: 404px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003efunction \u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003efoundAll = runTrial(boxes)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 9px; text-wrap-mode: nowrap; transform-origin: 404px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 100, 0); border-block-start-color: rgb(0, 100, 0); border-bottom-color: rgb(0, 100, 0); border-inline-end-color: rgb(0, 100, 0); border-inline-start-color: rgb(0, 100, 0); border-left-color: rgb(0, 100, 0); border-right-color: rgb(0, 100, 0); border-top-color: rgb(0, 100, 0); caret-color: rgb(0, 100, 0); color: rgb(0, 100, 0); column-rule-color: rgb(0, 100, 0); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(0, 100, 0); text-decoration-color: rgb(0, 100, 0); text-emphasis-color: rgb(0, 100, 0); \"\u003e        %%  Insert your code here. I solved this problem in 11 lines inside the function\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 9px; text-wrap-mode: nowrap; transform-origin: 404px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); \"\u003eend\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function foundAll = runTrial(boxes)\r\n  foundAll = true; % Set true only if the hackers find all the numbers\r\n                   % a number of trials equal to 1/2 the length of `boxes`.\r\nend","test_suite":"%% Test code\r\nnumTrials = 10000;\r\nnumBoxes = 100;\r\ntests = false([1,numTrials]);\r\nfor ii=1:numTrials\r\n   boxes = randperm(numBoxes);\r\n   tests(ii) = runTrial(boxes);\r\nend\r\ndisp([\"Number of times the hackers went free: \" nnz(tests)])\r\nproved_algorithm = nnz(tests) \u003e= numTrials * .30;\r\nassessVariableEqual('proved_algorithm', true);\r\ntoo_many_true = nnz(tests) \u003e= numTrials * .35;\r\nassessVariableEqual('too_many_true', false);","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2842368,"edited_by":2842368,"edited_at":"2026-01-23T15:14:01.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2023-10-08T19:02:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-10-08T18:58:11.000Z","updated_at":"2026-06-04T21:37:00.000Z","published_at":"2023-10-08T19:02:17.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe hacker parole problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e100 hackers have been imprisoned, but have been given a way to get parole.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach of the 100 prisoners has been given a number.  There is also a room with 100 numbered boxes.  Each box contains a number.  Each prisoner goes into the room and has 50 tries to find their number in a box.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf all 100 prisoners can find their number within 50 tries, then they all get parole.  But, if one prisoner cannot find their number within 50 tries all the hackers go back to prison for another year.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe hackers meet and devise an algorithm that has better than a 30 percent chance of going free that year.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe hacker's solution\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt is obvious that having each prisoner randomly open boxes will fail.  Each prisoner has a 0.5 chance of finding their number and so the chance that all 100 are able to do it is 0.5^100.  Essentially giving a 0 probablility.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe hacker solution is to have each prisoner go into the room and use their number to find a box.  They open the box, and if their number is in it they are done.  If their number is not in it, then they use the number in the box to choose another box.  They continue following the numbers and opening boxes until they find the box with their number on it.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis solution will free all the prisoners over 30% of the time.  This is because the random numbers in boxes form loops.  For example if we have five boxes and five number we might see this set of numbers stored in boxes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\left(\\\\begin{array}{cccccc} 1 \u0026amp; 2 \u0026amp; 3 \u0026amp; 4 \u0026amp; 5\\\\\\\\ 3 \u0026amp; 5 \u0026amp; 4 \u0026amp; 1 \u0026amp; 2 \\\\end{array}\\\\right)'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe hacker holding number 3 would open box 3 and find a 4.  Then the hacker would open box 4 and find a 1.  Then the hacker would open box 1 and find a 3. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis solution works because numbers stored this way always form at least one loop.  In this case we have the following loops:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3 -\u0026gt; 4 -\u0026gt; 1 -\u0026gt; 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e5 -\u0026gt; 2 -\u0026gt; 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe hackers know that they will get their freedom if the longest loop among the 100 boxes is 50 boxes or shorter.  This happens 30% of the time, thus they get their freedom 30% of the time.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTesting the solution\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe want to test the hacker's algorithm by running 10,000 trials and seeing how often the hackers won their freedom.  Math says that the number should be greater than or equal to 3000 times in 10,000 trials.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour assignment is to write a function named \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003erunTrial()\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that takes a vector of boxes in the room and runs a trial of the hacker's algorithm. It returns whether the hackers found the number after looking at only half the boxes. The boxes are a vector that contains randomized numbers from 1:numBoxes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe testbench will run your trial 10000 times and capture the number of times the hackers won their freedom. That number should be above 3000.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function looks like this:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[function foundAll = runTrial(boxes)\\n        %%  Insert your code here. I solved this problem in 11 lines inside the function\\nend]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44838,"title":"Pose from bearing angles in 2D","description":"A robot moving on the plane has a sensor that measures the bearing angle to two mapped landmarks, that is, the world frame coordinates of the landmarks are known and represented by position vectors |P1| and |P2| .  The bearing angles to the landmarks, with respect to the x-axis of the robot's coordinate frame are |th1| and |th2| respectively.  The robot's forward direction is parallel to its x-axis and its heading angle, with respect to magnetic north is |thb| .\r\n\r\nDetermine the pose of the robot expressed as a homogeneous transformation matrix with respect to the world coordinate frame.  In surveying this is known as a resection problem.","description_html":"\u003cp\u003eA robot moving on the plane has a sensor that measures the bearing angle to two mapped landmarks, that is, the world frame coordinates of the landmarks are known and represented by position vectors \u003ctt\u003eP1\u003c/tt\u003e and \u003ctt\u003eP2\u003c/tt\u003e .  The bearing angles to the landmarks, with respect to the x-axis of the robot's coordinate frame are \u003ctt\u003eth1\u003c/tt\u003e and \u003ctt\u003eth2\u003c/tt\u003e respectively.  The robot's forward direction is parallel to its x-axis and its heading angle, with respect to magnetic north is \u003ctt\u003ethb\u003c/tt\u003e .\u003c/p\u003e\u003cp\u003eDetermine the pose of the robot expressed as a homogeneous transformation matrix with respect to the world coordinate frame.  In surveying this is known as a resection problem.\u003c/p\u003e","function_template":"function T = user_function(P1, P2, th1, th2, thb)\r\n% Input:  P1 a 2x1 vector representing the coordinate of a point\r\n%         P2 a 2x1 vector representing the coordinate of a point\r\n%         th1 bearing, a scalar angle\r\n%         th2 bearing, a scalar angle\r\n%         thb heading, a scalar angle\r\n% Output: T a 3x3 homogeneous transformation matrix\r\n  T = ;\r\nend","test_suite":"%\r\nP1 = [10 20]';\r\nP2 = [20 20]';\r\nP = rand(2,1)*5 + [5 5]';\r\nthb = rand*0.2;\r\nx = P1 - P;\r\nth1 = atan2(x(2), x(1)) - thb;\r\nx = P2 - P;\r\nth2 = atan2(x(2), x(1)) - thb;\r\n\r\nT = user_function(P1, P2, th1, th2, thb);\r\n\r\n%% test size and complexity\r\nassert(all(size(T)==3), 'The matrix must be 3x3');\r\nassert(isreal(T), 'The matrix must be real, not complex');\r\n\r\n%% bottom row\r\nassert(isequal(T(3,:), [0 0 1]), 'The bottom row of the homogeneous transformation matrix is not correct')\r\n\r\n%% x coordinate\r\nassert(abs(T(1,3)-P(1))\u003c1e-4, 'The representation of the x-coordinate is not correct')\r\n\r\n%% y coordinate\r\nassert(abs(T(2,3)-P(2))\u003c1e-4, 'The representation of the y-coordinate is not correct')\r\n\r\n%% valid rotation matrix\r\nR = T(1:2,1:2);\r\nassert( abs(det(R)-1) \u003c 1e-4, 'The determinant of the rotation submatrix is not correct')\r\n\r\n%% correct rotation matrix\r\nR = T(1:2,1:2);\r\nassert( abs(atan2(R(2,1), R(1,1)) - thb) \u003c 1e-4, 'The rotation matrix is not correct, check your calculation of the heading SSW and whether you are using radians or degrees')\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":13332,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":23,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":77,"created_at":"2019-01-21T00:32:56.000Z","updated_at":"2026-06-26T14:08:35.000Z","published_at":"2019-01-21T00:37:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA robot moving on the plane has a sensor that measures the bearing angle to two mapped landmarks, that is, the world frame coordinates of the landmarks are known and represented by position vectors\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e . The bearing angles to the landmarks, with respect to the x-axis of the robot's coordinate frame are\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eth1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eth2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e respectively. The robot's forward direction is parallel to its x-axis and its heading angle, with respect to magnetic north is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the pose of the robot expressed as a homogeneous transformation matrix with respect to the world coordinate frame. In surveying this is known as a resection problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1740,"title":"Find number patterns in rows of a matrix...","description":"So I think this may be a hard one, may be it was only hard for me!  So here is what it is, I will give a matrix, with some number of rows by 5 columns, to make it simpler I will not repeat any number in a *single row*, so all numbers in a *single rows* are unique. So you need to find up to 2, 3 or 4 numbers that are found in a *single row* that repeat in *other rows* and the amount of times they repeat in a given matrix. To make it a little better, you only need to display the rows/numbers that repeat at lease twice or more. Examples are the best way to show what to do:\r\n  \r\n          %p is the given matrix\r\n          p = [1 2 3 4 5;\r\n               2 3 4 5 1;\r\n               3 4 6 7 8;\r\n               1 2 4 3 5;\r\n               4 6 3 2 1];\r\n          %v is the amount of elements per row that are being checked to see if they repeat in another row\r\n          v = 4;\r\n        %Output:\r\n        out =\r\n        \r\n             1     2     3     4     4\r\n             1     2     3     5     3\r\n             1     2     4     5     3\r\n             1     3     4     5     3\r\n             2     3     4     5     3\r\n      %So the first to the fourth column are the four number that were found to repeat in rows of matrix p (any and all combination that can appear in the rows of the matrix p). The fifth column is the amount of times the that particular set of matrix out(?,1:4) appear in matrix p. for for row one in matrix out, 1,2,3 and 4 in any combination appear 4 time in the rows of matrix p.\r\n      \r\n      So more examples...\r\n      \r\n      p = [1 2 3 4 9;\r\n           2 3 1 4 8]\r\n      v = 4;\r\n      \r\n      out =\r\n           1     2     3     4     2\r\n    %so any combination of 1,2,3 and 4 appear 2 times in matrix p\r\n    \r\n    and another:\r\n    \r\n    p = [1 2 3 4 9;\r\n         2 3 1 4 8;\r\n         3 4 2 7 1]\r\n    v = 3;\r\n      \r\n    out =\r\n         1     2     3     3\r\n         1     2     4     3\r\n         1     3     4     3\r\n         2     3     4     3\r\n    %so this uses any combo of 3 values, so in this case out(?,1:3) are the number combos that can be found in matrix p, and the out(?,4) is the amount of times that those combos are found\r\n    \r\n    last example:\r\n    \r\n    p = [1 2 3 4 9;\r\n         2 3 1 4 8]\r\n    v = 2;\r\n    \r\n    out =\r\n         1     2     2\r\n         1     3     2\r\n         1     4     2\r\n         2     3     2\r\n         2     4     2\r\n         3     4     2\r\n    %so in this case only combos of out(?,1:2) are found and out(?,3) is the amounts of times that combo of out(?,1:2) is found in matrix p. so row four of matrix out (so out(4,:)...) shows that the combo of 2 and 3 are found 2 times in matrix p.\r\n\r\nNOTE: only display any row number combos that occur at least 2 times or more!\r\n\r\nI hope I gave enough instructions and explanation, if not please let me know and I will add to it! Thanks and good luck!","description_html":"\u003cp\u003eSo I think this may be a hard one, may be it was only hard for me!  So here is what it is, I will give a matrix, with some number of rows by 5 columns, to make it simpler I will not repeat any number in a \u003cb\u003esingle row\u003c/b\u003e, so all numbers in a \u003cb\u003esingle rows\u003c/b\u003e are unique. So you need to find up to 2, 3 or 4 numbers that are found in a \u003cb\u003esingle row\u003c/b\u003e that repeat in \u003cb\u003eother rows\u003c/b\u003e and the amount of times they repeat in a given matrix. To make it a little better, you only need to display the rows/numbers that repeat at lease twice or more. Examples are the best way to show what to do:\u003c/p\u003e\u003cpre\u003e          %p is the given matrix\r\n          p = [1 2 3 4 5;\r\n               2 3 4 5 1;\r\n               3 4 6 7 8;\r\n               1 2 4 3 5;\r\n               4 6 3 2 1];\r\n          %v is the amount of elements per row that are being checked to see if they repeat in another row\r\n          v = 4;\r\n        %Output:\r\n        out =\u003c/pre\u003e\u003cpre\u003e             1     2     3     4     4\r\n             1     2     3     5     3\r\n             1     2     4     5     3\r\n             1     3     4     5     3\r\n             2     3     4     5     3\r\n      %So the first to the fourth column are the four number that were found to repeat in rows of matrix p (any and all combination that can appear in the rows of the matrix p). The fifth column is the amount of times the that particular set of matrix out(?,1:4) appear in matrix p. for for row one in matrix out, 1,2,3 and 4 in any combination appear 4 time in the rows of matrix p.\u003c/pre\u003e\u003cpre\u003e      So more examples...\u003c/pre\u003e\u003cpre\u003e      p = [1 2 3 4 9;\r\n           2 3 1 4 8]\r\n      v = 4;\u003c/pre\u003e\u003cpre\u003e      out =\r\n           1     2     3     4     2\r\n    %so any combination of 1,2,3 and 4 appear 2 times in matrix p\u003c/pre\u003e\u003cpre\u003e    and another:\u003c/pre\u003e\u003cpre\u003e    p = [1 2 3 4 9;\r\n         2 3 1 4 8;\r\n         3 4 2 7 1]\r\n    v = 3;\u003c/pre\u003e\u003cpre\u003e    out =\r\n         1     2     3     3\r\n         1     2     4     3\r\n         1     3     4     3\r\n         2     3     4     3\r\n    %so this uses any combo of 3 values, so in this case out(?,1:3) are the number combos that can be found in matrix p, and the out(?,4) is the amount of times that those combos are found\u003c/pre\u003e\u003cpre\u003e    last example:\u003c/pre\u003e\u003cpre\u003e    p = [1 2 3 4 9;\r\n         2 3 1 4 8]\r\n    v = 2;\u003c/pre\u003e\u003cpre\u003e    out =\r\n         1     2     2\r\n         1     3     2\r\n         1     4     2\r\n         2     3     2\r\n         2     4     2\r\n         3     4     2\r\n    %so in this case only combos of out(?,1:2) are found and out(?,3) is the amounts of times that combo of out(?,1:2) is found in matrix p. so row four of matrix out (so out(4,:)...) shows that the combo of 2 and 3 are found 2 times in matrix p.\u003c/pre\u003e\u003cp\u003eNOTE: only display any row number combos that occur at least 2 times or more!\u003c/p\u003e\u003cp\u003eI hope I gave enough instructions and explanation, if not please let me know and I will add to it! Thanks and good luck!\u003c/p\u003e","function_template":"function out = findRowPattern(p,v)\r\n  out = [p v];\r\nend","test_suite":"%%\r\np = [1 2 3 4 5;\r\n     2 3 4 5 1;\r\n     3 4 6 7 8;\r\n     1 2 4 3 5;\r\n     4 6 3 2 1];\r\nv = 4;\r\nout = [1 2 3 4 4;\r\n       1 2 3 5 3;\r\n       1 2 4 5 3;\r\n       1 3 4 5 3;\r\n       2 3 4 5 3]\r\nassert(isequal(findRowPattern(p,v),out))\r\n%%\r\np = [1 2 3 4 9;\r\n     2 3 1 4 8]\r\nv = 4;\r\nout = [1 2 3 4 2]\r\nassert(isequal(findRowPattern(p,v),out))\r\n%%\r\np = [1 2 3 4 9;\r\n     2 3 1 4 8;\r\n     3 4 2 7 1]\r\nv = 3;\r\nout = [1 2 3 3;\r\n       1 2 4 3;\r\n       1 3 4 3;\r\n       2 3 4 3]\r\nassert(isequal(findRowPattern(p,v),out))\r\n%%\r\np = [1 2 3 4 9;\r\n     2 3 1 4 8]\r\nv = 2;\r\nout = [1 2 2;\r\n       1 3 2;\r\n       1 4 2;\r\n       2 3 2;\r\n       2 4 2;\r\n       3 4 2]\r\nassert(isequal(findRowPattern(p,v),out))\r\n%%\r\np = [15 23 68 49 88;\r\n     69 58 78 21 35;\r\n     10 23 21 35 88;\r\n     99 58 63 24 10;\r\n     64 28 14 33 58;\r\n     85 69 21 45 55;\r\n     99 24 76 49 33;\r\n     89 69 33 98 21;\r\n     99 10 21 55 58;\r\n     35 68 69 44 21;\r\n     21 69 35 46 33];\r\nv = 3;\r\nout = [21 35 69 3;\r\n     10 58 99 2;\r\n     21 33 69 2]\r\nassert(isequal(findRowPattern(p,v),out))\r\n%%\r\np = [15 23 68 49 88;\r\n     69 58 78 21 35;\r\n     10 23 21 35 88;\r\n     99 58 63 24 10;\r\n     64 28 14 33 58;\r\n     85 69 21 45 55;\r\n     99 24 76 49 33;\r\n     89 69 33 98 21;\r\n     99 10 21 55 58;\r\n     35 68 69 44 21;\r\n     21 69 35 46 33];\r\nv = 2;\r\n\r\nout = [21    69     5;\r\n       21    35     4;\r\n       35    69     3;\r\n       10    21     2;\r\n       10    58     2;\r\n       10    99     2;\r\n       21    33     2;\r\n       21    55     2;\r\n       21    58     2;\r\n       23    88     2;\r\n       24    99     2;\r\n       33    69     2;\r\n       58    99     2]\r\nassert(isequal(findRowPattern(p,v),out))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":15013,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2013-07-23T17:11:41.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-07-23T16:51:20.000Z","updated_at":"2026-05-27T04:01:28.000Z","published_at":"2013-07-23T17:11:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo I think this may be a hard one, may be it was only hard for me! So here is what it is, I will give a matrix, with some number of rows by 5 columns, to make it simpler I will not repeat any number in a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esingle row\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, so all numbers in a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esingle rows\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are unique. So you need to find up to 2, 3 or 4 numbers that are found in a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esingle row\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that repeat in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eother rows\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and the amount of times they repeat in a given matrix. To make it a little better, you only need to display the rows/numbers that repeat at lease twice or more. Examples are the best way to show what to do:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[          %p is the given matrix\\n          p = [1 2 3 4 5;\\n               2 3 4 5 1;\\n               3 4 6 7 8;\\n               1 2 4 3 5;\\n               4 6 3 2 1];\\n          %v is the amount of elements per row that are being checked to see if they repeat in another row\\n          v = 4;\\n        %Output:\\n        out =\\n\\n             1     2     3     4     4\\n             1     2     3     5     3\\n             1     2     4     5     3\\n             1     3     4     5     3\\n             2     3     4     5     3\\n      %So the first to the fourth column are the four number that were found to repeat in rows of matrix p (any and all combination that can appear in the rows of the matrix p). The fifth column is the amount of times the that particular set of matrix out(?,1:4) appear in matrix p. for for row one in matrix out, 1,2,3 and 4 in any combination appear 4 time in the rows of matrix p.\\n\\n      So more examples...\\n\\n      p = [1 2 3 4 9;\\n           2 3 1 4 8]\\n      v = 4;\\n\\n      out =\\n           1     2     3     4     2\\n    %so any combination of 1,2,3 and 4 appear 2 times in matrix p\\n\\n    and another:\\n\\n    p = [1 2 3 4 9;\\n         2 3 1 4 8;\\n         3 4 2 7 1]\\n    v = 3;\\n\\n    out =\\n         1     2     3     3\\n         1     2     4     3\\n         1     3     4     3\\n         2     3     4     3\\n    %so this uses any combo of 3 values, so in this case out(?,1:3) are the number combos that can be found in matrix p, and the out(?,4) is the amount of times that those combos are found\\n\\n    last example:\\n\\n    p = [1 2 3 4 9;\\n         2 3 1 4 8]\\n    v = 2;\\n\\n    out =\\n         1     2     2\\n         1     3     2\\n         1     4     2\\n         2     3     2\\n         2     4     2\\n         3     4     2\\n    %so in this case only combos of out(?,1:2) are found and out(?,3) is the amounts of times that combo of out(?,1:2) is found in matrix p. so row four of matrix out (so out(4,:)...) shows that the combo of 2 and 3 are found 2 times in matrix p.]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNOTE: only display any row number combos that occur at least 2 times or more!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI hope I gave enough instructions and explanation, if not please let me know and I will add to it! Thanks and good luck!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":57765,"title":"Determine whether a hydrograph is a unit hydrograph","description":"A hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate  (or flow or discharge) as a function of time  resulting from a given excess rainfall (expressed as a depth ) for a storm of a specified duration. A unit hydrograph results from unit excess rainfall (e.g.,  = 1 cm). \r\nWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time  in minutes, the flow rate  in , and the catchment area  in . Allow for a tolerance of 0.01 cm in the excess rainfall depth.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 333.467px 8px; transform-origin: 333.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35px 8px; transform-origin: 35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (or flow or discharge) as a function of time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.267px 8px; transform-origin: 188.267px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e resulting from a given excess rainfall (expressed as a depth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.8333px 8px; transform-origin: 82.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) for a storm of a specified duration. A \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.575px 8px; transform-origin: 50.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eunit hydrograph \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 115.9px 8px; transform-origin: 115.9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eresults from unit excess rainfall (e.g., \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.3583px 8px; transform-origin: 29.3583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 1 cm). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 330.108px 8px; transform-origin: 330.108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.3917px 8px; transform-origin: 49.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in minutes, the flow rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m^3/s\" style=\"width: 33px; height: 19.5px;\" width=\"33\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79.3417px 8px; transform-origin: 79.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the catchment area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m^2\" style=\"width: 19.5px; height: 19px;\" width=\"19.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.642px 8px; transform-origin: 188.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Allow for a tolerance of 0.01 cm in the excess rainfall depth.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isUnitHydrograph(t,Q,A)\r\n  tf = isequal(Q*t/A,1);\r\nend","test_suite":"%%\r\nA = 2250000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2250000;                                                        %  Area (m2)\r\nt = 0:40:520;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2520000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 753601;                                                         %  Area (m2)\r\nt = linspace(0,180);                                                %  Time (min)\r\nQ = 0.1*t.*exp(-0.000398*t.^2);                                     %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 735601;                                                         %  Area (m2)\r\nt = linspace(0,180);                                                %  Time (min)\r\nQ = 0.1*t.*exp(-0.000398*t.^2);                                     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2100000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.4 3.2 1.5 1.2 1.1 1.0 0.66 0.49 0.36 0.28 0.25 0.17 0];    %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2100000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.4 2.3 1.5 1.2 1.1 1.0 0.66 0.49 0.36 0.28 0.25 0.17 0];    %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-11T12:56:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-11T01:14:20.000Z","updated_at":"2026-07-18T09:16:18.000Z","published_at":"2023-03-11T01:14:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (or flow or discharge) as a function of time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e resulting from a given excess rainfall (expressed as a depth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) for a storm of a specified duration. A \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eunit hydrograph \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eresults from unit excess rainfall (e.g., \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 1 cm). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in minutes, the flow rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m^3/s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m^3/s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the catchment area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Allow for a tolerance of 0.01 cm in the excess rainfall depth.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58548,"title":"Find the altitudes of a triangle","description":"Write a function that takes the x- and y-coordinates of three points describing the vertices of a triangle and returns the coordinates of the endpoints of the altitudes of the triangle as well as the coordinates of the orthocenter. The coordinates of the endpoints should be in the order of the corresponding vertices, and the function should work when one of the angles is obtuse.\r\n\r\n\r\n\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 516.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 258.35px; transform-origin: 407px 258.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 365.1px 8px; transform-origin: 365.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the x- and y-coordinates of three points describing the vertices of a triangle and returns the coordinates of the endpoints of the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Altitude_(triangle)\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ealtitudes of the triangle\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.85px 8px; transform-origin: 103.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as well as the coordinates of the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/Orthocenter.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eorthocenter\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.7833px 8px; transform-origin: 63.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The coordinates of the endpoints should be in the order of the corresponding vertices, and the function should work when one of the angles is obtuse.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan 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\" data-image-state=\"image-loaded\" width=\"438\" height=\"328\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [xa,ya,xoc,yoc] = altitudes(x,y)\r\n%  xa, ya = coordinates of the endpoints of the altitudes, in the order of the vertices provided to the function\r\n%  xoc, yoc = coordinates of the orthocenter\r\n   xa = x/2;\r\n   ya = y/2;\r\n   xoc = mean(x);\r\n   yoc = mean(y);\r\nend","test_suite":"%% \r\nx = [-1 0 1];\r\ny = [0 4 0];\r\n[xa,ya,xoc,yoc] = altitudes(x,y);\r\nxa_correct = [0.882352941176471 0 -0.882352941176471];\r\nya_correct = [0.470588235294118 0 0.470588235294118];\r\nxoc_correct = 0;\r\nyoc_correct = 0.25;\r\nassert(all(abs(xa-xa_correct)\u003c1e-10))\r\nassert(all(abs(ya-ya_correct)\u003c1e-10))\r\nassert(abs(xoc-xoc_correct)\u003c1e-10)\r\nassert(abs(yoc-yoc_correct)\u003c1e-10)\r\n\r\n%% \r\nx = [1 2 3];\r\ny = [4 6 5];\r\n[xa,ya,xoc,yoc] = altitudes(x,y);\r\nxa_correct = [2.5 2.6 1.8];\r\nya_correct = [5.5 4.8 5.6];\r\nxoc_correct = 2.333333333333333;\r\nyoc_correct = 5.333333333333333;\r\nassert(all(abs(xa-xa_correct)\u003c1e-10))\r\nassert(all(abs(ya-ya_correct)\u003c1e-10))\r\nassert(abs(xoc-xoc_correct)\u003c1e-10)\r\nassert(abs(yoc-yoc_correct)\u003c1e-10)\r\n\r\n%% \r\nx = [-1 2 3];\r\ny = [4 -2 5];\r\n[xa,ya,xoc,yoc] = altitudes(x,y);\r\nxa_correct = [2.78 0.411764705882353 -0.6];\r\nya_correct = [3.46 4.352941176470588 3.2];\r\nxoc_correct = 0.555555555555555;\r\nyoc_correct = 3.777777777777777;\r\nassert(all(abs(xa-xa_correct)\u003c1e-10))\r\nassert(all(abs(ya-ya_correct)\u003c1e-10))\r\nassert(abs(xoc-xoc_correct)\u003c1e-10)\r\nassert(abs(yoc-yoc_correct)\u003c1e-10)\r\n\r\n%% \r\nx = [0 0 1];\r\ny = [0 1 0];\r\n[xa,ya,xoc,yoc] = altitudes(x,y);\r\nxa_correct = [0.5 0 0];\r\nya_correct = [0.5 0 0];\r\nxoc_correct = 0;\r\nyoc_correct = 0;\r\nassert(all(abs(xa-xa_correct)\u003c1e-10))\r\nassert(all(abs(ya-ya_correct)\u003c1e-10))\r\nassert(abs(xoc-xoc_correct)\u003c1e-10)\r\nassert(abs(yoc-yoc_correct)\u003c1e-10)\r\n\r\n%% \r\nx = [0 2 4];\r\ny = [0 1 0];\r\n[xa,ya,xoc,yoc] = altitudes(x,y);\r\nxa_correct = [0.8 2 3.2];\r\nya_correct = [1.6 0 1.6];\r\nxoc_correct = 2;\r\nyoc_correct = 4;\r\nassert(all(abs(xa-xa_correct)\u003c1e-10))\r\nassert(all(abs(ya-ya_correct)\u003c1e-10))\r\nassert(abs(xoc-xoc_correct)\u003c1e-10)\r\nassert(abs(yoc-yoc_correct)\u003c1e-10)\r\n\r\n%% \r\nx = [3 3 5];\r\ny = [1 3 2];\r\n[xa,ya,xoc,yoc] = altitudes(x,y);\r\nxa_correct = [3.8 3.8 3];\r\nya_correct = [2.6 1.4 2];\r\nxoc_correct = 3.5;\r\nyoc_correct = 2;\r\nassert(all(abs(xa-xa_correct)\u003c1e-10))\r\nassert(all(abs(ya-ya_correct)\u003c1e-10))\r\nassert(abs(xoc-xoc_correct)\u003c1e-10)\r\nassert(abs(yoc-yoc_correct)\u003c1e-10)\r\n\r\n%% \r\na = 10*rand();\r\nx = [-1 0 1];\r\ny = [0 a 0];\r\n[~,~,~,yoc] = altitudes(x,y);\r\nyoc_correct = 1/a;\r\nassert(abs(yoc-yoc_correct)\u003c1e-10)\r\n\r\n%%\r\nfiletext = fileread('altitudes.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'classdef'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-07-16T02:31:52.000Z","updated_at":"2026-07-18T13:18:58.000Z","published_at":"2023-07-16T02:31:52.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes the 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/do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balanced primes","description":"A balanced prime of order  is one that equals the average of the  primes before it and the  primes after it. For example, 79 is the first balanced prime of order 2; it is the average of 71, 73, 83, and 89. \r\nCody Problem 47798 asks us to determine whether a number is a balanced prime of order one. For order one, balanced primes are equal to mean-of-2 primes. \r\nWrite a function that returns the th prime number that is the average of the  primes before it and the  primes after it. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 123px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 61.5px; transform-origin: 408px 61.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ebalanced prime\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is one that equals the average of the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e primes before it and the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e primes after it. For example, 79 is the first balanced prime of order 2; it is the average of 71, 73, 83, and 89. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/47798\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 47798\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asks us to determine whether a number is a balanced prime of order one. For order one, balanced primes are equal to \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60955\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003emean-of-2 primes\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth prime number that is the average of the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e primes before it and the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e primes after it. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = balancedPrimes(n,k)\r\n  p = primes(n);\r\n  y = mean(p(n-k:n+k));\r\nend","test_suite":"%%\r\nn = 2;\r\nk = 1; \r\ny = balancedPrimes(n,k);\r\ny_correct = 53;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 29;\r\nk = 1; \r\ny = balancedPrimes(n,k);\r\ny_correct = 2963;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 84;\r\nk = 1; \r\ny = balancedPrimes(n,k);\r\ny_correct = 13043;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1;\r\nk = 2; \r\ny = balancedPrimes(n,k);\r\ny_correct = 79;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 10;\r\nk = 2; \r\ny = balancedPrimes(n,k);\r\ny_correct = 1811;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 738;\r\nk = 2; \r\ny = balancedPrimes(n,k);\r\ny_correct = 263503;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 541;\r\nk = 3; \r\ny = balancedPrimes(n,k);\r\ny_correct = 290923;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 998;\r\nk = 4; \r\ny = balancedPrimes(n,k);\r\ny_correct = 1289303;\r\nassert(isequal(y,y_correct))\r\n\r\n%% \r\nn = 5421;\r\nk = 1:5;\r\ny = arrayfun(@(m) balancedPrimes(n,m),k);\r\ny_correct = [1992481 3043891 4567817 9315289 11783729];\r\nassert(isequal(y,y_correct))\r\n\r\n%% \r\nn = [278 3410 9665 12145 81883];\r\ny = NaN(5,5);\r\nfor k = 1:5\r\n    y(k,:) = arrayfun(@(m) balancedPrimes(m,k),n);\r\nend\r\ny_correct = [ 58067 1158569  3937567  5115653  44897621;\r\n              83843 1754713  6032437  7848769  69707753;\r\n             123401 2691163  9087901 11751227 107355631;\r\n             287681 5476697 18078337 23354423 205844297;\r\n             327251 6772049 23817359 30996871 275690651];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 145;\r\nk1 = 1;\r\nk2 = 2;\r\nyy = balancedPrimes(balancedPrimes(n,k1),k2);\r\nyy_correct = 17110147;\r\nassert(isequal(yy,yy_correct))\r\n\r\n%%\r\nn = 314;\r\nk1 = 3;\r\nk2 = 4;\r\nyy = balancedPrimes(balancedPrimes(n,k1),k2);\r\nyy_correct = 398106671;\r\nassert(isequal(yy,yy_correct))\r\n\r\n%%\r\nfor n = 1:800\r\n    y(1,n) = balancedPrimes(n,1); \r\n    y(2,n) = balancedPrimes(n,2); \r\n    y(3,n) = balancedPrimes(n,3); \r\nend\r\ny12_correct = [18731 25621 28069 30059 31051 44741 76913 97441 103669 106681 118831 128449 135089 182549 202999];\r\ny13_correct = [53 157 173 607 977 1187 2287 3313 4013 6323 17327 23893 26723 29173 30103 41479 46147 53617 53623 61637 62597 62633 63559 63697 75217 80917 83437 84443 85837 105367 109897 113963 123433 127663 140983 143483 149497 149867 152947 159521 169199 182893 187877 193757 208553];\r\ny23_correct = [349 439 4951 15077 23021 31249 42727 46229 46663 51869 54091 54979 56477 57791 58403 58427 61583 63337 64921 80819 90833 103349 116959 138143 165541 169913 170197 170843 172657 174991 179549 182617 209837 215483 236429 237161 243643 245291 249563 266027 270689];\r\nassert(isequal(intersect(y(1,:),y(2,:)),y12_correct))\r\nassert(isequal(intersect(y(1,:),y(3,:)),y13_correct))\r\nassert(isequal(intersect(y(2,:),y(3,:)),y23_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2025-07-09T13:20:39.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-09T13:18:36.000Z","updated_at":"2026-07-08T11:27:37.000Z","published_at":"2025-07-09T13:20:39.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ebalanced prime\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is one that equals the average of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e primes before it and the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e primes after it. For example, 79 is the first balanced prime of order 2; it is the average of 71, 73, 83, and 89. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/47798\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 47798\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asks us to determine whether a number is a balanced prime of order one. For order one, balanced primes are equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60955\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emean-of-2 primes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth prime number that is the average of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e primes before it and the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e primes after it. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51188,"title":"Number of Primitive Roots and Cyclic","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eDetermine the number of primitive roots of for each input number in an array or matrix (m) and whether each number will form a cyclic group. Output should be a corresponding array or matrix of the number of primitive roots and another logical array or matrix.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [num,cyclic] = numPrimitivePrimes(m)\r\n  num=m;\r\n  cyclic=zeros(size(m));\r\nend","test_suite":"%%\r\nm=[824149356327936,619505816445824,902925119282940,6781941268060,737940751495520,781679826661116\r\n   218232263733975,103814782651106,312512845986667,495871665666786,310719817391570,111533124684944\r\n   99642302961614,799061803589637,281589166159224,988482243012287,600407500351151,579329289388906];\r\nnum=[83230601379840,48499811942400,50584603410432,530841600000,87793796136960,58174134681600\r\n     30887903232000,13408979189760,62817473839104,35258302464000,36539825946624,18587454842880\r\n     11324072693760,122711350422528,15430396133376,312152287267008,225445593006080,50190719385600];\r\ncyclic=logical([0   0   0   0   0   0\r\n                0   0   0   0   0   0\r\n                0   0   0   0   1   0]);\r\n[p,c]=numPrimitivePrimes(m);\r\nassert(isequal(p,num))\r\nassert(isequal(c,cyclic))\r\n%%\r\nm=[859709       51839      346013      350111\r\n   667691      378997      488603      636319\r\n   213289      208099       75353      739799\r\n   311323      458921      901013      146917\r\n   516883      790793      179533      487979];\r\nnum=[427280       25918      165440      138528\r\n     255376      126328      244300      192192\r\n     71088       63000       37672      366336\r\n     91520      142080      386064       37440\r\n     171120      395392       59832      243988];\r\ncyclic=logical([1   1   1   1\r\n                1   1   1   1\r\n                1   1   1   1\r\n                1   1   1   1\r\n                1   1   1   1]);\r\n[p,c]=numPrimitivePrimes(m);\r\nassert(isequal(p,num))\r\nassert(isequal(c,cyclic))\r\n%%\r\nm=     [9954        7444        1947        4439        4185        1045        9381        6876        8115        6709\r\n        7077        4168        4175        9959        9978        6523        6054        2269        4481        9829\r\n         806        9074        2930        4366        9111        9918        6390        9791        8307        9369\r\n         434         944        7022        3045        5505        6781        7027        9757        1267        5763\r\n        4912        1814        2398        2466        5964        4285        8610        2896        5133         802\r\n        4466        9466        9595        9609         792        6549        3797        3385        7160        4139\r\n        4868        1009        3055        2229        5767        5888        7122        9965        2482        1809\r\n        1659        3881        1550        3957        8982        7451        5236        7890        5320        9957\r\n        3607        2893        5556        2246        4634        6409        3635        7950        3823        5204\r\n        8808         731        7906        2701        3984        5037        4347        6324        8018        8853];\r\nnum=   [864         960         448        1280         576         192        2688         576        1152        2016\r\n        1152         768        1312        2880        1104        2304         576         648        1536        2592\r\n          96        1344         576         672        1760         864         384        3520        1152        2064\r\n          48         224         864         384         960        1792        2340        3536         288        1536\r\n         768         300         288         256         384        1696         512         384        1344         160\r\n         384        1872        1920        3200          64        1344        1728        1248        1408        2068\r\n        1152         288         704         624        1728        1280        1184        2624         384         360\r\n         288        1536         160        1316         984        2960         512        1040         576        1872\r\n        1200        1040         480         320         480        1536         880         768        1008         960\r\n         960         192        1120         864         640         960         720         512         864        1792];\r\ncyclic=logical([0   0   0   0   0   0   0   0   0   1\r\n                0   0   0   0   0   0   0   1   1   1\r\n                0   0   0   0   0   0   0   1   0   0\r\n                0   0   1   0   0   1   1   0   0   0\r\n                0   1   0   0   0   0   0   0   0   1\r\n                0   1   0   0   0   0   1   0   0   1\r\n                0   1   0   0   0   0   0   0   0   0\r\n                0   1   0   0   0   1   0   0   0   0\r\n                1   0   0   1   0   0   0   0   1   0\r\n                0   0   0   0   0   0   0   0   0   0]);\r\n[p,c]=numPrimitivePrimes(m);\r\nassert(isequal(p,num))\r\nassert(isequal(c,cyclic))\r\n%%\r\nm=[2     4     5     6     7     8     9    10    11    12    13    14    15    16    17    18    19    20];\r\nnum=[1     1     2     1     2     2     2     2     4     2     4     2     4     4     8     2     6     4];\r\ncyclic=logical([1   1   1   1   1   0   1   1   1   0   1   1   0   0   1   1   1   0]);\r\n[p,c]=numPrimitivePrimes(m);\r\nassert(isequal(p,num))\r\nassert(isequal(c,cyclic))\r\n%%\r\nm=[47       14771       72211       82609       55229       49549        4957       79613       16249       16547\r\n       61043       59957       56611       23431       67219       66587       29851       74821        2503       22133\r\n       15607       89413       35447       74287       71191       47543       66898       79987       83003       18973\r\n       17989        7019       70583       28607       44549        9293         601       95339       55967       24611\r\n       13421       21991       72503       59621       15647        9661       15131        7733       32467       96128\r\n       52363       23339       11549       67261       74219        9173       81233       88363       60169       67589\r\n        1103       34877       44699       40093       61420       45281       90679       64657       92927       89891\r\n       48487       41351       23958       23609       36871       40169       63611       27239       67759       38723\r\n        3491        9803       59611       21124       67601       67021       53453        4549       42209       15137\r\n       45083       41149       60521       45737       97549       19470       41961       89107       56531       79259];\r\nnum=[ 22        5040       18368       27520       27612       16512        1392       36720        5408        8272\r\n       29172       27648       13824        5600       21056       30576        7920       18816         828       10040\r\n        4896       29800       17208       24756       16128       21600        7680       26660       40572        5760\r\n        5992        3080       35290       14302       18144        4400         160       46944       27982        9328\r\n        4800        5856       36250       21600        7822        2112        5632        1728        9264       12800\r\n       17448        9996        5772       16704       36204        4584       40608       16896       19008       33120\r\n         504       17436       22348       12288        7680       18048       24192       15360       45888       35200\r\n       16160       16520        1760       10848        9824       20080       25440       13618       21560       18324\r\n        1392        4368       15888        2560       24960       17856       21648        1512       21088        6720\r\n       22540       13608       22528       22864       29520        1792        9408       29700       22608       37884];\r\ncyclic=logical([1   1   1   1   1   1   1   1   1   1\r\n                1   1   1   1   1   1   1   1   1   1\r\n                1   1   1   1   1   1   0   1   1   1\r\n                1   1   1   1   1   1   1   1   1   1\r\n                1   1   1   1   1   1   1   0   1   0\r\n                1   1   1   1   1   1   1   0   1   1\r\n                1   1   1   1   0   1   1   0   1   1\r\n                1   1   0   1   1   1   1   1   1   1\r\n                1   1   1   0   1   1   1   1   1   1\r\n                1   1   1   1   1   0   0   1   1   1]);\r\n[p,c]=numPrimitivePrimes(m);\r\nassert(isequal(p,num))\r\nassert(isequal(c,cyclic))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-24T20:07:09.000Z","updated_at":"2026-07-08T17:24:09.000Z","published_at":"2021-03-24T20:59:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the number of primitive roots of for each input number in an array or matrix (m) and whether each number will form a cyclic group. Output should be a corresponding array or matrix of the number of primitive roots and another logical array or matrix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46696,"title":"Number Theoretic Transform (NTT)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven an input polynomial (r) of length \u0026lt;=n and a prime number (p) such that an nth root of unity exists and the modular inverse of (n) modulus p exists. Convert the polynominal coefficents by Number Theoretic Transform (NTT) using the primitive nth root of unity as the generator mod p.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function rhat = numberTheoreticTransform(r,n,p)\r\n  rhat=r;\r\nend","test_suite":"%%\r\nn=210;\r\np=5881;\r\nr=[8669,57047,39514,17386,56675,3808,29999,47330,22216,26294,34536,58604,51010,4546,18270,24862,...\r\n    56667,27522,15720,39167,31418,58887,61257,53601,46459,48707,58963,4275,22014,284,54270,33255,...\r\n    23996,14853,35050,18971,4480,5568,4478,26857,8085,29033,58912,23176,7875,37297,57346,22844,...\r\n    2747,9328,5019,48531,29918,43794,45825,37444,41202,57525,43407,57371,30639,9262,4465,46808,...\r\n    20184,43985,42757,34802,46865,33083,31981,32626,61340,25511,7677,15756,44886,55001,63579,14101,...\r\n    49829,38279,26407,33426,32482,42688,48739,19788,5872,54130,25531,50810,11755,7167,59320,57432,...\r\n    65522,56639,2416,35696,65379,33489,57246,4602,64719,60470,36979,28276,22140,47233,894,24514,...\r\n    60469,35814,31056,32541,20248,62314,64355,33656,65050,29874,27921,13973,12664,54575,47620,34717,...\r\n    54334,33546,36173,13977,38523,9356,3422,44781,39882,14395,26625,41281,36392,8361,11088,65,...\r\n    27404,32013,10477,43701,1174,7843,62398,63953,2026,32367,56539,15917,54674,53319,41220,146,...\r\n    24885,59271,44587,24826,41415,15942,37448,64338,55684,18575,44725,23470,64679,5504,16404,53172,...\r\n    5532,34816,52469,48419,9284,28697,22962,31358,38496,9555,59331,41955,10678,37087,61054,51321,...\r\n    44937,30554,17060,37307,16303,20925,59690,58013];\r\nrhat=[4391        3275        5259        1238        4797        2486         919        3786        5067        4389\r\n        2255        3368         968        3027        4274        3358        2953        3646        2967        4281\r\n        5348         229        5498        5448        3419        3720         100        5376        2968        3437\r\n         404        3686        3576        4743        4840        4942        4237        1414         102        2806\r\n        3832        5075        5084        1139        2483        2021        5541        1332        5022        5155\r\n        5235        4306         797        2739         911        3669        4133         547        5678        5162\r\n        1905        4772        2478        1657        1905        2539        4053        3185        3567         113\r\n        1985         674        1359         182        1645        1249        1752         922        1178        5427\r\n        2476        1241        2496        1703        3691        5044         802         304         905        2280\r\n        2211        4163        4845         690        4246        3016        3159        1555        3762        1416\r\n         105        4332        2706         308        2230        2117         787        1189        5549          72\r\n        4092        4428        4103        3397        5700        5630        1803         840        4153        4385\r\n        5537        1564        5437        5553         377        3468        2885        4827        3523        2618\r\n        2238        3633        2254        4028        3660        1909        5874        1850        3153        2253\r\n           3        2286        1953          81        5161        5764        5063        2887        4983        3481\r\n        5044         770        1225        4832        1673        5556        2434          21        1735        5422\r\n        1003        2672        3262         982        2344         269        2638        3485        3278        4882\r\n        4604        5118        4587        2136        3361         478        5289         808        3170        3752\r\n        2862        4604        4813        3077        5849         813        1214         135        3691        4774\r\n        1668        4361        5564        3949        5019          71        2441        4481         722        5462\r\n        4925        2693          41        3294        3971         361        1224         445        5386         186];\r\nassert(isequal(numberTheoreticTransform(r,n,p),rhat(:)'))\r\n%%\r\nn=1024\r\np=12289;\r\nr=[52074       13446       46646        7881       15396       46708        6135       41514       35944       46632\r\n       60673       28779       56867       40989       26142       30972       42638       64624       10831       31518\r\n       11720        1785        7753       22717       17571       46438       14101       13576       32367       47787\r\n       33917       57421        2557       21929       54559       62787       15982       49616       35069       61443\r\n       41091       39983       39203       37658       65232       33146       22261       58086       13029       33898\r\n       59846       13342       39604       56619       42582       19991       12967       30948       40839       59183\r\n       43513       34073       33844       13013       46134       51761       33215       10414        1724       14299\r\n       25506        3527         492       44069       61099       15491       62308       53144       20892       57227\r\n       48497       56504       45149       59102       45065       15355       25860       31228       34930        5419\r\n       53584       29028       61998       13051       37247       30454       38303        7621       21415       30500\r\n       39344       35914       57248       19548       24959       40592       39750       57391       39465        1437\r\n        5570       37149        7423       32539       41587       40326       46834       41627       23719       52971\r\n       60447       44590       23237       58320       23804        8036       26315        6375        8842       11744\r\n        3512       24338       15855       32860       26713        8112       56275       59535       59887       10839\r\n       34539        5126       36722       18153       24163       18642       60324        2294       41979       11901\r\n        7789       29907       40155       34993       30696       48216       49206        2605       43173       45313\r\n       24913        3135       19713       37634       32991       26955       18716       64786       44258       14009\r\n       53269       48382       52307       27053       59672       54328       52220       44969       48795       19536\r\n       15997        2490       52143         967       13528       61283        9356       24686       55192       50353\r\n       57961       62537       51189       46056       22190       26153       33066       33051       33859       32843\r\n       46704       48652       23009       33210       37625        3421       40022       50036        9952       59602\r\n       24782       61436        3558       24986       31911       37433       46124        3203       24947        3791\r\n       16313       33643       46445        4255       17184       48999       25122       47574       53806       28622\r\n       16571       15787       65072       23499       37984       20987       47754       45962       11230       37503\r\n       50282       17037       10648       15351       57562       32304       58149       30073       21625       37032\r\n        3267       49740        7442       13336        3994       14526        3660       38161       63338       53989\r\n       44911       65099       59826       53331       28893       61556        9058       22222       52841        8264\r\n       40650       23377       31565       25784        5521       31608       56561       11182       14561       19668\r\n       48934       49339       55823        3511       36912       35389       27639       26161       65521         139\r\n       64045        7212       53078       24579       35344       14487       26955       60278        4177       62331\r\n       25160       39127       12239       50790       50335        6287       62858       14814       27884       50220\r\n       17052       28219       16200       10832       15275        3943       49168       23658       26498       49237\r\n       57505       47888        3551       59783       38493       53707       64290       21270       26233        9100\r\n       52828       17116       39908       20919       30079       50559       15303        5477        7334       22893\r\n       30220        6213       50936       21612       56425       12825        6306       33598       27807        9918\r\n        5961       29554       33493       13384       43308       58662       25203       54582       40209       32553\r\n       36979       41947        1818       50280       23191       44846       32785       59284       64753       52995\r\n       12280        8653       64905        4585       22753       43047       37372       47421       14411       41475\r\n       34844       29676       32829       62261       16627       64905       64004       25100       23205       45115\r\n       23267       42742       21757       10368       62424        2208       32299       19530       17448       41914\r\n       20629       54198       11395       18772       19542       27803       26272       45332       19103       47796\r\n       47627       20190       41001       45031       10381       32111       65207       57701       12346       56350\r\n       33801       26369       37692        9250       23677       38240       17104       60591        1498       41088\r\n       51815       57948       49216       33560       48603        5457       43602        5324       29452       11835\r\n       13401       45913       10061       47272       46261       43263       63193       31632       15967       37572\r\n       44440       15851       23382       60872       45933        3427       43984        8405       56932       10719\r\n        3439       49796        9433       47979         408       36492       19606       16574       34643       59379\r\n       52505       19066       55745       49142       24533       46663       34807       57931       59908        5068\r\n       44470       18182       22142       26694       59080       31975          95       12863       63827       22186\r\n       61997         400       18035       15695       20863       40475       57919        7953       38366       38051\r\n        6000       24557         393       34134       39130       14010       26501       35631        7797       31145\r\n       59535       28634       52554       14357       19516       42313       19739       20618       60721       52777\r\n       33420       19942       32598       55206        8192       24945       62297       25037       38899       34785\r\n       40298       19061       35248       43445       25451        6796       30189       51874       57908       14897\r\n       20714       15893       57076       53492       53587       24740       18851       54996       27818       46496\r\n        5078       61386       47372       52027       64302       17226        5546       44579       39797        9740\r\n       55745       56373       43783       30743       56491       15812       38153       27323        4637       43130\r\n        9471       26032       11719       20285        5493       40823       10031       42132       60605       41548\r\n       24280       31419       36077       45061       22132       34270        4790       14030       42079       15027\r\n       40789       37027       62906       64674       15474       27081       38047       40453        6848       11942\r\n       65375       32087       39060       50458       20827       14273       18809       44249       45889       10902\r\n       33904       17682       52990       54367       64516       56266       23718       39388       25939        9804\r\n       64914       64863       64522       46273       35930       56427       47502       22695        5564       13287\r\n       14846       12037       58059       39015       49102       18608       56250       23881       14056       62584\r\n       26083       56469       14014       49340       55171       40330       22801       11238       16305        1042\r\n       45650        2138        2269       32553       10937       51084       63028       52124       14853       62751\r\n        4236       21755       29564       56697       59185       62576       62493       32287       46072        1683\r\n       48998       49069         904        4458        6889       60267       13502       23240       49424       63642\r\n       27551       42229       31045       63474       48830       25219       50347       50794       35866       19503\r\n       53170       11091       62337        6472       47800       10658       40339       15519       36273       34411\r\n       24877       62403       16315       35846       47020       52215       60222       55367       41325       56514\r\n       20910       35603       25324       26409        8744        7459       39487       53511       64582       58746\r\n       64621       16476       28274        7014       29215       10408       46015       55458       41568       12386\r\n       47066       37917       54452       47458       33343       23319       48737       24260       39351       43300\r\n       27078       59996       54044       40218       34766       55558       25238       25115       59584       61684\r\n        6463       58693       29687       51312       56342       38193       16482       56448       37410       63943\r\n       48140       31621       24940       37134       44415       38415        2409       30402       21982        7073\r\n       41766       29015       60677       53170       52811       60675       30941       37391       62727       11724\r\n        4839       20431       48551       37799       34815       37688       42275       45567       28830       48925\r\n        7897        3625       48341       61867       62645         653       18282       62974       39422        3241\r\n       64329       49400       62057       57111        4369       53043       33938       35803       47203        4671\r\n       32558        8647       33429       33266       35488       39898       16100       41718       44484       32055\r\n        1468       23325       51896       51696       18458       31451       19497       37414       13943       55698\r\n        3527       25943       29633       31000       31516       17592       42629       60759        5349       65342\r\n        9232       58033       55653       54316       44883       16914       58418       56607       17988         287\r\n       58554        1391       25587       21134       13648       31523       56433       11130       56853       35560\r\n       30527       55317       48390       63972       39856       14899       13756       11711       36658       56449\r\n       36756       18878       63991       18232       21376        3185       26155       15958       30449       59581\r\n       32404       16406       34294        4773       57727       11091       58188       49268       28200       55400\r\n        4442       32006       28174       49232        8742       16937       16811       13050       50723       57597\r\n       58828       47778       13576       54472        6711       12970       63360       64417       42855       48901\r\n       18911       13278       21194       60446       62856       39694       40577       46506       43104        7699\r\n       17632       14173        7265       21431       10020       53982       10836       11497       10552       33359\r\n       38941       63985       24589       52695        9996       53124       54145       56249       28336       11064\r\n       31187       38878       21620       35274       10194       52575       42971       59599       33101       54467\r\n       24137       19949       22420       30362        5870       46406       35812       63023       24597       60818\r\n       42966       63419       53550       53788       29781       56320       16471       37394       31481       11107\r\n       61485       58718       34844       62384       43836       51189        2631       36888       22440       57916\r\n       40660       12453       34152        4998       54480       13356       15294       11577       50931       25418\r\n       18536         117       50745       46443       51788       65099       23665       33664       25162       25072];\r\nrhat=[8149       10593         825        1418        8962        1559        3161         152\r\n        5086        9561       11949        5217        5798       11589        3150        5329\r\n        8984        3998        7095         390        2183        9925        6985       11431\r\n        3249        1053        7833        4160          13        1692        1976        8920\r\n        9291        9284        9074        2974        5068       10375          80        4023\r\n       11492        5804        6645        1044        7322          19        7192        7839\r\n        9217        4466       10449        3187        2137         119        9226        6202\r\n        7603        5162        8758       12104        7195        7646        6527        5506\r\n        6225       12166        3612        9329         470        7699        9996       11300\r\n       10722        1986        5330       10948         843        4540       11096        7298\r\n         446        7352        2390        5148        9522       11654        1156        8749\r\n        3736       11720       11276        6342        9275       11013         782        1253\r\n        3336        5994       12271       10025        4567        8321        1619        6205\r\n        2010        3243        4122        2079        9240         989       12020        7584\r\n        9610        6632        9036       11327       11665        9187        1417        4616\r\n        3768        1590       10149        3400        4707        5141        3973        5828\r\n        9623        3436         997        6446       10458        5845        8785        4056\r\n       10876        4226        7775        4853        8562        9793        8662        8391\r\n        6182        3663       10851        2565        5271        5953       11059         715\r\n        7529        4284        2244        8402       12053        7689         541        5153\r\n        8110        5951        6609         335        3517        6766        6683        3012\r\n        4955        3196        8713        6749         246        5847        2747        7607\r\n        8485        2656        4214         985        4827        2550       11484       11457\r\n        3124        1611        3563         382        1919        3058        8499        5773\r\n        1423        2757        1327       11084        6349         455        1929         417\r\n        9081       10604         613       10502        7325        8929        7125        8483\r\n        9465       10411        2134        3556         986         530        9950        1448\r\n       10951        8652        3309        7995        6767         315        3390         507\r\n       11937        8868       12228        5740        6625        1837         388       11209\r\n        3858         829        1248       12057        7320        3536        2756        5663\r\n       10974        3976        8957       11721        4338        9767       11429        8609\r\n        6564        1713        9831       10924         912        9766        6373        7233\r\n        3700        1269        4315        8607        4546        8196        9941        7644\r\n         878       11980       10491        2706        3912        9513        2567        8190\r\n         643         379        4709        9262       11112        1860        4737       11022\r\n        1323        3739        8110        8196       11511        2236        8007        9557\r\n       12024       10027       11760       11831        2394         500        6894         389\r\n        8560        4490         168        8370        1272        5988        6261        8753\r\n        4943        2775        2362        2464       10956       12172        2558        5757\r\n        1707        7697        6861        2490        6732        4772        9887        8195\r\n        4315        3792        1287         580        3928        6061        9571        1812\r\n         783        5756        2086        9790        5118        7639        6449        7058\r\n       11898        3862        2787       12173        4520        5695         212        1507\r\n        5346        9561         654        9830        5535        5850        4702        3448\r\n        5173        7945         740        8601        2757        3408        1153        7755\r\n        8707        6923        4891       11539        7076       10827       10657        1702\r\n       11981        8090        5301         856       10035        6307       10356       11679\r\n        9453        2222        1223        9948       10545        6152        6122        5565\r\n       10032         113        4049        4053        8376       11269       10270        1305\r\n        2126        1286        6659         881        3528        8590       10609        9754\r\n       11887        3876        1784        6936        1034        6381        1763       12219\r\n        5357        1336        7692        2667        7716        9060        8531        5530\r\n        5945       11985        2654        2560        6865        4738       11695         801\r\n        5824        6645        6710        6940        2131        2231        1940        4950\r\n         746        3214        6012        8276        8247        3992        9384        5457\r\n        7807        4112        9317        2273        1130       10350        8548        8193\r\n        3642        8624        8082        4908       10678        1835        7296         848\r\n       10867       11073        9696        2669        5746        1260        7347        4877\r\n       11495        5170         991       10986        8479        5253        2646       10197\r\n        5326        2942       11788        1621        2984         294       10203        9804\r\n        4494        2383         294        5111        1339       10478        8541        9356\r\n        2187         172        5127        8875        8915         789        2201        5140\r\n        5160       10441        4096        9010       10106       11593        6362        9775\r\n        4295       10907        1824        1894        5510        5337        9922        3371\r\n        8127        5345        4006        5209       10033        2859        4601        5742\r\n        3793        8908        6314        7883        8653       11031       10085        5403\r\n        3859        7385        4404        8611        5490        3923        8187         480\r\n        9766       12182         901        3569       10257        6668        3709        6931\r\n        2481        9841        9271        2472       11437         391       12053        4980\r\n       11992        3545       10994        9307       11791         322        3678        9815\r\n        1904        6151       10952        4868       10935        8320        9856        9570\r\n        6752         254        9868        7270        9019        3920        1414        1270\r\n       10364        4598       11037        3621        3234        9263       10271       11024\r\n        5000        1675        5510        7650         440        5417       10452        1974\r\n        5922        4450        6056        5245        1126        2867        2645        7398\r\n        1290        5398        5692        8986        3751        7506        2269         488\r\n        1909        5213        4327        8275        5794         534       11630       11908\r\n          53        6833        5782        5954        9629        5503        2239        5699\r\n       10980       10804        4193       10615         236        6096        2895        8953\r\n        5824       11122        7883        2053        6154        4548        5701        5575\r\n        1747        6519        6826        4063       11574        7423        9720        4636\r\n       11375        6605        1810       10176        6039         587       10520       10310\r\n        1100        3029        3862        8091       10427        4614       10870        2274\r\n        8785       11559        6971        4077         925        4907        5804        7863\r\n        3296       12221        8683        3445        3022        7680       11201        3591\r\n         773        3117        2404         968        4600        2668       10518         468\r\n         215        6056        7487       11731        2328        6050        2762        8744\r\n         677        1468        5443        8970        9622        8609         391        9362\r\n         850        9053        2676       10194        5487       10187        1917        5679\r\n        2586         415        8841        4002        8329        9123        1706        6923\r\n        4346        8013       11694        7230        4849        5346         958        9474\r\n        5828       10768        3592       11256       12214        6209        5772        4820\r\n        8719        3551        5014         187        8099        3338        9425        8455\r\n       11193        3088        2025        7193        3726        6393        4237       10983\r\n        7306        3335        9019        6401       11140        9163        2214        8141\r\n        2901        2598        7927        9127        3635        7468        2931        9271\r\n        6188          83        8923        5051         213        3750       10987       11744\r\n        3529         829        6394        6310        8428       11624         392       10014\r\n       10407        6190        4717       10647        8578        4959        8400        9476\r\n       11730        3977        3410       10130        8954        3171        6364        1588\r\n        9146        6763       11717        2289       12045         329        1489        4830\r\n        6135        7211         568       10450        9554        3037        5529           9\r\n        3995        1662       12272       11074        5671        1469        7367        4854\r\n        4549        8081        2025        3242        8687        5009        9142        2004\r\n       10161        2020        4083        1333        4743        5254         194        6885\r\n         226       11966        6259        3939        5004       11828        3961       10006\r\n        3966        8223        9013        2152        7274       11391         120        3271\r\n       12189        1703        2227        5125        5269        7245        8442        8137\r\n        4036        7892        8282        9848        5536        4409        7306        8365\r\n        4788       10993       10891        2650        5180        9379        5748        3115\r\n        1578       10933        4035        6497        8116        7574        4788        9184\r\n        7292        2637        2829        2197        6402        5607        8814        3297\r\n       12163        6864        3905        4982        6710        7802       10831        1012\r\n        8629        6883        3876        2358        3998        1465        7663        5577\r\n        1940        6499        1233       11847        8131        8283         577        8690\r\n        8536        1709       11555        7614        1606        7021        2479       10991\r\n        7673        6724        9074        5707        3131       11008       10835        5567\r\n        6706         321       12276        3407        4790       11852        3340        4209\r\n         887        6216         706        7716        9370        2905        8846         170\r\n        9563        7171        5219        7938        3769        7095          68        2976\r\n        3914        3867       11656         347        7395        8967        5517         894\r\n        2589        4130       10205        5493        3040        4057       10259        5751\r\n         248       10770        3157        1900        1428       11496        3608        7411\r\n       11099        5378        8023        1291       11427        1273       10747        9407\r\n        1600         586        9694        4493        2681        3073        2814        9289\r\n       11724       11813        7932        7385        3639        1582         135        5276\r\n        8990       10675       10619       10670        6193       10730        4885       10384\r\n        5511        2999        4965        9346         562        3131       11572        6417];\r\nassert(isequal(numberTheoreticTransform(r(:)',n,p),rhat(:)'))\r\n%%\r\nn=256;\r\np=3329;\r\nr=[17789       14064       31398        7235        4452       54042       17029        9244       41506       19221       25101       62219       54529       40064       62923       42789\r\n       56877       51841       65136       14198       13625       50288       57544       47986       60999        3380       64958       16802       49403        3404       61808       25001\r\n       48595       42905       39615       53151        2595       65348       12338       45289       64079       33038       18797       64871       40754       37730        7385       19662\r\n       29351        1713       61925        9087       30759       14919       49754        2260        6133       50356       46280       22925       25827       55203       42486       22291\r\n       46506       51496       32141       57796        9836       60263        2076       32037       43367       18545       35075       13665       23545       32750       31509       60222\r\n       61887       60461       28701       60526       64966       42074       42096       63661       39503       14769       12662       43635        5823       28771        4359       29901\r\n       11410       32264       50636         835       27987        6902       37150        7369       31052       21711       45182       63789       22392        9768       58836       28999\r\n       16029       54657       48763       24717       62611       17574       24668       48707       23347       29704        3306       40809       35957        1853       32586       29765\r\n       42003        8608       29026       10997       47464       50059       13929       41847       31167       48325       12087        4164       30182       49589       50548       61950\r\n       52993       49793        3473       35404       38069       52789       51914       38940       43976       33415        2992       24478       42300       52173        3955       14360\r\n       55926       60669        5755        6662       35406        6832        9531       32677       62891       25068       58002       10895       33654       19238       17200       57829\r\n       26091       54572       52296        2573       46231       30786       32056       37214        5838       59341       55036       15157       53374        7550       42668        1302\r\n        7569       17000       42964       61160         329       14356         841       27951       52280       63259        7743        3421        6368       24582        8755       22397\r\n        5261       13960        2119       63674       51282       60470       12229        4996       38717       41174       26896       59097       30389       54322       41847       50202\r\n       23623       34230       36507       23653       60742       20992       31800       19043       59781        8652        7879       51989       38654       55166       25227       22465\r\n       54323       26041       47172       42218         543       56199       54933       36787        6627       40521       37492       24445       12266       43597       50180       40554];\r\nrhat=[1004        2562          12        2074         386         769        3081         923         234         324        3276        3310        1457        2786        1538        1203\r\n        2725 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3065];\r\nassert(isequal(numberTheoreticTransform(r(:)',n,p),rhat(:)'))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-06T20:08:10.000Z","updated_at":"2026-07-07T16:10:12.000Z","published_at":"2020-10-06T20:17:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an input polynomial (r) of length \u0026lt;=n and a prime number (p) such that an nth root of unity exists and the modular inverse of (n) modulus p exists. Convert the polynominal coefficents by Number Theoretic Transform (NTT) using the primitive nth root of unity as the generator mod p.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":502,"title":"Would Homer Like It?","description":"\r\nGiven a matrix of ones and zeros, you must determine if there are any doughnuts present (would Homer Simpson like it?). A doughnut is a 4-connected region of ones completely enclosing a 4-connected region of zeros. You can assume that any regions of ones are either blobs (or genus 0) or doughnuts (genus 1). Thus if you find any hole in a region of ones, it is a doughnut. Also, there are no nested doughnuts.\r\nReturn true if any doughnuts are present, otherwise false.\r\nExamples:\r\nThis is a doughnut:\r\n 1 1 1\r\n 1 0 1 \r\n 1 1 1\r\nHere is another doughnut:\r\n 0 0 0 1 1 1\r\n 0 1 1 1 0 1\r\n 0 0 1 0 0 1\r\n 0 0 1 1 1 1\r\nThis is not a doughnut:\r\n 0 1 0\r\n 1 0 1\r\n 0 1 0\r\nbecause the ones are not 4-connected and so can't surround anything.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 655.833px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 327.917px; transform-origin: 407px 327.917px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 145.5px; font-family: Helvetica, Arial, sans-serif; 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.5px 8px; transform-origin: 383.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a matrix of ones and zeros, you must determine if there are any doughnuts present (would Homer Simpson like it?). A doughnut is a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e4-connected region\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 261.5px 8px; transform-origin: 261.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of ones completely enclosing a 4-connected region of zeros. You can assume that any regions of ones are either blobs (or\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003egenus 0\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 231px 8px; transform-origin: 231px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) or doughnuts (genus 1). Thus if you find any hole in a region of ones, it is a doughnut. Also, there are no nested doughnuts.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 182px 8px; transform-origin: 182px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn true if any doughnuts are present, otherwise false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExamples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 60.5px 8px; transform-origin: 60.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis is a doughnut:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 61.3px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 30.65px; transform-origin: 404px 30.65px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 24px 8.5px; tab-size: 4; transform-origin: 24px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 1 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 8.5px; tab-size: 4; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 0 1 \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 24px 8.5px; tab-size: 4; transform-origin: 24px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 1 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.5px 8px; transform-origin: 82.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHere is another doughnut:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.7333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 40.8667px; transform-origin: 404px 40.8667px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 0 0 0 1 1 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 0 1 1 1 0 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 0 0 1 0 0 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 0 0 1 1 1 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.5px 8px; transform-origin: 72.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis is not a doughnut:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 61.3px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 30.65px; transform-origin: 404px 30.65px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 24px 8.5px; tab-size: 4; transform-origin: 24px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 0 1 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 24px 8.5px; tab-size: 4; transform-origin: 24px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 0 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 24px 8.5px; tab-size: 4; transform-origin: 24px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 0 1 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 224.5px 8px; transform-origin: 224.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ebecause the ones are not 4-connected and so can't surround anything.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = has_doughnut(a)\r\n  tf = true;\r\nend","test_suite":"%%\r\na = [ ...\r\n 1 1 1;\r\n 1 0 1;\r\n 1 1 1;\r\n];\r\ntf = true;\r\nassert(isequal(has_doughnut(a),tf))\r\n\r\n%%\r\na = [ ...\r\n 1 0 0;\r\n 1 0 0;\r\n 1 1 0;\r\n];\r\ntf = false;\r\nassert(isequal(has_doughnut(a),tf))\r\n\r\n%% \r\na = [ ...\r\n 1 1 1 0;\r\n 1 0 1 0;\r\n 1 1 1 0;\r\n 0 0 0 0;\r\n]; \r\ntf = true;\r\nassert(isequal(has_doughnut(a),tf))\r\n\r\n%%\r\na = [ ...\r\n 0 0 0 0;\r\n 0 1 1 0;\r\n 0 1 1 0;\r\n 0 0 0 0;\r\n];\r\ntf = false\r\nassert(isequal(has_doughnut(a),tf))\r\n\r\n%%\r\na = [ ...\r\n 0 1 0 1 0;\r\n 0 1 0 1 1;\r\n 0 1 0 0 1;\r\n 0 1 1 1 1;\r\n 0 0 0 0 0;\r\n];\r\ntf = false;\r\nassert(isequal(has_doughnut(a),tf))\r\n\r\n%%\r\na = [ ...\r\n 0 1 1 1 0;\r\n 0 1 0 1 1;\r\n 0 1 0 0 1;\r\n 0 1 1 1 1;\r\n 0 0 0 0 0;\r\n];\r\ntf = true;\r\nassert(isequal(has_doughnut(a),tf))\r\n\r\n%%\r\na = [ ...\r\n 0 1 0 1;\r\n 1 0 1 0;\r\n 0 1 0 1;\r\n];\r\ntf = false;\r\nassert(isequal(has_doughnut(a),tf))\r\n\r\n%%\r\na = zeros(3,4);\r\na(1,3)=1;\r\ntf = false;\r\nassert(isequal(has_doughnut(a),tf))","published":true,"deleted":false,"likes_count":5,"comments_count":4,"created_by":7,"edited_by":223089,"edited_at":"2022-10-28T10:25:50.000Z","deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":"2022-10-28T10:25:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-15T17:46:33.000Z","updated_at":"2026-07-09T11:17:54.000Z","published_at":"2012-03-19T15:21:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"140\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"200\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a matrix of ones and zeros, you must determine if there are any doughnuts present (would Homer Simpson like it?). A doughnut is a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e4-connected region\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of ones completely enclosing a 4-connected region of zeros. You can assume that any regions of ones are either blobs (or\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003egenus 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e) or doughnuts (genus 1). Thus if you find any hole in a region of ones, it is a doughnut. Also, there are no nested doughnuts.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn true if any doughnuts are present, otherwise false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is a doughnut:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ 1 1 1\\n 1 0 1 \\n 1 1 1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere is another doughnut:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ 0 0 0 1 1 1\\n 0 1 1 1 0 1\\n 0 0 1 0 0 1\\n 0 0 1 1 1 1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is not a doughnut:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ 0 1 0\\n 1 0 1\\n 0 1 0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ebecause the ones are not 4-connected and so can't surround 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44961,"title":"RSA decryption","description":"Decrypt a large integer string using RSA decryption given the public key (n) and private key (d). Convert the large integer decryption into an output message string with UTF-8 representation.\r\n\r\nExample:\r\n\r\n encrypted_message = '158037161019988039882393476857386648994978438821991287680442802412825849535544067751541256843540494019';%input\r\nn='418336393847020647250825879743341651032293545176800777981294580200903315345456262337972725306797613061';%input\r\nd='8444986024072025211908427894173383040354675378319105204646840203847580180874615752845913488969020869';%input\r\ndecrypted_message = 'I like to swim!';%output\r\n\r\n\r\n","description_html":"\u003cp\u003eDecrypt a large integer string using RSA decryption given the public key (n) and private key (d). Convert the large integer decryption into an output message string with UTF-8 representation.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e encrypted_message = '158037161019988039882393476857386648994978438821991287680442802412825849535544067751541256843540494019';%input\r\nn='418336393847020647250825879743341651032293545176800777981294580200903315345456262337972725306797613061';%input\r\nd='8444986024072025211908427894173383040354675378319105204646840203847580180874615752845913488969020869';%input\r\ndecrypted_message = 'I like to swim!';%output\u003c/pre\u003e","function_template":"function decrypted_message = RSA_Decrypt(encrypted_message,d,n)\r\n  decrypted_message = 'I like to swim!';\r\nend","test_suite":"%%\r\nm='158037161019988039882393476857386648994978438821991287680442802412825849535544067751541256843540494019';\r\nn='418336393847020647250825879743341651032293545176800777981294580200903315345456262337972725306797613061';\r\nd='8444986024072025211908427894173383040354675378319105204646840203847580180874615752845913488969020869';\r\nmessage = 'I like to swim!';\r\nassert(isequal(RSA_Decrypt(m,d,n),message))\r\n%%\r\nm='99761240327251194937668282784881225946299704960682605372368300120848092908591455333889649815054891832920433772438140697229743047905660648016064750862552787515723449901585029566883857331537912668878918706229773460108043130645834201085405226084010413433457258525704626839479467337463012332940952234541291286602023412313079939518264986360860440514106228995186076871512459300140814669747884371890194124';\r\nn='2044371069952561243871813747701535503388267616657953475148898181142012590397809234167373308955772082860082985954286137615597515257087506574051530104475374974920093127841789408014496870693507622812332673504654584870100580476794800708440785082437228308551107726064054828640053321250498545183042994878498928173976370185712833904492317580152665428272199317847097773542066059565512439224992672101163367819';\r\nd='131358569595346680469722564224349085322306406056832660693226883146757023027681686453130430199929142940992255578581548217026735077095312421736286269892515739496597527524021166625708322359741224036234988705082882699895245449017415856831226734459122764117157172961113990706104659539690141481103935528273973382371183154438463086325519326121228923730136467766036183357672350586091588640276470994058874793';\r\nmessage = 'First, have a definite, clear practical ideal; a goal, an objective. Second, have the necessary means to achieve your ends; wisdom, money, materials, and methods.';\r\nout=RSA_Decrypt(m,n,d);\r\nassert(isequal(RSA_Decrypt(m,d,n),message))\r\n%%\r\nm='23055330962704323769878549529115024711681463755869375992447358448257597289666397997393945478297323372847937346015110864832142828615195632399869833059964395947034849804307978652470092440225822549097020437344501330227622390881049097656181781980124142659454562923055085607225529541369345564097544873012395850084756321027482195140106724706102857159831541577386517426252851135917933602432485339455137853480425755360413522537180403768732770990453717801905433194599201771294559164174484366213507079896512750859909040228686293902666244968559905065091421969981123917913807285202549025830873320919273470513619143052127674709353494599047667391749001044180280253098309127910967801244777547067797257847396027373615105278074126621948502699483945442597921239032762535839481741386676784123570880434889025648597593711911259097408384527597630246903648267481820555872340696607290773027177673329986283293168575528258578575033034179306629426942699054620008867304832513427178319015491321861291086200676826846740503213061372327825278234127270730394825241275398344604061667061892125034848354745243512927194104643800196788262228848172689053393410972717679060779374106225778531311917434399927265718394014531619654762559111657295163989321031700962115070401533540746801357628868609255941469541707984326602981168016264720519340003693219403163278843126513912057794102645161814569893320900148891952732032827189210372803453777673309727629845360314416264926243414888253428149538146304399700653423118791724424837155323935319171814705469113037576054893140065594406360362408167462563925199225169055130480445976569760198217276692195730775524801021060293503580957364539210146595506177369243830063105693396808209631409860229448190041996912370291877581261016834769083953407597967437841733812344230896457097759403613339974363380556576775192238298546579676296359906794868505900966056565863994904406875527092603782089107591766239203672780399852597928423220774857864301715176837587724591257928112610743311445186658958007825888475800717425136849205837547536117562642680';\r\nn='44842008376687803367401704855862174057751658874412319214254366772513580664834338103711248053800336314605433363839051280089244765499067546768593375603554906634041005882836398715141891796137918851678901692978242458027064144613729242304549721699241688731628849316717564354846304644497408201649639245333007226999680183209765262168096747256549932760714835163829498814356014506466022681051474161134416048209239076204778228261950266231966892099194904195589855692846886804440024833800891898474520523721428667143505915995217245366095168045283186412220277535584022415882288464175935131208288146822299727657938865855853054174274144036081729604573534323903573564345990066095029031133576597298513883268061041004553754062342541175017746399640362184228727837219293246060058323563065371426108553463224921179093569734439828568435658070810483844709529476015493154462587917722806971578721201741643550136095893915598053953011321347017522943202801820158823344592288227452688958887872572522782675644714289349442555731461112275849176682816627205790162163242534462778708459909915826953853537650009043468930450287584181263070727575137424307931682948818963610116434419852585517456098152109913486868606969385133300794635427715727859479612757775192862801547635779921771426233897718528292667112148507798722127322607462037572360649156150337532940752245966765201596748120586383127825681873289878451591957019880886587602576426267683951317718936847177641679183717321862429721190212389237395890951104472937261743929446841800523276218816808066432194473964294708564511969507018959711475230849760902049071415838600456901108854663197095849833602808088094456341330276320302662577163562657750920481798540333412112880539002713127873625438212479154166226846436038698572615482646490520911334607730484144343834476612603467400722323562384577281087071440008144012534847478593412147312743274523095010025887231371129897419306984829625295595332434377173711414555784685658774002600022998291909172576630780759729269867715816511099791566815282862210319017784751883446582453959';\r\nd='6565816445407878925089441991498747612160839198603241148969054176252198301108538816900577327681584864655900309129187116952811278662878254707896639032786256375181309679291058212467790617143590175026484896254317631677185521639888090836542092702228103896557828982761215001435908561096741216458335569193212038242350596427680660630865867932219252556141104387324837429582683296520255026128293117631961432452139374326884841820676484348718346835892309697741432400454075190738155214690226263908349465883864526754491093121291860880617807231984031261908018115438062149668224668541927056762969514272957080528641551440449912383177971011340773567381595669197227397095749281691989236351340479846140946699426488082757798251098448588056674770754671643802109836061405587518383808732642252532232749119323532411226969424472963287039513173436339822906642733903667734412972727748722945805719038892729473535651253460092450459024621811281873600606895132005494130257832946742084673535377347237875132451694131873556170785954511701761479583203082125987308962572083138475191433479413530168163642321800669575367485309537509082240852273955663933547032858727060003363699057579114677450927657082252183166216411898446363400905797006665507108575986344278988745322935954278566001664060256959781130851422164231215979527541890717097899466088129536122753240075629363188908753526503257284825826946057815889269456925910606842810401392503996936381736547569711529540423604489529836981870198914784848089842823822656591932437295439032050213520000125621624734133380868707883468507784350355251698659006842220673722867592264770652693364873913361956132623339827358272992906883218249723187904101702943978747751691915678242891407493339828656260188711974558580485287404900248093520605466868886511014909072710668999090169680693653605673085931199903788603401848851956524927526592113342563256817891019122155938256416456381627581783190684277329685396205824988569434587069719626936811661218907123975873968219302538615272967013401476757929690613750478379916399826582503908605565505';\r\nmessage = 'People who succeed have momentum. The more they succeed, the more they want to succeed and the more they find a way to succeed. Similarly, when someone is failing, the tendency is to get on a downward spiral that can even become a self-fulfilling prophecy.';\r\nout=RSA_Decrypt(m,n,d);\r\nassert(isequal(RSA_Decrypt(m,d,n),message))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2019-09-08T23:48:25.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-08-29T18:26:28.000Z","updated_at":"2026-07-16T15:42:37.000Z","published_at":"2019-09-05T14:41:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDecrypt a large integer string using RSA decryption given the public key (n) and private key (d). Convert the large integer decryption into an output message string with UTF-8 representation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ encrypted_message = '158037161019988039882393476857386648994978438821991287680442802412825849535544067751541256843540494019';%input\\nn='418336393847020647250825879743341651032293545176800777981294580200903315345456262337972725306797613061';%input\\nd='8444986024072025211908427894173383040354675378319105204646840203847580180874615752845913488969020869';%input\\ndecrypted_message = 'I like to swim!';%output]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":57517,"title":"Easy Sequences 90: Triple Summation of a Combinatorial Function","description":"Given a positive integer , we are asked to evaluate the following triple summation:\r\n                \r\nThe symbol  is the combination function, nchoosek in Matlab. Therefore, we can write the function in Matlab as follows:\r\n    \u003e\u003e S = @(x) sum(arrayfun(@(y) sum(arrayfun(@(n) sum(arrayfun(@(k) ((-4)^k*nchoosek(n,k)/nchoosek(2*k,k)),0:n)),0:y)),0:x));\r\nHence, for , we have:\r\n    \u003e\u003e S(5)\r\n    \u003e\u003e ans =\r\n       -1.3302\r\nPlease round-off the output to the nearest 4 decimal places.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 313px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 563.71875px 156.5px; transform-origin: 563.71875px 156.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a positive integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, we are asked to evaluate the following triple summation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 57px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 28.5px; text-align: left; transform-origin: 384px 28.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-25px\"\u003e\u003cimg 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\" width=\"169\" height=\"57\" style=\"width: 169px; height: 57px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 55px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 27.5px; text-align: left; transform-origin: 384px 27.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe symbol \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-14px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"28.5\" height=\"34\" style=\"width: 28.5px; height: 34px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is the combination function, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003enchoosek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e in Matlab. Therefore, we can write the function in Matlab as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 560.71875px 10px; transform-origin: 560.71875px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; S = @(x) sum(arrayfun(@(y) sum(arrayfun(@(n) sum(arrayfun(@(k) ((-4)^k*nchoosek(n,k)/nchoosek(2*k,k)),0:n)),0:y)),0:x));\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHence, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAkCAYAAADFGRdYAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAASaADAAQAAAABAAAAJAAAAABLVRfgAAAC/ElEQVRoBe2XS4iOURjHPzIxLtkIjVtyWdgqshgWymVcFsKCKGSh2ZBYEFv3KSlZoayUWCgbl9XUsECUTNJ8SVjIEJrI9fcf3zOdjjPf+77zjrzzfeep33ee85znnO88z3vOec9bKkWJGYgZiBmIGRhSGRg2pGabf7JNDDElMIzysBBaYGWgva5MHUT7qwqtdZWNQLDNVZKjxH2EcYF+pREhY43a9hPXdzgOPwIx3sD2KWCvG9M8Iv0Jl+om4gEEep4+2lLrod5eVqnSpTfaV7AD+x36ddgCYyC3NDLCGjgMB2EsuLKcyglY6xoLph9jPpYgv+ymbVOe+WpwHWQ65Gzwk86Apxz7Z/TRTluR1L1M5h4oFovDLw8NdMJz6aiVMxWUBA38FCR7QDbt9S64CWnkKk5a7nlZmubPPB+dRdNhK5TBT9Q6bLnkGr1t0GXoX0BbLasomTZOnnJF1j/2/EdS15XAPas6qQ/3/HqraU96rZw2ZwBtu31OPa2qFTArrXMVPz20t1Xa0zbtwvGs49yM3u7UM6n6rrEn/wK9qOdPpqAqzped2DaHBggur4DjQ2zaYpL70NOr1cbPFSeMiY7ep6ZNkj5fdFBLFv0paub3gRPJB0fvU9N+u+kMmlDpNZlyNjyv1LMUerstydKhH9+N2G/305bVbDtE/d5k7Wz+q1F0V9IBZ+fSNmvMWBbl7eZOu6US13vKRrfB9KS32yQcH8NFOAq636jPBdgODXAGDkA3JEnR3m6a7y3QvE7DbkgUbb9VMAdGQTt0gG3LR+haTVqWsp2DO5CUbFz+i+iTowxPoBX8M3gnNsXTCcFDG/tfsgOLOgld43UXmQEmR1Cs/TW6Vpbbbn5FKXUG2nxV6oEvhvnQBrI9gyZILRvwtEG1ffw32UxsdkvVHtblq8iygMm9AovJLWXX9kq884W2iS6O40FbrQd80bKUz10YjFuvP/5g1xsYUA97GighL6EMXfANosQMxAzEDMQMxAzEDMQMxAzEDPy7DPwGCjXem+ac7dYAAAAASUVORK5CYII=\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 60px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 560.71875px 30px; transform-origin: 560.71875px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 560.71875px 10px; transform-origin: 560.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; S(5)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 560.71875px 10px; transform-origin: 560.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; ans =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 560.71875px 10px; transform-origin: 560.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e       -1.3302\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ePlease round-off the output to the nearest 4 decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = S(x)\r\n    s = sum(arrayfun(@(y) sum(arrayfun(@(n) sum(arrayfun(@(k) ((-4)^k*nchoosek(n,k)/nchoosek(2*k,k)),0:n)),0:y)),0:x));\r\nend","test_suite":"%%\r\nx = 1:20;\r\ns_correct = [1.0000 0.6667 0.1333 -0.5429 -1.3302 -2.2084 -3.1635 -4.1853 -5.2659 -6.3992 -7.5801 -8.8044 -10.0688 -11.3702 -12.706 -14.0742 -15.4726 -16.8996 -18.3536 -19.8333];\r\nassert(isequal(arrayfun(@S,x),s_correct))\r\n%%\r\nx = 25;\r\ns_correct = -27.5763;\r\nassert(isequal(S(x),s_correct))\r\n%%\r\nx = 50;\r\ns_correct = -72.3576;\r\nassert(isequal(S(x),s_correct))\r\n%%\r\nx = 100;\r\ns_correct = -179.0764;\r\nassert(isequal(S(x),s_correct))\r\n%%\r\nx = 1000;\r\ns_correct = -2936.8505;\r\nassert(isequal(S(x),s_correct))\r\n%%\r\nx = 10000;\r\ns_correct = -40871.0455;\r\nassert(isequal(S(x),s_correct))\r\n%%\r\nx = 100000;\r\ns_correct = -523824.1437;\r\nassert(isequal(S(x),s_correct))\r\n%%\r\nx = 1000000;\r\ns_correct = -6389513.2367;\r\nassert(isequal(S(x),s_correct))\r\n%%\r\nxs = 1000001:2000000;\r\ns = arrayfun(@(x) S(x),xs);\r\nss_correct = [-9902420 -9888371 -13472171 2045750];\r\nassert(isequal(floor([mean(s) median(s) mode(s) std(s)]),ss_correct))\r\n%%\r\nfiletext = fileread('S.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'java') || contains(filetext, 'py') || contains(filetext, 'regexp') || contains(filetext, 'eval') || contains(filetext, 'assignin');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-01-07T10:58:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-07T09:14:32.000Z","updated_at":"2026-08-01T15:00:25.000Z","published_at":"2023-01-07T10:58:56.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a positive integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, we are asked to evaluate the following triple summation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS(x) = \\\\sum_{y=0}^{x} \\\\sum_{n=0}^{y} \\\\sum_{k=0}^n \\\\frac_{(-4)^{k} {n \\\\choose k}}^{2k \\\\choose k}.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe symbol \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \\\\choose k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the combination function, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enchoosek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e in Matlab. Therefore, we can write the function in Matlab as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    \u003e\u003e S = @(x) sum(arrayfun(@(y) sum(arrayfun(@(n) sum(arrayfun(@(k) ((-4)^k*nchoosek(n,k)/nchoosek(2*k,k)),0:n)),0:y)),0:x));]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHence, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex=5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    \u003e\u003e S(5)\\n    \u003e\u003e ans =\\n       -1.3302]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePlease round-off the output to the nearest 4 decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45355,"title":"Connect Four - 03","description":"Previous Problem \u003chttps://www.mathworks.com/matlabcentral/cody/problems/45354-connect-four-01\u003e\r\n       \u003chttps://www.mathworks.com/matlabcentral/cody/problems/45356-connect-four-02\u003e\r\n\r\nIn addition to previous problem\r\n\r\n In this case, there can be empty places on the board represented by 0.\r\n \r\n Also no of consecutive elements can be more than 4.\r\n\r\n\r\n","description_html":"\u003cp\u003ePrevious Problem \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/45354-connect-four-01\"\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/45354-connect-four-01\u003c/a\u003e\r\n       \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/45356-connect-four-02\"\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/45356-connect-four-02\u003c/a\u003e\u003c/p\u003e\u003cp\u003eIn addition to previous problem\u003c/p\u003e\u003cpre\u003e In this case, there can be empty places on the board represented by 0.\u003c/pre\u003e\u003cpre\u003e Also no of consecutive elements can be more than 4.\u003c/pre\u003e","function_template":"function y = connect_four_2(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx =  [ 1 1 1 1 1 1 1 1;\r\n       2 2 2 2 2 2 2 2;\r\n       2 1 2 1 2 1 2 1;\r\n       1 2 1 2 1 2 1 2;\r\n       2 1 2 1 2 1 2 1;\r\n       1 2 1 2 1 2 1 1];\r\nassert(isequal(connect_four_2(x),2))\r\n%%\r\nx =  [ 1 1 1 1 1 1 1 1;\r\n       2 2 2 2 2 2 2 2;\r\n       2 1 2 1 0 1 2 1;\r\n       1 2 1 2 1 2 1 2;\r\n       2 1 2 1 2 1 2 1;\r\n       1 2 1 2 1 2 1 1];\r\nassert(isequal(connect_four_2(x),'invalid'))\r\n%%\r\nx =  [ 1 1 1 1 1 1 1 1 2;\r\n       2 2 2 2 2 2 2 2 1;\r\n       2 1 2 1 2 1 2 1 2;\r\n       1 2 1 2 1 2 1 2 2;\r\n       2 1 2 1 2 1 2 1 2;\r\n       1 2 1 2 1 2 1 1 2];\r\nassert(isequal(connect_four_2(x),2))\r\n%%\r\nx =  [1     1     1     1     1     1     1     1     2\r\n     2     2     2     2     2     2     2     2     1\r\n     2     1     2     1     2     1     2     1     2\r\n     1     2     1     2     1     2     1     2     2\r\n     2     1     2     1     2     1     2     1     2\r\n     1     2     1     1     1     2     1     1     2\r\n     1     1     1     1     1     1     1     1     1];\r\nassert(isequal(connect_four_2(x),0))\r\n%%\r\nx = [2     2     1     1     2     1     2     1\r\n     1     2     2     1     1     1     1     2\r\n     1     2     1     1     1     2     2     2\r\n     2     1     2     2     2     1     1     2\r\n     1     1     2     1     2     1     2     2\r\n     2     1     1     2     2     2     2     1\r\n     1     1     2     1     2     1     2     1\r\n     1     2     1     1     1     1     2     1];\r\nassert(isequal(connect_four_2(x),0))\r\n\r\n%%\r\nx = [2     2     1     1     2     1     2     1\r\n     1     2     2     1     1     1     1     2\r\n     1     2     1     1     1     2     2     2\r\n     2     1     2     2     2     1     1     2\r\n     1     1     2     1     2     1     2     2\r\n     2     1     1     2     2     2     2     1\r\n     1     1     2     1     2     1     2     1\r\n     1     2     1     1     1     1     2     1\r\n     1     1     1     1     1     1     1     1];\r\nassert(isequal(connect_four_2(x),1))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-02-22T21:18:15.000Z","updated_at":"2026-07-29T13:51:35.000Z","published_at":"2020-02-23T06:10:14.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrevious Problem\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45354-connect-four-01\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/45354-connect-four-01\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt; \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45356-connect-four-02\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/45356-connect-four-02\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn addition to previous problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ In this case, there can be empty places on the board represented by 0.\\n\\n Also no of consecutive elements can be more than 4.]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45366,"title":"Connect Four - 04","description":"Previous Problem\r\n\r\n\u003chttps://www.mathworks.com/matlabcentral/cody/problems/45355-connect-four-03\u003e\r\n\r\n\r\nIn addition to the previous problem, in this case\r\n\r\n a 2 by 2 block will also be considered as a winning move.\r\n\r\nFor example,\r\n\r\n  x=[ 1 1 2 1 2\r\n      1 1 2 2 1\r\n      2 1 2 2 1\r\n      2 2 1 1 2]\r\n\r\nhere, there is a 2-by-2 block of 1 and 2. \r\n  ","description_html":"\u003cp\u003ePrevious Problem\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/45355-connect-four-03\"\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/45355-connect-four-03\u003c/a\u003e\u003c/p\u003e\u003cp\u003eIn addition to the previous problem, in this case\u003c/p\u003e\u003cpre\u003e a 2 by 2 block will also be considered as a winning move.\u003c/pre\u003e\u003cp\u003eFor example,\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ex=[ 1 1 2 1 2\r\n    1 1 2 2 1\r\n    2 1 2 2 1\r\n    2 2 1 1 2]\r\n\u003c/pre\u003e\u003cp\u003ehere, there is a 2-by-2 block of 1 and 2.\u003c/p\u003e","function_template":"function win=connect_four_4(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx=  [1     1     2     1     2\r\n     1     1     2     2     1\r\n     2     1     2     2     1\r\n     2     2     1     1     2]\r\nassert(isequal(connect_four_4(x),2))\r\n%%\r\nx =  [ 1 1 1 1 1 1 1 1;\r\n       2 2 2 2 2 2 2 2;\r\n       2 1 2 1 0 1 2 1;\r\n       1 2 1 2 1 2 1 2;\r\n       2 1 2 1 2 1 2 1;\r\n       1 2 1 2 1 2 1 1];\r\nassert(isequal(connect_four_4(x),'invalid'))\r\n%%\r\nx =  [ 1 1 1 1 1 1 1 1;\r\n       2 2 2 2 2 2 2 2;\r\n       2 1 2 1 2 1 2 1;\r\n       1 2 1 2 1 2 1 2;\r\n       2 1 2 1 2 1 2 1;\r\n       1 2 1 2 1 2 1 1];\r\nassert(isequal(connect_four_4(x),2))\r\n %%\r\n x =  [1     1     1     1     1     1     1     1     2\r\n     2     2     2     2     2     2     2     2     1\r\n     2     1     2     1     2     1     2     1     2\r\n     1     2     1     2     1     2     1     2     2\r\n     2     1     2     1     2     1     2     1     2\r\n     1     2     1     1     1     2     1     1     2\r\n     1     1     1     1     1     1     1     1     1];\r\n assert(isequal(connect_four_4(x),1))\r\n %%\r\n x = [2     2     1     1     2     1     2     1\r\n     1     2     2     1     1     1     1     2\r\n     1     2     1     1     1     2     2     2\r\n     2     1     2     2     2     1     1     2\r\n     1     1     2     1     2     1     2     2\r\n     2     1     1     2     2     2     2     1\r\n     1     1     2     1     2     1     2     1\r\n     1     2     1     1     1     1     2     1]\r\n assert(isequal(connect_four_4(x),1))\r\n %%\r\n x = [2     2     1     1     2     1     2     1\r\n     1     2     2     2     1     1     1     2\r\n     1     2     1     1     1     2     2     2\r\n     2     1     2     2     2     1     1     2\r\n     1     1     2     1     2     1     2     2\r\n     2     1     1     2     2     2     2     1\r\n     1     1     2     1     2     1     2     1\r\n     1     2     1     1     1     1     2     1]\r\nassert(isequal(connect_four_4(x),2))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2020-03-16T18:43:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-03-16T18:31:40.000Z","updated_at":"2026-07-29T14:01:01.000Z","published_at":"2020-03-16T18:43:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrevious Problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45355-connect-four-03\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/45355-connect-four-03\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn addition to the previous problem, in this case\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ a 2 by 2 block will also be considered as a winning move.]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x=[ 1 1 2 1 2\\n    1 1 2 2 1\\n    2 1 2 2 1\\n    2 2 1 1 2]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ehere, there is a 2-by-2 block of 1 and 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1907,"title":"Capture the flag(s)","description":"Flags are distributed randomly on a large board. Starting from the corner position your goal is to capture as many flags as possible in at most N moves.\r\nDescription:\r\nThe board is described by a matrix B with 1's at the flag positions, and 0's otherwise.\r\nE.g.\r\n B = [0 0 1 1; \r\n      0 0 1 1;\r\n      0 0 1 0];\r\n\r\n N = 6;\r\nYou are starting at the top-left corner (row=1, col=1) and are allowed N steps (steps are up/down/left/right movements, no diagonal movements allowed).\r\nReturn a trajectory attempting to maximize the number of flags captured. The output of your function should be a Nx2 matrix of the form [row, col] (not including the initial [1,1] position) visiting as many flags as possible.\r\nE.g.\r\n path = [1 2;\r\n         1 3;\r\n         1 4;\r\n         2 4;\r\n         2 3;\r\n         3 3];\r\nThis solution captures all 5 flags on the board.\r\nScoring:\r\nYour function will receive a score equal to the number of non-visited flags across all 50 of the testsuite problems. You need to leave at most 10,000 flags univisited (among 50,000 total flags) to pass this problem.\r\nNote:\r\nThe boards and number of movements allowed will be large. Optimizing over all possible trajectories is very likely to time out.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 676px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 338px; transform-origin: 401px 338px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 21px; text-align: left; transform-origin: 377px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFlags are distributed randomly on a large board. Starting from the corner position your goal is to capture as many flags as possible in at most N moves.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDescription\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe board is described by a matrix\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eB\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with 1's at the flag positions, and 0's otherwise.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eE.g.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 90px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 397px 45px; transform-origin: 397px 45px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); 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text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e B = [0 0 1 1; \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e      0 0 1 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e      0 0 1 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e N = 6;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 21px; text-align: left; transform-origin: 377px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are starting at the top-left corner (row=1, col=1) and are allowed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e steps (steps are up/down/left/right movements, no diagonal movements allowed).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 21px; text-align: left; transform-origin: 377px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn a trajectory attempting to maximize the number of flags captured. The output of your function should be a\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eNx2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix of the form\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[row, col]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (not including the initial [1,1] position) visiting as many flags as possible.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eE.g.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 108px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 397px 54px; transform-origin: 397px 54px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e path = [1 2;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e         1 3;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e         1 4;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e         2 4;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e         2 3;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e         3 3];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis solution captures all 5 flags on the board.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eScoring\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 21px; text-align: left; transform-origin: 377px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour function will receive a score equal to the number of non-visited flags across all 50 of the testsuite problems. You need to leave at most 10,000 flags univisited (among 50,000 total flags) to pass this problem.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNote\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 21px; text-align: left; transform-origin: 377px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe boards and number of movements allowed will be large. Optimizing over all possible trajectories is very likely to time out.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function path = capture_the_flag(B,N)\r\npath=[1 2];\r\n","test_suite":"%%\r\n% test cases\r\n\r\nrandn('seed',0);\r\nrand('seed',0);\r\nN=randi([1000 4000],50,1);\r\nS=randi([1,50],50,1);\r\nBoards=arrayfun(@(s)convn(randn(100),ones(s)/s^2,'same'),S,'uni',0); \r\n\r\nFLAGSLEFT=0;\r\nDOPLOT=false;\r\ntic;\r\nfor board=1:50\r\n B=Boards{board};\r\n sB=sort(B(:));\r\n B=double(B\u003esB(round(numel(sB)*.9)));\r\n n=N(board);\r\n path=capture_the_flag(B,n);\r\n assert(size(path,1)\u003c=n,'too many steps');\r\n assert(all(sum(abs(diff([1,1;path])),2)\u003c=1),'no jumping allowed');\r\n if DOPLOT\r\n    imagesc(B);\r\n    hold on;\r\n    plot(path(:,2),path(:,1),'y-');\r\n    hold off;\r\n    axis equal;\r\n    axis off;\r\n    set(gcf,'color',0*[1 1 1]);\r\n    colormap(.5*gray);\r\n    drawnow;\r\n end\r\n B(1)=0;\r\n B((path-1)*[1;size(B,1)]+1)=0;\r\n fprintf('test %d; left %d flags\\n',board,nnz(B));\r\n FLAGSLEFT=FLAGSLEFT+nnz(B);\r\nend\r\ntoc;","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":43,"edited_by":1,"edited_at":"2026-02-11T16:03:17.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2026-02-11T16:03:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-10-01T05:38:22.000Z","updated_at":"2026-07-28T14:22:02.000Z","published_at":"2013-10-01T06:27:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFlags are distributed randomly on a large board. Starting from the corner position your goal is to capture as many flags as possible in at most N moves.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDescription\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe board is described by a matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with 1's at the flag positions, and 0's otherwise.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eE.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ B = [0 0 1 1; \\n      0 0 1 1;\\n      0 0 1 0];\\n\\n N = 6;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are starting at the top-left corner (row=1, col=1) and are allowed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e steps (steps are up/down/left/right movements, no diagonal movements allowed).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn a trajectory attempting to maximize the number of flags captured. The output of your function should be a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNx2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix of the form\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[row, col]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (not including the initial [1,1] position) visiting as many flags as possible.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eE.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ path = [1 2;\\n         1 3;\\n         1 4;\\n         2 4;\\n         2 3;\\n         3 3];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis solution captures all 5 flags on the board.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour function will receive a score equal to the number of non-visited flags across all 50 of the testsuite problems. You need to leave at most 10,000 flags univisited (among 50,000 total flags) to pass this problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNote\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe boards and number of movements allowed will be large. Optimizing over all possible trajectories is very likely to time out.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42829,"title":"Number construction III","description":"Given a positive integer, n, return a, b and c, such that\r\n\r\n1. n = a^1.5+b^2.5+c^3.5\r\n\r\n2. a, b and c are all positive integers greater than 1\r\n\r\nIf a solution does not exist, set all three output variables to zero.\r\n\r\nExample 1:\r\n\r\nn = 168\r\n\r\na = 4\r\n\r\nb = 4\r\n\r\nc = 4\r\n\r\nExample 2:\r\n\r\nn = 100\r\n\r\na = 0\r\n\r\nb = 0\r\n\r\nc = 0","description_html":"\u003cp\u003eGiven a positive integer, n, return a, b and c, such that\u003c/p\u003e\u003cp\u003e1. n = a^1.5+b^2.5+c^3.5\u003c/p\u003e\u003cp\u003e2. a, b and c are all positive integers greater than 1\u003c/p\u003e\u003cp\u003eIf a solution does not exist, set all three output variables to zero.\u003c/p\u003e\u003cp\u003eExample 1:\u003c/p\u003e\u003cp\u003en = 168\u003c/p\u003e\u003cp\u003ea = 4\u003c/p\u003e\u003cp\u003eb = 4\u003c/p\u003e\u003cp\u003ec = 4\u003c/p\u003e\u003cp\u003eExample 2:\u003c/p\u003e\u003cp\u003en = 100\u003c/p\u003e\u003cp\u003ea = 0\u003c/p\u003e\u003cp\u003eb = 0\u003c/p\u003e\u003cp\u003ec = 0\u003c/p\u003e","function_template":"function [a b c] = numcons(n)\r\n  a = n;\r\n  b = n;\r\n  c = n;\r\nend","test_suite":"%%\r\nn = 100;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 888;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 19666;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 314159;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 1100;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 116600;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 16999;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 10000040;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 94940;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 9990;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":"2016-04-28T18:19:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-04-25T11:29:04.000Z","updated_at":"2026-08-04T19:45:23.000Z","published_at":"2016-04-25T11:29:04.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a positive integer, n, return a, b and c, such that\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1. n = a^1.5+b^2.5+c^3.5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2. a, b and c are all positive integers greater than 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf a solution does not exist, set all three output variables to zero.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 168\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eb = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eb = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1533,"title":"Criss-Cross Verification: NHL","description":"This Challenge is to verify a Criss-Cross matrix has no invalid words,contains all of the word set, and all are simply connected (Up/Down/Left/Right). Separation, UDLR, must exist between non-intersecting words. Diagonal is considered separate.\r\n\r\nThe word set is a cell array. The matrix is an array of Char with spaces being represented by '`', char(96), which is under the tilde on my keyboard.\r\n\r\n*Example:*\r\n\r\n*Input:*\r\n\r\n  dict={'abcd' 'cag'}\r\n  \r\n  Achar=['abcd'\r\n         '``a`'\r\n         '``g`'];\r\n\r\n*Output:* Validity (1 for Valid, 0 for Invalid)\r\n\r\n\r\n*Related Challenges:*\r\n\r\nThis Challenge is derived from GAMES August 2013 Contest \"On the Ice\" to fit all NHL Team names into a minimum area grid using the Criss-Cross rules.\r\nCurrent Best solution is 19x19, 6/3/2013. Contest ends 8/31/2013.\r\n\r\n1) Create an NHL Criss-Cross  (Score by Area)\r\n\r\n2) Complete a Criss-Cross\r\n\r\n3) Create a Criss-Cross dictionary from a matrix","description_html":"\u003cp\u003eThis Challenge is to verify a Criss-Cross matrix has no invalid words,contains all of the word set, and all are simply connected (Up/Down/Left/Right). Separation, UDLR, must exist between non-intersecting words. Diagonal is considered separate.\u003c/p\u003e\u003cp\u003eThe word set is a cell array. The matrix is an array of Char with spaces being represented by '`', char(96), which is under the tilde on my keyboard.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003edict={'abcd' 'cag'}\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eAchar=['abcd'\r\n       '``a`'\r\n       '``g`'];\r\n\u003c/pre\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e Validity (1 for Valid, 0 for Invalid)\u003c/p\u003e\u003cp\u003e\u003cb\u003eRelated Challenges:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eThis Challenge is derived from GAMES August 2013 Contest \"On the Ice\" to fit all NHL Team names into a minimum area grid using the Criss-Cross rules.\r\nCurrent Best solution is 19x19, 6/3/2013. Contest ends 8/31/2013.\u003c/p\u003e\u003cp\u003e1) Create an NHL Criss-Cross  (Score by Area)\u003c/p\u003e\u003cp\u003e2) Complete a Criss-Cross\u003c/p\u003e\u003cp\u003e3) Create a Criss-Cross dictionary from a matrix\u003c/p\u003e","function_template":"function valid=check_crisscross(Achar,dict_cell)\r\n valid=1;\r\nend","test_suite":"%%\r\ndict_cell={'abcd'\r\n'cat'\r\n'dot'};\r\n\r\nAchar=['abcd'\r\n'``a`'\r\n'dot`'];\r\n\r\nvalid=check_crisscross(Achar,dict_cell);\r\nassert(valid==1)\r\n%%\r\ndict_cell={'abcd'\r\n'cat'\r\n'dot'\r\n'bcd'};\r\n\r\nAchar=['abcd'\r\n'``a`'\r\n'dot`'];\r\n% Need a unique bcd word\r\nvalid=check_crisscross(Achar,dict_cell);\r\nassert(valid==0)\r\n%%\r\ndict_cell={'abcd'\r\n'cat'\r\n'dot'\r\n'acd'};\r\n\r\nAchar=['abcd'\r\n'c`a`'\r\n'dot`'];\r\n% valid matrix\r\nvalid=check_crisscross(Achar,dict_cell);\r\nassert(valid==1)\r\n%%\r\ndict_cell={'avalanche'\r\n'bluejackets'\r\n'blackhawks'\r\n'blues'\r\n'bruins'\r\n'canadiens'\r\n'canucks'\r\n'capitals'\r\n'coyotes'\r\n'devils'\r\n'ducks'\r\n'flames'\r\n'flyers'\r\n'hurricanes'\r\n'islanders'\r\n'jets'\r\n'kings'\r\n'lightning'\r\n'mapleleafs'\r\n'oilers'\r\n'panthers'\r\n'penguins'\r\n'predators'\r\n'rangers'\r\n'redwings'\r\n'sabres'\r\n'senators'\r\n'sharks'\r\n'stars'\r\n'wild'};\r\n\r\nAchar=['```````hurricanes``s'\r\n'rangers`````o````m`e'\r\n'e`````t```flyers`a`n'\r\n'd`````a`````o````p`a'\r\n'w`````r`capitals`l`t'\r\n'i`ducks`````e````e`o'\r\n'n```a``sabres````l`r'\r\n'g`kings``l````oilers'\r\n's```u``bruins````a``'\r\n'````c````e`````p`f``'\r\n'blackhawks``sharks``'\r\n'``v`s``````````e````'\r\n'``a````````i```d``p`'\r\n'`bluejackets```a``e`'\r\n'``a````````lightning'\r\n'canadiens``a```o``g`'\r\n'``c``````panthers`u`'\r\n'``h`w``````d```s``i`'\r\n'`devils```jets````n`'\r\n'````l``````r``````s`'\r\n'````d`flames````````'];\r\n\r\nvalid=check_crisscross(Achar,dict_cell);\r\nassert(valid==1)\r\n%%\r\ndict_cell={'avalanche'\r\n'bluejackets'\r\n'blackhawks'\r\n'blues'\r\n'bruins'\r\n'canadiens'\r\n'canucks'\r\n'capitals'\r\n'coyotes'\r\n'devils'\r\n'ducks'\r\n'flames'\r\n'flyers'\r\n'hurricanes'\r\n'islanders'\r\n'jets'\r\n'kings'\r\n'lightning'\r\n'mapleleafs'\r\n'oilers'\r\n'panthers'\r\n'penguins'\r\n'predators'\r\n'rangers'\r\n'redwings'\r\n'sabres'\r\n'senators'\r\n'sharks'\r\n'stars'\r\n'wild'};\r\n\r\nAchar=['```````hurricanes``s'\r\n'rangers`````o````m`e'\r\n'e`````t```flyers`a`n'\r\n'd`````a`````o````p`a'\r\n'w`````r`capitals`l`t'\r\n'i`ducks`````e````e`o'\r\n'n```a``sabres````l`r'\r\n'g`kings``l````oilers'\r\n's```u``bruins````a``'\r\n'````c````e`````p`f``'\r\n'blackhawks``sharks``'\r\n'``v`s``````````e````'\r\n'``a````````i```d``p`'\r\n'`bluejackets```a``e`'\r\n'``a````````lightning'\r\n'canadiens``a```o``g`'\r\n'``c``````panthers`u`'\r\n'``h`w``````d```s``i`'\r\n'`devils```jets````n`'\r\n'````l``````r```jets`'\r\n'````d`flames````````'];\r\n\r\n% jets is duplicated\r\n\r\nvalid=check_crisscross(Achar,dict_cell);\r\nassert(valid==0)\r\n%%\r\ndict_cell={'avalanche'\r\n'bluejackets'\r\n'blackhawks'\r\n'blues'\r\n'bruins'\r\n'canadiens'\r\n'canucks'\r\n'capitals'\r\n'coyotes'\r\n'devils'\r\n'ducks'\r\n'flames'\r\n'flyers'\r\n'hurricanes'\r\n'islanders'\r\n'jets'\r\n'kings'\r\n'lightning'\r\n'mapleleafs'\r\n'oilers'\r\n'panthers'\r\n'penguins'\r\n'predators'\r\n'rangers'\r\n'redwings'\r\n'sabres'\r\n'senators'\r\n'sharks'\r\n'stars'\r\n'wild'};\r\n\r\nAchar=['```````hurricanes``s'\r\n'rangers`````o````m`e'\r\n'e`````t```flyers`a`n'\r\n'd`````a`````o````p`a'\r\n'w`````r`capitals`l`t'\r\n'i`ducks`````e````e`o'\r\n'n```a``sabres````l`r'\r\n'g`kings``l````oilers'\r\n's```u``bruins````a``'\r\n'````c````e`````p`f``'\r\n'blackhawks``sharks``'\r\n'``v`s``````````e````'\r\n'``a````````i```d``p`'\r\n'`bluejackets```a``e`'\r\n'``a````````lightning'\r\n'canadiens``a```o``g`'\r\n'``c``````panthers`u`'\r\n'``h`w``````d```s``i`'\r\n'`devils````e``````n`'\r\n'````l``````r``````s`'\r\n'````d`flames``jets``'];\r\n\r\n% Non-Connected jets\r\n\r\nvalid=check_crisscross(Achar,dict_cell);\r\nassert(valid==0)\r\n%%\r\ndict_cell={'avalanche'\r\n'bluejackets'\r\n'blackhawks'\r\n'blues'\r\n'bruins'\r\n'canadiens'\r\n'canucks'\r\n'capitals'\r\n'coyotes'\r\n'devils'\r\n'ducks'\r\n'flames'\r\n'flyers'\r\n'hurricanes'\r\n'islanders'\r\n'jets'\r\n'kings'\r\n'lightning'\r\n'mapleleafs'\r\n'oilers'\r\n'panthers'\r\n'penguins'\r\n'predators'\r\n'rangers'\r\n'redwings'\r\n'sabres'\r\n'senators'\r\n'sharks'\r\n'stars'\r\n'wild'};\r\n\r\nAchar=['```````hurricanes``s'\r\n'rangers`````o````m`e'\r\n'e`````t```flyers`a`n'\r\n'd`````a`````o````p`a'\r\n'w`````r`capitals`l`t'\r\n'i`ducks`````e````e`o'\r\n'n```a``sabres````l`r'\r\n'g`kings``l````oilers'\r\n's```u``bruins````a``'\r\n'````c````e`````p`f``'\r\n'blackhawks``sharks``'\r\n'``v`s``````````e````'\r\n'``a````````i```d````'\r\n'`bluejackets```a````'\r\n'``a````````lightning'\r\n'canadiens``a```o````'\r\n'``c``````panthers```'\r\n'``h`w``````d```s````'\r\n'`devils```jets``````'\r\n'````l``````r````````'\r\n'````d`flames````````'];\r\n% Missing penguins\r\nvalid=check_crisscross(Achar,dict_cell);\r\nassert(valid==0)\r\n%%\r\ndict_cell={'avalanche'\r\n'bluejackets'\r\n'blackhawks'\r\n'blues'\r\n'bruins'\r\n'canadiens'\r\n'canucks'\r\n'capitals'\r\n'coyotes'\r\n'devils'\r\n'ducks'\r\n'flames'\r\n'flyers'\r\n'hurricanes'\r\n'islanders'\r\n'jets'\r\n'kings'\r\n'lightning'\r\n'mapleleafs'\r\n'oilers'\r\n'panthers'\r\n'penguins'\r\n'predators'\r\n'rangers'\r\n'redwings'\r\n'sabres'\r\n'senators'\r\n'sharks'\r\n'stars'\r\n'wild'};\r\n\r\nAchar=['```````hurricanes``s'\r\n'rangers`````o````m`e'\r\n'e```jets``flyers`a`n'\r\n'd`````a`````o````p`a'\r\n'w`````r`capitals`l`t'\r\n'i`ducks`````e````e`o'\r\n'n```a``sabres````l`r'\r\n'g`kings``l````oilers'\r\n's```u``bruins````a``'\r\n'````c````e`````p`f``'\r\n'blackhawks``sharks``'\r\n'``v`s``````````e````'\r\n'``a````````i```d``p`'\r\n'`bluejackets```a``e`'\r\n'``a````````lightning'\r\n'canadiens``a```o``g`'\r\n'``c``````panthers`u`'\r\n'``h`w``````d```s``i`'\r\n'`devils````e``````n`'\r\n'````l``````r``````s`'\r\n'````d`flames````````'];\r\n% invalid jets on row 3\r\nvalid=check_crisscross(Achar,dict_cell);\r\nassert(valid==0)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-06-02T16:57:18.000Z","updated_at":"2026-07-23T08:49:46.000Z","published_at":"2013-06-02T17:33:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to verify a Criss-Cross matrix has no invalid words,contains all of the word set, and all are simply connected (Up/Down/Left/Right). Separation, UDLR, must exist between non-intersecting words. Diagonal is considered separate.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe word set is a cell array. The matrix is an array of Char with spaces being represented by '`', char(96), which is under the tilde on my keyboard.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[dict={'abcd' 'cag'}\\n\\nAchar=['abcd'\\n       '``a`'\\n       '``g`'];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Validity (1 for Valid, 0 for Invalid)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRelated Challenges:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is derived from GAMES August 2013 Contest \\\"On the Ice\\\" to fit all NHL Team names into a minimum area grid using the Criss-Cross rules. Current Best solution is 19x19, 6/3/2013. Contest ends 8/31/2013.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1) Create an NHL Criss-Cross (Score by Area)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2) Complete a Criss-Cross\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3) Create a Criss-Cross dictionary from a matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":58468,"title":"ICFP 2022 - Create Command Script from Color-Region-Fill","description":"The ICFP2023 Challenge is Jul 7-10, registraion opens late June. Updates at TwitICFP2023. These contests are insanely complicated and competitive. The challenge evolves every 12 hours with new files and rule updates.\r\nThe ICFP2022 HomePage has details of the RoboPaint contest. Twit2022, WriteUps, PriorEvents, Spec, ImageSubmissions, Puzzles, SawickiSolutions are useful links. Posted 6/27/23.\r\nThe of Command Scripting is detailed in the function template. The commands have been matrixed and simplified but are based onthe Spec. Commands are Horiz split, Vertical split, Quad split, Color, and Reset.\r\nGiven a sequence of regions and colors writes that produce the Lower Right image, Img 13999, create commands to fill the image. The Goal 21.png.  Base costs  Cmds:1525, Img 13999, Submission combined score must be less than 17000.\r\nVisualizations of Image creation: [21 FBS Draw], adjust speed in settings.\r\nInput: Color regions  [M,7] of [r1 r2 c1 c2 r g b] where r1,c1 is TopLeft of a square and r2,c2 is BotRight\r\nOutput: cmds  [N,5] matrix of integer cmd, index, and parameters that vary based on cmd\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 659.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 329.75px; transform-origin: 407px 329.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://icfpcontest2023.github.io/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eICFP2023\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 197.5px 8px; transform-origin: 197.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Challenge is Jul 7-10, registraion opens late June. Updates at \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://twitter.com/icfpcontest2023\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eTwitICFP2023\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 95px 8px; transform-origin: 95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. These contests are insanely complicated and competitive. The challenge evolves every 12 hours with new files and rule updates.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://icfpcontest2022.github.io/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eICFP2022 HomePage\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 120px 8px; transform-origin: 120px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has details of the RoboPaint contest. \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://twitter.com/icfpcontest2022\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eTwit2022\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://icfpcontest2022.github.io/writeups/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWriteUps\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.icfpconference.org/contest.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePriorEvents\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://icfpcontest2022.github.io/Specifications/spec_v2_4.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSpec\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://gist.github.com/RafaelBocquet/e464c2d199f2d7a725cafdc22b30df7f\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eImageSubmissions\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://github.com/icfpc-unagi/icfpc2022/tree/main/problems\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePuzzles\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSawickiSolutions\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.5px 8px; transform-origin: 103.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are useful links. Posted 6/27/23.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.5px 8px; transform-origin: 381.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe of Command Scripting is detailed in the function template. The commands have been matrixed and simplified but are based onthe Spec. Commands are Horiz split, Vertical split, Quad split, Color, and Reset.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376px 8px; transform-origin: 376px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a sequence of regions and colors writes that produce the Lower Right image, Img 13999, create commands to fill the image. The Goal 21.png.  Base costs  Cmds:1525, Img 13999, Submission combined score must be less than 17000.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 105px 8px; transform-origin: 105px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eVisualizations of Image creation: [\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://drive.google.com/file/d/19MSfeGmn223KCGujl8Le6tQPqbW4EFXT/view?usp=drive_link\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e21 FBS Draw\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.5px 8px; transform-origin: 82.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e], adjust speed in settings.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 323.5px 8px; transform-origin: 323.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInput: Color regions  [M,7] of [r1 r2 c1 c2 r g b] where r1,c1 is TopLeft of a square and r2,c2 is BotRight\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 278.5px 8px; transform-origin: 278.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOutput: cmds  [N,5] matrix of integer cmd, index, and parameters that vary based on cmd\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 365.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 182.75px; text-align: left; transform-origin: 384px 182.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 360px;height: 360px\" 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\" 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data-image-state=\"image-loaded\" width=\"360\" height=\"360\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function cmds = create_cmds(regions,G)\r\n% regions is r1 r2 c1 c2 r g bof color regions to create\r\n% G is goal image [400,400,3]\r\n%The FSB set of paint commands balances Img and Cmd costs\r\n% Initial Commands could be\r\n% 4     1   254   254   254\r\n% 1     1   397     0     0\r\n% 4     1   209    88    58\r\n% 0     0     0     0     0\r\n% 3     1   392   381     0\r\n% 4     1    39    12    10\r\n% ...\r\n% 1     1   381     0     0\r\n% 2     1   380     0     0\r\n% 2     1   103     0     0\r\n% 4     4    10     2     4\r\n%\r\n%Painting small regions is very expensive thus overwrites are used\r\n%Creating small regions is expensive. Goal is to cut on largest region possible\r\n\r\n%Create Image script\r\n%  Image Delta Cost ranges around 10K\r\n%  Efficient cmds can be \u003c5K while direct coloring is \u003e100K\r\n%\r\n%Score it for commands\r\n%score it for image deviation \r\n%cost(move,block,canvas)=round(base_cost(move)*size(canvas)/size(block)\r\n%Point Cut 10  Done on abs of canvas, creates 4 sub-indices\r\n%Line Cut   7  Done on abs of canvas, creates 2 sub-indices\r\n%Color      5  Index filled by r,g,b\r\n%Swap       3  Index to Index swaps r,g,b contents\r\n%Merge      1  Index with Index creates new Level0 index\r\n%Reset      1\r\n% size(rect)=width*height\r\n%Similarity Checker\r\n%alpha=.005\r\n% for each pixel\r\n% rdist=(p1.r-p2.r)^2\r\n% gdist=(p1.g-p2.g)^2\r\n% bdist=(p1.b-p2.b)^2\r\n% dist=(rdist+gdist+bdist)^.5\r\n%scr_diff=round(alpha*sum(dist(:))\r\n%\r\n%Command costs\r\n%Reset/H/V/XY/C/M/S 1/7/7/10/5/1/3  [0:6] cmd ids\r\n%cmds have various numbers of parameters\r\n% cmd: cmdId region p1 p2 p3    Note: no region for reset\r\n% Reset cost is based on 1*(160000/(sum of min+max regions) \r\n% Reset is a matlab variant to simplify cmds\r\n% [1] is the starting regions andafter reset, ones(400)\r\n% H: 1 1 100 0 0 creates [1;2] where 1 is [1:100,1:400] 2 is [101:400 1:400]\r\n%  the cost is based on orig ones(400) thus 7, 1\u003c=p1\u003c400\r\n% V: 2 1 100 0 0 creates [1 2] where 1 is [1:400,1:100] 2 is [1:400 101:400]\r\n%  the cost is based on orig ones(400) thus 7, 1\u003c=p1\u003c400\r\n% XY: 3 1 100 150 0 creates [1 2;4 3] cost uses orig ones(400) thus 10, p1\u003c400, p2\u003c400\r\n%  1 is [  1:100,  1:150] 2 is [  1:100 151:400]\r\n%  4 is [101:400,  1:150] 3 is [101:400 151:400]\r\n% Color: 4 1 r g b sets all points in reg 1 to rgb, cost 5, 0\u003c=rgb\u003c=255\r\n% Swap: Not implemented\r\n% Merge: 6 idx1 idx2 0 0, Cost based on combined area idx1+idx2\r\n%  For XY example a cmd 6 1 2 0 0 sets idx2 to 1. [1:100 1:400] cost 1*4\r\n%\r\n% Commanding examples for the various regions\r\n% S=255*ones(400,400,3) is starting canvas, White\r\n%Image with (1,1,:)=0, Black square at pixel 1,1\r\n% Direct using XY and Color\r\n% 3 1 1 1 0    Cost 10*1\r\n% 4 1 255 255 255   Cost 5*160000   Coloring small points is costly\r\n% Using H,V,Color\r\n% 1 1 1 0 0    Cost 7*1  creates regions [1;2]\r\n% 2 1 1 0 0    Cost 7*400 with regions [1 3;2 2]\r\n% 5 1 255 255 255   Cost 5*160000   Coloring small points is costly\r\n% Using Color,V,Color,Reset,H,Color\r\n% 4 1 0 0 0   Cost 5   Coloring large areas is cheap\r\n% 2 1 1 0 0   Cost 7   [1 2], 1 is [1:400 1]  2 is [1:400 2:400]\r\n% 4 2 2555 255 255   Cost 5*round(400/400*400/399)=5  Low cost color\r\n% 0 0 0 0 0   Cost 1*1  Merge of 1,2 is whole img\r\n% 1 1 1 0 0   Cost 7   [1; 2], 1 is [1 1:400]  2 is [2:400 1:400]\r\n% 4 2 2555 255 255   Cost 5*round(400/399*400/400)=5  Low cost color\r\n% Total Cost 30\r\n%\r\n% Image with central rectangle [190:230, 210:240,:] set to blk [0 0 0]\r\n%Using  XY,XY,Color\r\n% 3 1 189 209 0   [1 2;4 3] regions [1:189 1:209] [1:189 210:400] 4[190:400 1:209]\r\n%   region 3: [190:400 210:400]  Cost 10\r\n% 3 3 230 240 0] regions [1 2 2;4 3 5;4 7 6] with 3 becoming [190:230, 210:240]\r\n%  New regions are numbers CW/L-R,T-B with base region value unchanged\r\n%  cost 10*round(400/211*400/191)=10*4=40\r\n% 4 3 0 0 0   Cost 5*round(400/41*400/31)=5*126=630  Moderate cost color\r\n% Total Cost 680    XY,XY,Color\r\n%Using V,V,H,H,C\r\n% 2 1 209 0 0  [1 2] regs [1:400 1:209] [1:400 210:400]  Cost 7\r\n% 2 2 240 0 0  [1 2 3] regs 2[1:400 210:240] 3[1:400 241:400]  Cost 14\r\n% 1 2 230 0 0  [1 2 3;1 4 3] regs 2[1:230 210:240] 4[231:400 210:240]  Cost 91\r\n% 1 2 209 0 0  [1 2 3;1 5 3;1 4 3] regs 2[1:209 210:240] 5[210:230 210:240]  Cost 154\r\n% 4 5 0 0 0   Cost 5*round(400/41*400/31)=5*126=630  Moderate cost color\r\n% Total Cost 896  V,V,H,H,C\r\n\r\n%Using XY,Color,Reset,V,Color,Reset,H,Color\r\n% 3 1 189 209 0  [1 2;4 3] regs [1:189 1:209] [1:189 210:400] 4[190:400 1:209]\r\n%   region 3: [190:400 210:400]  Cost 10\r\n% 4 3 0 0 0  Cost 5*round(400/211*400/191)=5*4=20\r\n% 0 0 0 0 0  Cost 1*round(160000/(44099+40301))=2   Reset\r\n% 2 1 240 0 0  [1 2] regs [1:400 1:240] [1:400 241:400]  Cost 7\r\n% 4 2 0 0 0  Cost 5*round(400/400*400/160)=5*3=15\r\n% 0 0 0 0 0  Cost 1   Reset\r\n% 1 1 230 0 0  [1; 2] regs [1:230 1:4000] [231:400 1:400]  Cost 7\r\n% 4 2 0 0 0  Cost 5*round(400/171*400/400)=5*2=10\r\n% Total Cost 72   XY,Color,Reset,V,Color,Reset,H,Color\r\n\r\n  cmds=[];\r\n  \r\n  %Suggested outline : Focus is on optimizing cuts in Best_Draw2\r\n  Gidx=ones(size(G,1));\r\n  bArea=400*400;\r\n  for ireg=1:size(regions,1) % Draw2\r\n   vrrcc=regions(ireg,:);\r\n   GregA=(vrrcc(2)-vrrcc(1)+1)*(vrrcc(4)-vrrcc(3)+1);\r\n   ptr=1; \r\n   Gidx=Gidx*0+1; % Assume start each region with a clean idx board\r\n  \r\n   while nnz(Gidx==ptr)\u003eGregA % Algorithm does not allow to be \u003c GregA\r\n    [bGidx,bcmd,p1,p2]=Best_Draw2(Gidx,vrrcc);\r\n    cmds=[cmds;bcmd ptr p1 p2 0]; % H/V/XY  Multiple H/V/XY cmds to create region\r\n    Gidx=bGidx;\r\n    ptr=Gidx(vrrcc(1),vrrcc(3)); % used in while for next H/V/XY cmd and  Color cmd\r\n   end\r\n  \r\n   cmds=[cmds;4 ptr vrrcc(5:7)]; % Color Command\r\n  \r\n   if nnz(Gidx==1)==bArea,continue;end\r\n   if ireg==size(regions,1),continue;end % No final reset\r\n   cmds=[cmds;0 0 0 0 0]; % Reset Command     ptr=1 Gidx(:,:)=1 \r\n  end % ireg \r\nend % create cmds\r\n\r\nfunction [bGidx,bcmd,p1,p2]=Best_Draw2(Gidx,vrrcc)\r\n %vrrcc goal region draw/color  r1 r2 c1 c2 r g b\r\n % Hr1 Hr2 Vc1 Vc2 xyTL xyLR xyTR xyLL\r\n bcmd=0;p1=0;p2=0;bGidx=Gidx;\r\n ptrmax=max(Gidx(:));\r\n Amax=0; %\r\n \r\n gr1=vrrcc(1);gr2=vrrcc(2);gc1=vrrcc(3);gc2=vrrcc(4); %goal region\r\n gA=(gr2-gr1+1)*(gc2-gc1+1); % Goal region Area\r\n ptr=Gidx(gr1,gc1); % region idx to process\r\n [r1, c1]=find(Gidx==ptr,1,'first'); %Common to H/V/XY/C\r\n [r2, c2]=find(Gidx==ptr,1,'last');\r\n \r\n %Update region that maximizes area unless cmd achieves r1 r2 c1 c2\r\n \r\n %H r1  Gidx(p1+1:r2,c1:c2)=ptrmax+1;  p1=cmd param\r\n  if gr1\u003er1\r\n   nGidx=Gidx;\r\n   nGidx(gr1:r2,c1:c2)=ptrmax+1; %Set new region\r\n   if nnz(nGidx==ptrmax+1)\u003eAmax || nnz(nGidx==ptrmax+1)==gA\r\n    Amax=nnz(nGidx==ptrmax+1);\r\n    p1=gr1-1; %r1\u003c=p1\u003cr2\u003c=400\r\n    bGidx=nGidx;\r\n    bcmd=1;\r\n    if nnz(nGidx==ptrmax+1)==gA, return;end\r\n   end\r\n  end\r\n  \r\n  \r\n  %H r2  Gidx(p1+1:r2,c1:c2)=ptrmax+1;  p1=cmd param\r\n  if r2\u003egr2\r\n   nGidx=Gidx;\r\n   \r\n  end\r\n  \r\n %V c1  Gidx(r1:r2,p1+1:c2)=ptrmax+1;\r\n  if gc1\u003ec1\r\n   nGidx=Gidx;\r\n   nGidx(r1:r2,gc1:c2)=ptrmax+1; %Set new region\r\n   if nnz(nGidx==ptrmax+1)\u003eAmax || nnz(nGidx==ptrmax+1)==gA\r\n    Amax=nnz(nGidx==ptrmax+1);\r\n    p1=gc1-1; %c1\u003c=p1\u003cc2\u003c=400\r\n    bGidx=nGidx;\r\n    bcmd=2;\r\n    if nnz(nGidx==ptrmax+1)==gA, return;end\r\n   end\r\n  end\r\n  \r\n %V c2  Gidx(r1:r2,p1+1:c2)=ptrmax+1;\r\n  if c2\u003egc2\r\n   nGidx=Gidx;\r\n   \r\n  end\r\n  \r\n%   Gidx(r1:p1,c1:p2)=ptr; % TL region\r\n%   Gidx(r1:p1,p2+1:c2)=ptrmax+1; % region to right is new\r\n%   Gidx(p1+1:r2,p2+1:c2)=ptrmax+2; % region to right and down is new\r\n%   Gidx(p1+1:r2,c1:p2)=ptrmax+3; % region to below  is new\r\n    \r\n % XY r1c1 gr1gc1 TL reg3\r\n  if r1\u003cgr1 \u0026\u0026 c1\u003cgc1 % Process only if gr1gc1 contained within r1, skip r1==gr1,c1=gc1\r\n   nGidx=Gidx; %p1=gr1-1  p2=gc1-1\r\n   %nGidx(r1:gr1-1,c1:gc1-1)=ptr; % Unchanged sectionID when move TL\r\n   nGidx(r1:gr1-1,gc1:c2)=ptrmax+1; \r\n   nGidx(gr1:r2,gc1:c2)=ptrmax+2; % Keep region TL to BR\r\n   nGidx(gr1:r2,c1:gc1-1)=ptrmax+3;\r\n   if nnz(nGidx==ptrmax+2)\u003eAmax || nnz(nGidx==ptrmax+2)==gA\r\n    p1=gr1-1; %r1\u003c=p1\u003cr2\u003c=400\r\n    p2=gc1-1; %c1\u003c=p2\u003cc2\u003c=400\r\n    bGidx=nGidx;\r\n    bcmd=3;\r\n    if nnz(nGidx==ptrmax+2)==gA, return;end\r\n   end\r\n  end\r\n    \r\n  % XY r2c2 gr2gc2  BR Corner gives reg1, +0\r\n  if r2\u003egr2 \u0026\u0026 c2\u003egc2 % Process only if gr2gc2 contained within r2, skip r2==gr2,c2=gc2\r\n   nGidx=Gidx; %p1=gr1-1  p2=gc1-1\r\n   \r\n  end\r\n    \r\n  % XY r1c2 gr1gc2  TR corner gives reg4, +3\r\n  if r1\u003cgr1 \u0026\u0026 c2\u003egc2 % Process only if gr1gc1 contained within r1, skip r1==gr1,c1=gc1\r\n   nGidx=Gidx; %p1=gr1-1  p2=gc1-1\r\n   \r\n  end\r\n  \r\n  % XY r2c1 gr2 gc1 BL corner gives reg2, +1\r\n  if r2\u003egr2 \u0026\u0026 c1\u003cgc1 % Process only if gr2gc1 contained within r2, skip r2==gr2,c1=gc1\r\n   nGidx=Gidx; %p1=gr1-1  p2=gc1-1\r\n   \r\n  end\r\n  \r\nend % Best_Draw2\r\n\r\n\r\n\r\nfunction [S,Gidx,CmdCost]=cmd_exec(cmd,S,Gidx,CmdCost)\r\n%This is how commands are executed and cmd costs evaluated\r\n%cmd: [cmd_id idx p1 p2 p3]\r\n%S image [400,400,3] initially all 255\r\n%Gidx working matrix of prior cmd idx updates. Set to all 1s upon Reset\r\n%CmdCost is running command costs based on area to be split/colored/reset\r\n ptrmax=max(Gidx(:));\r\n bArea=160000; % 400*400\r\n cmdscale=[7 7 10 5 1 3];\r\n \r\n %Calc cmd cost\r\n if cmd(1)==0 % reset  bArea/sum(max+min)\r\n  \r\n  qH=bArea; qL=0;\r\n  if ptrmax\u003e1\r\n   qH=0;\r\n   qL=bArea;\r\n  end\r\n  \r\n  for j=1:ptrmax\r\n   qt=nnz(Gidx(:)==j);\r\n   if qt\u003eqH\r\n    qH=qt;\r\n   end\r\n   if qt\u003cqL\r\n    qL=qt;\r\n   end\r\n  end\r\n  \r\n  Lcmdcost=1*round(bArea/(qH+qL));\r\n  CmdCost=CmdCost+Lcmdcost;\r\n else % H/V/XY/C  ignore merge and swap\r\n  Acmd=nnz(Gidx==cmd(2));\r\n  Lcmdcost=cmdscale(cmd(1))*round(bArea/Acmd);\r\n  CmdCost=CmdCost+Lcmdcost;\r\n end\r\n \r\n if cmd(1)==0 % reset\r\n  Gidx=0*Gidx+1;\r\n  return;\r\n end % Reset\r\n \r\n [r1, c1]=find(Gidx==cmd(2),1,'first'); %Common to H/V/XY/C\r\n [r2, c2]=find(Gidx==cmd(2),1,'last');\r\n \r\n if cmd(1)==4 % color 4 ptr r g b\r\n  S(r1:r2,c1:c2,1)=cmd(3); %r\r\n  S(r1:r2,c1:c2,2)=cmd(4); %g\r\n  S(r1:r2,c1:c2,3)=cmd(5); %b  \r\n end % Color\r\n \r\n if cmd(1)==1 %H  1 ptr p1 0 0\r\n  p1=cmd(3); %r r1\u003c=p1\u003cr2\u003c=400\r\n  Gidx(p1+1:r2,c1:c2)=ptrmax+1; % region below line gets increased\r\n end\r\n \r\n if cmd(1)==2 %V  2 ptr p1 0 0\r\n  p1=cmd(3); %c c1\u003c=p1\u003cc2\u003c=400\r\n  Gidx(r1:r2,p1+1:c2)=ptrmax+1; % region below line gets increased\r\n end\r\n \r\n if cmd(1)==3 %XY  3 ptr p1 p2 0 [1 1;1 1] becomes [1 2;4 3]\r\n  p1=cmd(3); %r r1\u003c=p1\u003cr2\u003c=400\r\n  p2=cmd(4); %c c1\u003c=p2\u003cc2\u003c=400\r\n  Gidx(r1:p1,p2+1:c2)=ptrmax+1; % region to right is new\r\n  Gidx(p1+1:r2,p2+1:c2)=ptrmax+2; % region to right and down is new\r\n  Gidx(p1+1:r2,c1:p2)=ptrmax+3; % region to below  is new\r\n end\r\n \r\nend % cmd_exec","test_suite":"%%\r\n%Google Drive Dowloads need to come from shared files\r\n% Tweak link: file/d/ to uc?export=download\u0026id=   while removing /view?usp=sharing\r\n% https://drive.google.com/file/d/1v3GsGgP3p905wzdvUqypL_-djYmxiyzK/view?usp=sharing\r\n% https://drive.google.com/uc?export=download\u0026id=1v3GsGgP3p905wzdvUqypL_-djYmxiyzK\r\n\r\n%21.png\r\nG=imread('https://drive.google.com/uc?export=download\u0026id=1ExUg4hujk4-kH9YWDvbFeRvKj2l5ujKl');\r\n% rT rBL cL cR r g b\r\nregions=[1 400 1 400 254 254 254 255 \r\n1 397 1 400 209 88 58 255 \r\n1 392 1 381 39 12 10 255 \r\n1 397 1 374 217 218 210 255 \r\n1 381 104 380 10 2 4 255 \r\n1 396 103 144 231 230 219 255 \r\n1 387 1 49 46 34 27 255 \r\n1 354 1 144 161 150 133 255 \r\n1 347 1 245 199 200 200 255 \r\n1 375 252 375 42 41 163 255 \r\n1 353 1 151 28 10 13 255 \r\n1 397 1 41 227 202 116 255 \r\n1 297 1 400 232 235 230 255 \r\n1 299 1 382 40 41 41 255 \r\n1 305 1 375 22 14 19 255 \r\n1 297 1 246 204 203 199 255 \r\n1 360 1 41 243 214 122 255 \r\n1 297 254 375 229 230 222 255 \r\n1 304 7 151 28 10 14 255 \r\n1 253 1 381 29 26 26 255 \r\n1 253 1 253 14 3 5 255 \r\n1 246 1 383 50 51 50 255 \r\n1 245 1 375 245 244 231 255 \r\n1 245 1 318 48 47 48 255 \r\n1 245 1 311 229 230 216 255 \r\n1 246 1 253 43 21 21 255 \r\n1 246 1 246 195 69 42 255 \r\n1 226 1 246 202 73 44 255 \r\n1 297 1 41 227 233 226 255 \r\n1 199 1 319 53 51 50 255 \r\n1 200 1 311 237 238 227 255 \r\n1 200 32 284 229 226 211 255 \r\n1 200 42 254 210 80 51 255 \r\n1 151 10 382 31 21 13 255 \r\n1 144 1 391 229 231 223 255 \r\n1 143 4 384 251 251 240 255 \r\n1 144 42 384 242 217 135 255 \r\n5 152 42 255 211 84 57 255 \r\n12 50 9 384 37 21 16 255 \r\n1 43 256 377 241 215 133 255 \r\n1 42 1 247 238 235 225 255];\r\n\r\ncmds = create_cmds(regions,G);\r\n\r\n%Evaluate cmds\r\nS=G*0+255;\r\nGidx=ones(400);\r\nCmdCost=0;\r\nbArea=400*400;\r\ncmdscale=[7 7 10 5 1 3]; %Reset/H/V/XY/C/M/S 1/7/7/10/5/1/3  [0:6] cmd ids\r\n\r\nfor icmd=1:size(cmds,1)\r\n cmd=cmds(icmd,:);\r\n ptrmax=max(Gidx(:));\r\n %Calc cmd cost\r\n if cmd(1)==0 % reset  bArea/sum(max+min)\r\n  \r\n  qH=bArea; qL=0;\r\n  if ptrmax\u003e1\r\n   qH=0;\r\n   qL=bArea;\r\n  end\r\n  \r\n  for j=1:ptrmax\r\n   qt=nnz(Gidx(:)==j);\r\n   if qt\u003eqH\r\n    qH=qt;\r\n   end\r\n   if qt\u003cqL\r\n    qL=qt;\r\n   end\r\n  end\r\n  Lcmdcost=1*round(bArea/(qH+qL));\r\n else % H/V/XY/C  ignore merge and swap\r\n  Acmd=nnz(Gidx==cmd(2));\r\n  Lcmdcost=cmdscale(cmd(1))*round(bArea/Acmd);\r\n end\r\n CmdCost=CmdCost+Lcmdcost;\r\n \r\n if cmd(1)==0 % reset\r\n  Gidx=0*Gidx+1;\r\n  continue;\r\n end % Reset\r\n \r\n [r1, c1]=find(Gidx==cmd(2),1,'first'); %Common to H/V/XY/C\r\n [r2, c2]=find(Gidx==cmd(2),1,'last');\r\n \r\n if cmd(1)==4 % color 4 ptr r g b\r\n  S(r1:r2,c1:c2,1)=cmd(3); %r\r\n  S(r1:r2,c1:c2,2)=cmd(4); %g\r\n  S(r1:r2,c1:c2,3)=cmd(5); %b  \r\n end % Color\r\n \r\n if cmd(1)==1 %H  1 ptr p1 0 0\r\n  p1=cmd(3); %r r1\u003c=p1\u003cr2\u003c=400\r\n  Gidx(p1+1:r2,c1:c2)=ptrmax+1; % region below line gets increased\r\n end\r\n \r\n if cmd(1)==2 %V  2 ptr p1 0 0\r\n  p1=cmd(3); %c c1\u003c=p1\u003cc2\u003c=400\r\n  Gidx(r1:r2,p1+1:c2)=ptrmax+1; % region below line gets increased\r\n end\r\n \r\n if cmd(1)==3 %XY  3 ptr p1 p2 0 [1 1;1 1] becomes [1 2;4 3]\r\n  p1=cmd(3); %r r1\u003c=p1\u003cr2\u003c=400\r\n  p2=cmd(4); %c c1\u003c=p2\u003cc2\u003c=400\r\n  Gidx(r1:p1,p2+1:c2)=ptrmax+1; % region to right is new\r\n  Gidx(p1+1:r2,p2+1:c2)=ptrmax+2; % region to right and down is new\r\n  Gidx(p1+1:r2,c1:p2)=ptrmax+3; % region to below  is new\r\n end\r\nend % icmd\r\n\r\n\r\n%Evaluate Img Score\r\n GmSsq=(double(G)-double(S)).^2;\r\n dis=sqrt(sum(GmSsq,3));\r\n scr=round(0.005*sum(dis(:)));\r\n \r\n fprintf('CmdScore: %i    Img Score:%i\\nTotal:%i\\n',CmdCost,scr,CmdCost+scr)\r\n if CmdCost+scr\u003e17000\r\n  fprintf('Combined Score Too High\\n')\r\n end\r\n \r\nvalid=(scr+CmdCost)\u003c=17000;\r\nassert(valid)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":3097,"edited_by":3097,"edited_at":"2023-06-28T01:46:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-06-27T23:57:46.000Z","updated_at":"2026-07-26T10:47:24.000Z","published_at":"2023-06-28T01:46:44.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://icfpcontest2023.github.io/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eICFP2023\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e Challenge is Jul 7-10, registraion opens late June. Updates at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://twitter.com/icfpcontest2023\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eTwitICFP2023\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. These contests are insanely complicated and competitive. The challenge evolves every 12 hours with new files and rule updates.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://icfpcontest2022.github.io/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eICFP2022 HomePage\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e has details of the RoboPaint contest. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://twitter.com/icfpcontest2022\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eTwit2022\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://icfpcontest2022.github.io/writeups/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWriteUps\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.icfpconference.org/contest.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePriorEvents\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://icfpcontest2022.github.io/Specifications/spec_v2_4.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSpec\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://gist.github.com/RafaelBocquet/e464c2d199f2d7a725cafdc22b30df7f\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eImageSubmissions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://github.com/icfpc-unagi/icfpc2022/tree/main/problems\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePuzzles\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSawickiSolutions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e are useful links. Posted 6/27/23.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe of Command Scripting is detailed in the function template. The commands have been matrixed and simplified but are based onthe Spec. Commands are Horiz split, Vertical split, Quad split, Color, and Reset.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a sequence of regions and colors writes that produce the Lower Right image, Img 13999, create commands to fill the image. The Goal 21.png.  Base costs  Cmds:1525, Img 13999, Submission combined score must be less than 17000.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVisualizations of Image creation: [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://drive.google.com/file/d/19MSfeGmn223KCGujl8Le6tQPqbW4EFXT/view?usp=drive_link\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e21 FBS Draw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e], adjust speed in settings.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput: Color regions  [M,7] of [r1 r2 c1 c2 r g b] where r1,c1 is TopLeft of a square and r2,c2 is BotRight\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput: cmds  [N,5] matrix of integer cmd, index, and parameters that vary based on cmd\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"360\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"360\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"360\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"360\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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Sequences 43: Least Common Fibonacci Number","description":"The Fibonacci sequence  is a series whose elements are numbers starting with  and , and subsequent Fibonacci numbers are defined recursively: . The first 20 Fibonacci numbers are:\r\n                            \r\nGiven two indices  and , write a program to return the least common Fibonacci number, , which is defined as the smallest Fibonacci number divisible by both  and . For example,, which is , since  and  both divide .\r\nSince. the value of  may become large even if the values of  and  are relatively small, please output a vector containing the number of digits and the last  digits of . Therefore, in the example above the output of , which has  digits, should be .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 216px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe Fibonacci sequence \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003eF\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e is a series whose elements are numbers starting with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"43.5\" height=\"20\" style=\"width: 43.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"43.5\" height=\"20\" style=\"width: 43.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, and subsequent \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Fibonacci_number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eFibonacci numbers\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e are defined recursively: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"107\" height=\"20\" style=\"width: 107px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. The first 20 Fibonacci numbers are:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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\" width=\"519.5\" height=\"19\" style=\"width: 519.5px; height: 19px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven two indices \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, write a program to return the least common Fibonacci number, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"69\" height=\"19\" style=\"width: 69px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e, which is defined as the smallest Fibonacci number divisible by both \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"20\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACcAAAAoCAYAAAB99ePgAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAJ6ADAAQAAAABAAAAKAAAAAC8ZFV5AAACoklEQVRYCe2WSWgVQRCG474hQdyJ4DuIEBAPoiLEBXNxRVAvIrl7FhEUBT148OBBxJuHBBRyEMQElYDRg4KgIi64oBdFSIISERUUMS7fn1cFbeiXmXk6Qw5T8KV6/q7XVa863fMaGkorO1B2oOzAP3dgXMIKF5jfBklxsWUOIp6LTaTVJiYEtjE/Cy7D+iD2NuNr8Am0xkxYCi2wBGQDVZf/37Ok+G18wauYmKnQq6DY+bGALNr4lMHLgribjFVgzIYQ1eW38C4WkEVLU9x0FlwTLNoTjGPDX4j3YxN5aFtZ1LdUvpIiyYQUMYkhaTq3KVjlJeM3wbOGC2AQGvVg9tMHeXsV5J07PSKZvlwn3Buh/5fHpKukQhZdEW76J18NOq3NsBNa4RAUbvvI6F0bzfvdVmiBl4LibjFeBetAHTsOujqeQOGmLdcbwDt2IFLBC7RjET13SR3ywuTDi9iTf6ih+3xu/gQre3F9kSw6qYcjeiGSbnkvrr2QjCmTzCFOF6kXtyfl5woJ2xsUpneliq3X9FswfJ1NiSwU0yJhVekGzrv2rGZU7Ykmps6Afvd9Bl3cK+AhaEf85G9nrBP/HTZDou0gwguTH4Csv83UieWge1AneiU8haOgNbtBu/MAOkDaSRjVXjEbFuZjfdusHazYWr34R7AY1pp2BX8X9Bo8YlobvjBTMv9yGy2rrh5p32CRab2mZd0d+3h9rt2SdgQfv27aftO0/V/hsT0X4nRC+0GJ51nGaXh17DVMMm0DXp08Zc9/Od3yeZhO5kLogveWQIVMhfPwwzTfbnV0F8w2fdjlVZyuCNnFqhv+u8XGKtitxQZN+N3w0Sfy9HdYXFs4I0jynPEghA1Rx4agEybDmDIVP3dMVVQWU3ag7EAdHfgDdZGTuQ+F7fkAAAAASUVORK5CYII=\" width=\"19.5\" height=\"20\" style=\"width: 19.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e For example,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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width=\"43.5\" height=\"20\" style=\"width: 43.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"43.5\" height=\"20\" style=\"width: 43.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e both divide \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"33\" height=\"18\" style=\"width: 33px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eSince. the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"33\" height=\"18\" style=\"width: 33px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e may become large even if the values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e are relatively small, please output a vector containing the number of digits and the last \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);\"\u003e6\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e digits of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"33\" height=\"18\" style=\"width: 33px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. Therefore, in the example above the output of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"65.5\" height=\"19\" style=\"width: 65.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, which has \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);\"\u003e4\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e digits, should be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"58\" height=\"19\" style=\"width: 58px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = LCF(n,m)\r\n  y = x;\r\nend","test_suite":"%%\r\nn = 3; m = 4;\r\ny_correct = [4 6765];\r\nassert(isequal(LCF(n,m),y_correct))\r\n%%\r\nn = 31; m = 61;\r\ny_correct = [207 308229];\r\nassert(isequal(LCF(n,m),y_correct))\r\n%%\r\nn = 123; m = 456;\r\ny_correct = [11843 575091];\r\nassert(isequal(LCF(n,m),y_correct))\r\n%%\r\nn = 999; m = 99999;\r\ny_correct = [20899 746875];\r\nassert(isequal(LCF(n,m),y_correct))\r\n%%\r\nn = 98765; m = 43210;\r\ny_correct = [891912775 944568];\r\nassert(isequal(LCF(n,m),y_correct))\r\n%%\r\nn = double(intmax); m = 12345;\r\ny_correct = [2770427214858 134203];\r\nassert(isequal(LCF(n,m),y_correct))\r\n%%\r\nns = floor(double(intmax)./(1:100));\r\nys = arrayfun(@(i) log10(sum(LCF(ns(i-1),i))),2:101);\r\nss = round([sum(ys) mean(ys) median(ys) mode(ys) std(ys)],4);\r\nss_correct = [842.8233 8.4282 8.6618 7.1199 0.3808];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('LCF.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-21T07:09:35.000Z","updated_at":"2026-09-24T12:42:48.000Z","published_at":"2021-10-21T11:42:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Fibonacci sequence \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a series whose elements are numbers starting with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_{1} =1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_{2} =2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and subsequent \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Fibonacci_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eFibonacci numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e are defined recursively: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_{n} =F_{n-1}+F_{n-2} \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The first 20 Fibonacci numbers are:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{1, \\t2, \\t3, \\t5, \\t8, \\t13, \\t21, \\t34, \\t55, \\t89, \\t144, \\t233, \\t377, \\t610, \\t987, \\t1597, \\t2584, \\t4181, \\t6765, 10946\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven two indices \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, write a program to return the least common Fibonacci number, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eLCF(n,m)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, which is defined as the smallest Fibonacci number divisible by both \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_{n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_{m}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e For example,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eLCF(3,4)=6765\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, which is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_{19}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, since \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_{3}=3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF_{4}=5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e both divide \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e6765\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince. the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eLCF\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e may become large even if the values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are relatively small, please output a vector containing the number of digits and the last \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e digits of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eLCF\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore, in the example above the output of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eLCF(3,4)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, which has \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e digits, should be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[4\\\\  6765]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1917,"title":"click away","description":"Write a function that clicks on a GUI button.\r\n\r\n*Description*:\r\n\r\nSome times one wishes to use Matlab to automate some time consuming repetitive process that requires filling fields or clicking buttons on the screen. Matlab offers a simple way to control the cursor position (e.g. |set(0,'pointerlocation',...)|, but it is not so clear how one would perform mouse or keyboard clicks.\r\n\r\nThis problem creates a simple message box:\r\n\r\n msgbox('Click the OK button','')\r\n\r\nwhich displays the above message and an 'OK' button. \r\n\r\nYour function just needs to actually click on the OK button (or use equivalent keyboard shortcuts) to pass this problem. Simple, right?\r\n\r\n","description_html":"\u003cp\u003eWrite a function that clicks on a GUI button.\u003c/p\u003e\u003cp\u003e\u003cb\u003eDescription\u003c/b\u003e:\u003c/p\u003e\u003cp\u003eSome times one wishes to use Matlab to automate some time consuming repetitive process that requires filling fields or clicking buttons on the screen. Matlab offers a simple way to control the cursor position (e.g. \u003ctt\u003eset(0,'pointerlocation',...)\u003c/tt\u003e, but it is not so clear how one would perform mouse or keyboard clicks.\u003c/p\u003e\u003cp\u003eThis problem creates a simple message box:\u003c/p\u003e\u003cpre\u003e msgbox('Click the OK button','')\u003c/pre\u003e\u003cp\u003ewhich displays the above message and an 'OK' button.\u003c/p\u003e\u003cp\u003eYour function just needs to actually click on the OK button (or use equivalent keyboard shortcuts) to pass this problem. Simple, right?\u003c/p\u003e","function_template":"function y = clickOK()\r\nend","test_suite":"%%\r\nh=msgbox('Click the OK button','');\r\nclickOK();\r\nassert(ishandle(h),'do not simply delete the figure');\r\ndrawnow;\r\nassert(~ishandle(h),'failed to click the OK button');\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":29,"created_by":43,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2013-10-06T17:23:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-10-06T06:04:42.000Z","updated_at":"2026-09-24T15:38:05.000Z","published_at":"2013-10-06T08:41:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that clicks on a GUI button.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDescription\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSome times one wishes to use Matlab to automate some time consuming repetitive process that requires filling fields or clicking buttons on the screen. Matlab offers a simple way to control the cursor position (e.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eset(0,'pointerlocation',...)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, but it is not so clear how one would perform mouse or keyboard clicks.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem creates a simple message box:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ msgbox('Click the OK button','')]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhich displays the above message and an 'OK' button.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour function just needs to actually click on the OK button (or use equivalent keyboard shortcuts) to pass this problem. Simple, right?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1000,"title":"Image Processing 004: Zernike Coefficients","description":"*Fit Zernike Terms to a wavefront.*\r\n\r\nThe class notes of \u003chttp://www.visualopticslab.com/OPTI535/Lectures/Class06_08.pdf Schwiegerling UofA\u003e on ANSI Standard Zernike terms is the basis for this challenge.  Pages 13 and 14 give the term definitions implemented in the zern_data_v01.m routine provided in the function template.\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/_/rsrc/1350774824076/matlab_cody/Zernike_UA_480.jpg\u003e\u003e\r\n\r\n\r\nANSI Standard Zernike Chart:\r\n\r\n\r\n\r\n*Algorithm Description:*\r\n\r\n  M=surface array to be fit by Zernike terms; \r\n  -valid data is circle of normalized radius\u003c=1\r\n  Use the R and T arrays to create the A array\r\n  R=radial normalized distance from center of array\r\n  T=angular radian value from center of array\r\n  A=fitting array [valid_data_pts,terms]\r\n\r\n  Create A * z_fit = M(valid_data_pts)\r\n  [valid_pts,terms] * [terms,1] = [valid_pts,1]\r\n\r\n  Loop term=0:terms-1\r\n  - Create the 2-D array of z-terms uisng z=zern_data_v01(term,R,T)\r\n  - A(:,term+1) = z(valid_data_pts)\r\n  End Loop\r\n  \r\n  Solve for z_fit: pinv(A)*M(valid_pts)  or A\\M(valid_pts)\r\n\r\n*Inputs:* [M N R T] where N is number of Zernike terms for fit\r\n\r\n*Outputs:* [v] Zernike fit vector of length N\r\n\r\nCreation of the M surface and expected v fit vector can be seen in the Test Suite.\r\n\r\n\r\n\r\n\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 888.85px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 444.433px; transform-origin: 407px 444.433px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109.15px 7.91667px; transform-origin: 109.15px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFit Zernike Terms to a wavefront.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.7833px 7.91667px; transform-origin: 56.7833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe class notes of\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://www.visualopticslab.com/OPTI535/Lectures/Class06_08.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSchwiegerling UofA\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 253.6px 7.91667px; transform-origin: 253.6px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e on ANSI Standard Zernike terms is the basis for this challenge. Pages 13 and 14 give the term definitions implemented in the zern_data_v01.m routine provided in the function template.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 319.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 159.967px; text-align: center; transform-origin: 384px 159.967px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.9667px 7.91667px; transform-origin: 92.9667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eANSI Standard Zernike Chart:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75.8333px 7.91667px; transform-origin: 75.8333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eAlgorithm Description:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 326.933px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 163.467px; transform-origin: 404px 163.467px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 169.4px 7.91667px; transform-origin: 169.4px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 61.6px 7.91667px; transform-origin: 61.6px 7.91667px; \"\u003eM=surface array \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 100.1px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 100.1px 7.91667px; \"\u003eto be fit by Zernike terms\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; \"\u003e; \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 173.25px 7.91667px; transform-origin: 173.25px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 46.2px 7.91667px; transform-origin: 46.2px 7.91667px; \"\u003e-valid data \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 127.05px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 127.05px 7.91667px; \"\u003eis circle of normalized radius\u0026lt;=1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 169.4px 7.91667px; transform-origin: 169.4px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; \"\u003eUse \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 154px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 154px 7.91667px; \"\u003ethe R and T arrays to create the A array\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 188.65px 7.91667px; transform-origin: 188.65px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 77px 7.91667px; transform-origin: 77px 7.91667px; \"\u003eR=radial normalized \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 111.65px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 111.65px 7.91667px; \"\u003edistance from center of array\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 165.55px 7.91667px; transform-origin: 165.55px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 65.45px 7.91667px; transform-origin: 65.45px 7.91667px; \"\u003eT=angular radian \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 100.1px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 100.1px 7.91667px; \"\u003evalue from center of array\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 146.3px 7.91667px; transform-origin: 146.3px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 61.6px 7.91667px; transform-origin: 61.6px 7.91667px; \"\u003eA=fitting array \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 84.7px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 84.7px 7.91667px; \"\u003e[valid_data_pts,terms]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 138.6px 7.91667px; transform-origin: 138.6px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 26.95px 7.91667px; transform-origin: 26.95px 7.91667px; \"\u003eCreate \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 111.65px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 111.65px 7.91667px; \"\u003eA * z_fit = M(valid_data_pts)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 173.25px 7.91667px; transform-origin: 173.25px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e[valid_pts,terms] * [terms,1] = [valid_pts,1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 73.15px 7.91667px; transform-origin: 73.15px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 19.25px 7.91667px; transform-origin: 19.25px 7.91667px; \"\u003eLoop \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 53.9px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 53.9px 7.91667px; \"\u003eterm=0:terms-1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 250.25px 7.91667px; transform-origin: 250.25px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 7.91667px; transform-origin: 50.05px 7.91667px; \"\u003e- Create the \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 200.2px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 200.2px 7.91667px; \"\u003e2-D array of z-terms uisng z=zern_data_v01(term,R,T)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 127.05px 7.91667px; transform-origin: 127.05px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e- A(:,term+1) = z(valid_data_pts)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 7.91667px; transform-origin: 30.8px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; \"\u003eEnd \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 15.4px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 15.4px 7.91667px; \"\u003eLoop\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 215.6px 7.91667px; transform-origin: 215.6px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 23.1px 7.91667px; transform-origin: 23.1px 7.91667px; \"\u003eSolve \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 119.35px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 119.35px 7.91667px; \"\u003efor z_fit: pinv(A)*M(valid_pts)\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; \"\u003e  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 65.45px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 65.45px 7.91667px; \"\u003eor A\\M(valid_pts)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.3333px 7.91667px; transform-origin: 23.3333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInputs:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 162.55px 7.91667px; transform-origin: 162.55px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e [M N R T] where N is number of Zernike terms for fit\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.1667px 7.91667px; transform-origin: 29.1667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutputs:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.7833px 7.91667px; transform-origin: 98.7833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e [v] Zernike fit vector of length N\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 250.083px 7.91667px; transform-origin: 250.083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCreation of the M surface and expected v fit vector can be seen in the Test Suite.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function v = Zernike_Fit(M,N,R,T)\r\n% M surface array\r\n% N Number of Zernike terms for fit  0:N-1\r\n% R Radial distance from center of M array for each M location\r\n% T angle from center of M array to each M location\r\n  v=zeros(N,1);\r\nend\r\n\r\n% The function zern_data_v01 has been loaded and rehashed\r\n% z = zern_data_v01(j,r,t) % is sufficient in the main routine\r\n\r\n%% zern_data_v01.m\r\n% Author: Team\r\n% function to create a zernike polynomial\r\n% Using ANSI standard zernikes\r\n\r\n% input\r\n%  j = term #\r\n%  r = normalized radial vector\r\n%  t = theta\r\n\r\nfunction z = zern_data_v01(j,r,t)\r\n\r\n    % Convert single index term to standard\r\n    n= ceil((sqrt(9+8*j)-1)/2)-1; % 0-0; 2-1; 5-2; 9-3; ...\r\n    m= 2*j-n*(n+2);\r\n    \r\n    % zernike term\r\n   \r\n    z = r*0; %zeros(size(r));\r\n        \r\n        % radial component\r\n    for s = 0:(n-abs(m))/2\r\n     z = z + (-1)^s * factorial(n-s) * r.^(n-2*s) ./ ...\r\n        (factorial(s) * factorial((n+abs(m))/2 - s) * factorial((n-abs(m))/2 - s));\r\n    end\r\n        \r\n        % angular component\r\n    z = z .* ((m\u003e=0)*cos(m*t) - (m\u003c0)*sin(m*t));\r\n    \r\n    % normalization\r\n    z = z * sqrt(2*(n+1)/(1+(m==0)));\r\n    \r\n    % value added processing\r\n    z = z .* (r\u003c=1);\r\n    \r\nend\r\n\r\n","test_suite":"fname='https://sites.google.com/site/razapor/matlab_cody/zern_data_v01.m?attredirects=0\u0026d=1';\r\nurlwrite(fname,'zern_data_v01.m')\r\n%urlwrite('http://tinyurl.com/matlab-zernike','zern_data_v01.m')\r\nrehash path\r\n% z = zern_data_v01(j,r,t) % is sufficient in the main routine\r\n%%\r\nM=zeros(256);\r\nterms=6; % Number of Terms to fit  0:terms-1\r\n% Test Suite portion using zern_data_v01\r\n[ ydim xdim ] = size(M);\r\nx = linspace(-1,1,xdim);\r\ny = linspace(1,-1,ydim);\r\n[X Y] = meshgrid(x,y);\r\nR = sqrt(X.^2 + Y.^2);\r\nT = atan2(Y,X);\r\n% Create surface\r\nz_fit=zeros(terms,1); % Map 0:9 to 1:10\r\nz_fit(2)=1.0;\r\n\r\n% Build a Surface\r\nM = M +  zern_data_v01(0,R,T); % Force NaN for non-data\r\nM(M==0)=NaN;\r\nM(M\u003e0)=0;\r\nfor term = 0:terms-1\r\n M = M + z_fit(term+1) * zern_data_v01(term,R,T);\r\n% figure(3);imagesc(data_fit) % Visualization\r\n% pause (0.5)\r\nend\r\n\r\n% Data is a circle\r\n% Non-data is assigned NaN\r\n\r\ntic\r\nv = Zernike_Fit(M,terms,R,T)\r\ntoc\r\nassert(max(abs(v-z_fit))\u003c0.01,sprintf('v=%i %i %i %i %i %i',v))\r\n\r\n\r\n%%\r\nM=zeros(256);\r\nterms=10; % Number of Terms to fit  0:terms-1\r\n% Test Suite portion using zern_data_v01\r\n[ ydim xdim ] = size(M);\r\nx = linspace(-1,1,xdim);\r\ny = linspace(1,-1,ydim);\r\n[X Y] = meshgrid(x,y);\r\nR = sqrt(X.^2 + Y.^2);\r\nT = atan2(Y,X);\r\n\r\n% Create surface\r\nz_fit= round(2*rand(terms,1)-1).*rand(terms,1);\r\n\r\n% Build a Surface\r\nM = M +  zern_data_v01(0,R,T); % Force NaN for non-data\r\nM(M==0)=NaN;\r\nM(M\u003e0)=0;\r\nfor term = 0:terms-1\r\n M = M + z_fit(term+1) * zern_data_v01(term,R,T);\r\n% figure(3);imagesc(data_fit) % Visualization\r\n% pause (0.5)\r\nend\r\n\r\ntic\r\nv = Zernike_Fit(M,terms,R,T)\r\ntoc\r\nassert(max(abs(v-z_fit))\u003c0.01)\r\n\r\n\r\n%%\r\nM=zeros(128);\r\nterms=15; % Number of Terms to fit  0:terms-1\r\n% Test Suite portion using zern_data_v01\r\n[ ydim xdim ] = size(M);\r\nx = linspace(-1,1,xdim);\r\ny = linspace(1,-1,ydim);\r\n[X Y] = meshgrid(x,y);\r\nR = sqrt(X.^2 + Y.^2);\r\nT = atan2(Y,X);\r\n\r\n% Create surface\r\nz_fit= round(2*rand(terms,1)-1).*rand(terms,1);\r\n\r\n% Build a Surface\r\nM = M +  zern_data_v01(0,R,T); % Force NaN for non-data\r\nM(M==0)=NaN;\r\nM(M\u003e0)=0;\r\nfor term = 0:terms-1\r\n M = M + z_fit(term+1) * zern_data_v01(term,R,T);\r\n% figure(3);imagesc(data_fit) % Visualization\r\n% pause (0.5)\r\nend\r\n\r\ntic\r\nv = Zernike_Fit(M,terms,R,T)\r\ntoc\r\nassert(max(abs(v-z_fit))\u003c0.01)\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":5,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2020-09-29T23:07:58.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2012-10-18T13:25:52.000Z","updated_at":"2026-09-24T16:53:35.000Z","published_at":"2012-10-21T01:08:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFit Zernike Terms to a wavefront.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe class notes of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.visualopticslab.com/OPTI535/Lectures/Class06_08.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSchwiegerling UofA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e on ANSI Standard Zernike terms is the basis for this challenge. Pages 13 and 14 give the term definitions implemented in the zern_data_v01.m routine provided in the function template.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eANSI Standard Zernike Chart:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAlgorithm Description:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[M=surface array to be fit by Zernike terms; \\n-valid data is circle of normalized radius\u003c=1\\nUse the R and T arrays to create the A array\\nR=radial normalized distance from center of array\\nT=angular radian value from center of array\\nA=fitting array [valid_data_pts,terms]\\n\\nCreate A * z_fit = M(valid_data_pts)\\n[valid_pts,terms] * [terms,1] = [valid_pts,1]\\n\\nLoop term=0:terms-1\\n- Create the 2-D array of z-terms uisng z=zern_data_v01(term,R,T)\\n- A(:,term+1) = z(valid_data_pts)\\nEnd Loop\\n\\nSolve for z_fit: pinv(A)*M(valid_pts)  or A\\\\M(valid_pts)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [M N R T] where N is number of Zernike terms for fit\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [v] Zernike fit vector of length N\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreation of the M surface and expected v fit vector can be seen in the Test 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46838,"title":"The most decentralized RGB colors","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 222px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 111px; transform-origin: 407px 111px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eInput number of colors and try to find the most decentralized combination.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor n=1, any color is OK.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor n=2, the 2 colors should have an euclidean distance of sqrt(255^2*3), such as [0 0 0] and [255 255 255].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor n=3, the 3 colors have 3 distances. We measure the smallest one, which should be sqrt(255^2*2). One possible combination may be [255 255 255;255 0 0;0 0 255].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor n=8, apparently we capture the 8 vertecies of the cube, the smallest distance is 255.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThen, more?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYour function should return a n×3 matrix with each row represent an RGB color.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Colors=ColorDistribute(N)\r\nColors=[0 0 0];\r\nend","test_suite":"%%\r\nassert(MinDistance(ColorDistribute(1),1)\u003e=500);\r\nfunction Md=MinDistance(ColorMatrix,NumberOfColors)\r\narguments\r\n    ColorMatrix(:,3)uint8\r\n\tNumberOfColors(1,1)uint8\r\nend\r\nMd=500;\r\nColorMatrix=double(ColorMatrix);\r\nfor a=1:NumberOfColors-1\r\n    Color1=ColorMatrix(a,:);\r\n    for b=a+1:NumberOfColors\r\n        Md=min(Md,norm(Color1-ColorMatrix(b,:)));\r\n    end\r\nend\r\nend\r\n%%\r\nassert(MinDistance(ColorDistribute(2),2)\u003e441);\r\nfunction Md=MinDistance(ColorMatrix,NumberOfColors)\r\narguments\r\n    ColorMatrix(:,3)uint8\r\n\tNumberOfColors(1,1)uint8\r\nend\r\nMd=500;\r\nColorMatrix=double(ColorMatrix);\r\nfor a=1:NumberOfColors-1\r\n    Color1=ColorMatrix(a,:);\r\n    for b=a+1:NumberOfColors\r\n        Md=min(Md,norm(Color1-ColorMatrix(b,:)));\r\n    end\r\nend\r\nend\r\n%%\r\nassert(MinDistance(ColorDistribute(3),3)\u003e360);\r\nfunction Md=MinDistance(ColorMatrix,NumberOfColors)\r\narguments\r\n    ColorMatrix(:,3)uint8\r\n\tNumberOfColors(1,1)uint8\r\nend\r\nMd=500;\r\nColorMatrix=double(ColorMatrix);\r\nfor a=1:NumberOfColors-1\r\n    Color1=ColorMatrix(a,:);\r\n    for b=a+1:NumberOfColors\r\n        Md=min(Md,norm(Color1-ColorMatrix(b,:)));\r\n    end\r\nend\r\nend\r\n%%\r\nassert(MinDistance(ColorDistribute(4),4)\u003e360);\r\nfunction Md=MinDistance(ColorMatrix,NumberOfColors)\r\narguments\r\n    ColorMatrix(:,3)uint8\r\n\tNumberOfColors(1,1)uint8\r\nend\r\nMd=500;\r\nColorMatrix=double(ColorMatrix);\r\nfor a=1:NumberOfColors-1\r\n    Color1=ColorMatrix(a,:);\r\n    for b=a+1:NumberOfColors\r\n        Md=min(Md,norm(Color1-ColorMatrix(b,:)));\r\n    end\r\nend\r\nend\r\n%%\r\nassert(MinDistance(ColorDistribute(5),5)\u003e284);\r\nfunction Md=MinDistance(ColorMatrix,NumberOfColors)\r\narguments\r\n    ColorMatrix(:,3)uint8\r\n\tNumberOfColors(1,1)uint8\r\nend\r\nMd=500;\r\nColorMatrix=double(ColorMatrix);\r\nfor a=1:NumberOfColors-1\r\n    Color1=ColorMatrix(a,:);\r\n    for b=a+1:NumberOfColors\r\n        Md=min(Md,norm(Color1-ColorMatrix(b,:)));\r\n    end\r\nend\r\nend\r\n%%\r\nassert(MinDistance(ColorDistribute(6),6)\u003e266);\r\nfunction Md=MinDistance(ColorMatrix,NumberOfColors)\r\narguments\r\n    ColorMatrix(:,3)uint8\r\n\tNumberOfColors(1,1)uint8\r\nend\r\nMd=500;\r\nColorMatrix=double(ColorMatrix);\r\nfor a=1:NumberOfColors-1\r\n    Color1=ColorMatrix(a,:);\r\n    for b=a+1:NumberOfColors\r\n        Md=min(Md,norm(Color1-ColorMatrix(b,:)));\r\n    end\r\nend\r\nend\r\n%%\r\nassert(MinDistance(ColorDistribute(7),7)\u003e255);\r\nfunction Md=MinDistance(ColorMatrix,NumberOfColors)\r\narguments\r\n    ColorMatrix(:,3)uint8\r\n\tNumberOfColors(1,1)uint8\r\nend\r\nMd=500;\r\nColorMatrix=double(ColorMatrix);\r\nfor a=1:NumberOfColors-1\r\n    Color1=ColorMatrix(a,:);\r\n    for b=a+1:NumberOfColors\r\n        Md=min(Md,norm(Color1-ColorMatrix(b,:)));\r\n    end\r\nend\r\nend\r\n%%\r\nassert(MinDistance(ColorDistribute(8),8)\u003e=255);\r\nfunction Md=MinDistance(ColorMatrix,NumberOfColors)\r\narguments\r\n    ColorMatrix(:,3)uint8\r\n\tNumberOfColors(1,1)uint8\r\nend\r\nMd=500;\r\nColorMatrix=double(ColorMatrix);\r\nfor a=1:NumberOfColors-1\r\n    Color1=ColorMatrix(a,:);\r\n    for b=a+1:NumberOfColors\r\n        Md=min(Md,norm(Color1-ColorMatrix(b,:)));\r\n    end\r\nend\r\nend\r\n%%\r\nassert(MinDistance(ColorDistribute(9),9)\u003e=219);\r\nfunction Md=MinDistance(ColorMatrix,NumberOfColors)\r\narguments\r\n    ColorMatrix(:,3)uint8\r\n\tNumberOfColors(1,1)uint8\r\nend\r\nMd=500;\r\nColorMatrix=double(ColorMatrix);\r\nfor a=1:NumberOfColors-1\r\n    Color1=ColorMatrix(a,:);\r\n    for b=a+1:NumberOfColors\r\n        Md=min(Md,norm(Color1-ColorMatrix(b,:)));\r\n    end\r\nend\r\nend\r\n%%\r\nassert(MinDistance(ColorDistribute(64),64)\u003e=85);\r\nfunction Md=MinDistance(ColorMatrix,NumberOfColors)\r\narguments\r\n    ColorMatrix(:,3)uint8\r\n\tNumberOfColors(1,1)uint8\r\nend\r\nMd=500;\r\nColorMatrix=double(ColorMatrix);\r\nfor a=1:NumberOfColors-1\r\n    Color1=ColorMatrix(a,:);\r\n    for b=a+1:NumberOfColors\r\n        Md=min(Md,norm(Color1-ColorMatrix(b,:)));\r\n    end\r\nend\r\nend","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":362068,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-17T04:34:30.000Z","updated_at":"2026-09-22T12:08:38.000Z","published_at":"2020-10-17T04:34:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput number of colors and try to find the most decentralized combination.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor n=1, any color is OK.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor n=2, the 2 colors should have an euclidean distance of sqrt(255^2*3), such as [0 0 0] and [255 255 255].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor n=3, the 3 colors have 3 distances. We measure the smallest one, which should be sqrt(255^2*2). One possible combination may be [255 255 255;255 0 0;0 0 255].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor n=8, apparently we capture the 8 vertecies of the cube, the smallest distance is 255.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen, more?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour function should return a n×3 matrix with each row represent an RGB color.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54275,"title":"Get twenty-four","description":"Inpur four integers in 1 to 10, you may use plus, minus, multiply and divid to get 24. Note that every integer should be used once and only once. Brackets are of no limit, and the result should exactly be 24 once you calculate by hand. (Calculation in computer will lead to a tolerance to the computer precision.) \r\nYou need to return a format and a vector with the same four integers, such that you can print the expression.\r\nE.g., input                            x = [5 5 7 7]\r\n        you may return            f  = '(%d*%d)-(%d/%d)'\r\n                     and                 z = [5 5 7 7]\r\n      so  24 is obatined by     eval(sprintf(f,z)).\r\n     The answer is not necessary unique, e.g., other acceptable answers are\r\n                                            f  = '(%d*%d)-(%d*%d)'  \r\n                                            z =  [7 7 5 5]\r\n                   and                   f = '(%d-%d)*(%d+%d)'\r\n                                            z = [7 5 7 5]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 363px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 181.5px; transform-origin: 407px 181.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInpur four integers in 1 to 10, you may use plus, minus, multiply and divid to get 24. Note that every integer should be used once and only once. Brackets are of no limit, and the result should exactly be 24 once you calculate by hand. (Calculation in computer will lead to a tolerance to the computer precision.) \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou need to return a format and a vector with the same four integers, such that you can print the expression.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eE.g., input                            x = [5 5 7 7]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        you may return            f  = '(%d*%d)-(%d/%d)'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                     and                 z = [5 5 7 7]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e      so  24 is obatined by     eval(sprintf(f,z)).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e     The answer is not necessary unique, e.g., other acceptable answers are\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                            f  = '(%d*%d)-(%d*%d)'  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                            z =  [7 7 5 5]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                   and                   f = '(%d-%d)*(%d+%d)'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                            z = [7 5 7 5]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [f,z] = get24(x)\r\n  z = 23;\r\n  f = '(%d%d+%s%s)'\r\nend","test_suite":"%%\r\nx = [1 2 3 4];\r\ntry \r\n    [f,z] = get24(x);\r\n    s = sprintf(f,z); s(s\u003e'9'|s\u003c'0')=' '; assert(length(str2num(s))==4);    \r\n    assert(ischar(f));\r\n    assert(all( sort(z)==sort(x) ));\r\n    assert(length(f(f=='-'|f=='+'|f=='*'|f=='/'))==3);\r\n    assert( abs( eval(sprintf(f,z))-24 )\u003c=1e-8 );\r\n    w = f(f~='('\u0026f~=')'\u0026f~='+'\u0026f~='-'\u0026f~='*'\u0026f~='/'\u0026f~='%'\u0026f~='s'\u0026f~='d');\r\n    assert(isempty(w),'unusual format character!');\r\ncatch\r\n    assert(false,'no result or something wrong!');\r\nend\r\n%%\r\nx = [6 9 9 10];\r\ntry \r\n    [f,z] = get24(x);\r\n    s = sprintf(f,z); s(s\u003e=9'|s\u003c'0')=' '; assert(length(str2num(s))==4);    \r\n    assert(ischar(f));\r\n    assert(all( sort(z)==sort(x) ));\r\n    assert(length(f(f=='-'|f=='+'|f=='*'|f=='/'))==3);\r\n    assert( abs( eval(sprintf(f,z))-24 )\u003c=1e-8 );\r\n    w = f(f~='('\u0026f~=')'\u0026f~='+'\u0026f~='-'\u0026f~='*'\u0026f~='/'\u0026f~='%'\u0026f~='s'\u0026f~='d');\r\n    assert(isempty(w),'unusual format character!');\r\ncatch\r\n    assert(false,'no result or something wrong!');\r\nend\r\n%%\r\nx = [4 4 10 10];\r\ntry \r\n    [f,z] = get24(x);\r\n    s = sprintf(f,z); s(s\u003e'9'|s\u003c'0')=' '; assert(length(str2num(s))==4);    \r\n    assert(ischar(f));\r\n    assert(all( sort(z)==sort(x) ));\r\n    assert(length(f(f=='-'|f=='+'|f=='*'|f=='/'))==3);\r\n    assert( abs( eval(sprintf(f,z))-24 )\u003c=1e-8 );\r\n    w = f(f~='('\u0026f~=')'\u0026f~='+'\u0026f~='-'\u0026f~='*'\u0026f~='/'\u0026f~='%'\u0026f~='s'\u0026f~='d');\r\n    assert(isempty(w),'unusual format character!');\r\ncatch\r\n    assert(false,'no result or something wrong!');\r\nend\r\n%%\r\nx = [3 3 7 7];\r\ntry \r\n    [f,z] = get24(x);\r\n    s = sprintf(f,z); s(s\u003e'9'|s\u003c'0')=' '; assert(length(str2num(s))==4);    \r\n    assert(ischar(f));\r\n    assert(all( sort(z)==sort(x) ));\r\n    assert(length(f(f=='-'|f=='+'|f=='*'|f=='/'))==3);\r\n    assert( abs( eval(sprintf(f,z))-24 )\u003c=1e-8 );\r\n    w = f(f~='('\u0026f~=')'\u0026f~='+'\u0026f~='-'\u0026f~='*'\u0026f~='/'\u0026f~='%'\u0026f~='s'\u0026f~='d');\r\n    assert(isempty(w),'unusual format character!');\r\ncatch\r\n    assert(false,'no result or something wrong!');\r\nend\r\n%%\r\nx = [1 4 5 6];\r\ntry \r\n    [f,z] = get24(x);\r\n    s = sprintf(f,z); s(s\u003e'9'|s\u003c'0')=' '; assert(length(str2num(s))==4);    \r\n    assert(ischar(f));\r\n    assert(all( sort(z)==sort(x) ));\r\n    assert(length(f(f=='-'|f=='+'|f=='*'|f=='/'))==3);\r\n    assert( abs( eval(sprintf(f,z))-24 )\u003c=1e-8 );\r\n    w = f(f~='('\u0026f~=')'\u0026f~='+'\u0026f~='-'\u0026f~='*'\u0026f~='/'\u0026f~='%'\u0026f~='s'\u0026f~='d');\r\n    assert(isempty(w),'unusual format character!');\r\ncatch\r\n    assert(false,'no result or something wrong!');\r\nend","published":true,"deleted":false,"likes_count":0,"comments_count":3,"created_by":2197980,"edited_by":2197980,"edited_at":"2024-08-29T05:32:43.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2024-08-29T05:32:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-04-13T12:52:09.000Z","updated_at":"2026-09-26T12:16:40.000Z","published_at":"2022-04-13T12:52:22.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInpur four integers in 1 to 10, you may use plus, minus, multiply and divid to get 24. Note that every integer should be used once and only once. Brackets are of no limit, and the result should exactly be 24 once you calculate by hand. (Calculation in computer will lead to a tolerance to the computer precision.) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou need to return a format and a vector with the same four integers, such that you can print the expression.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eE.g., input                            x = [5 5 7 7]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        you may return            f  = '(%d*%d)-(%d/%d)'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                     and                 z = [5 5 7 7]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e      so  24 is obatined by     eval(sprintf(f,z)).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e     The answer is not necessary unique, e.g., other acceptable answers are\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                            f  = '(%d*%d)-(%d*%d)'  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                            z =  [7 7 5 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                   and                   f = '(%d-%d)*(%d+%d)'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                            z = [7 5 7 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46691,"title":"Kaggle: Planetoid Game of Life - Solve 40 non-trivial Puzzles","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 482.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 241.083px; transform-origin: 407px 241.083px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.kaggle.com/c/conways-reverse-game-of-life-2020\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eKaggle's Conway's Reverse Game of Life 2020 \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 203.05px 7.91667px; transform-origin: 203.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003econtest inspires this Life challenge. The kaggle contest runs from Oct-01-2020 thru Nov-30-2020. References:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://mathworld.wolfram.com/GameofLife.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eGame of Life at Wolfram\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWiki Life\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 138.467px 7.91667px; transform-origin: 138.467px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The Kaggle event is 50K cases to solve for a state 1 to 5 iterations prior to a given state. Imperfect solutions are allowed but penalized. Input file to Kaggle is a csv so Matlab solutions can be posted at the Kaggle site for this event.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 7.91667px; transform-origin: 384px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis Challenge is to Solve at least 40, excluding trivials, of the 50K puzzles per these revised Life Laws. Trivial solutions are where the Final state may match the Start State.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 51.0833px; transform-origin: 404px 51.0833px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 350.35px 7.91667px; transform-origin: 350.35px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 26.95px 7.91667px; transform-origin: 26.95px 7.91667px; \"\u003e1. Any \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 188.65px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 188.65px 7.91667px; \"\u003elive cell with fewer than two live neighbors dies\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 19.25px 7.91667px; transform-origin: 19.25px 7.91667px; \"\u003e, as \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 115.5px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 115.5px 7.91667px; \"\u003eif caused by under-population.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 315.7px 7.91667px; transform-origin: 315.7px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 26.95px 7.91667px; transform-origin: 26.95px 7.91667px; \"\u003e2. Any \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 288.75px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 288.75px 7.91667px; \"\u003elive cell with two or three live neighbors lives on to the next generation.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 311.85px 7.91667px; transform-origin: 311.85px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 26.95px 7.91667px; transform-origin: 26.95px 7.91667px; \"\u003e3. Any \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 192.5px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 192.5px 7.91667px; \"\u003elive cell with more than three live neighbors dies\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 19.25px 7.91667px; transform-origin: 19.25px 7.91667px; \"\u003e, as \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 73.15px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 73.15px 7.91667px; \"\u003eif by overcrowding.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 361.9px 7.91667px; transform-origin: 361.9px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 26.95px 7.91667px; transform-origin: 26.95px 7.91667px; \"\u003e4. Any \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 242.55px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 242.55px 7.91667px; \"\u003edead cell with exactly three live neighbors becomes a live cell\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 19.25px 7.91667px; transform-origin: 19.25px 7.91667px; \"\u003e, as \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 73.15px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 73.15px 7.91667px; \"\u003eif by reproduction.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 265.65px 7.91667px; transform-origin: 265.65px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 34.65px 7.91667px; transform-origin: 34.65px 7.91667px; \"\u003e5. Edges \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 231px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 231px 7.91667px; \"\u003ewrap around. Eight Neighbors. (Change to normal planar life)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 221.317px 7.91667px; transform-origin: 221.317px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNote: The edges wrap so the matrix represents the surface of a sphere.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4333px 7.91667px; transform-origin: 19.4333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 354.317px 7.91667px; transform-origin: 354.317px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (mtest,numtosolve) the Finish state matrix of 50K rows of [casenumber, iterations, 625 values], number of case to solve (40)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.2667px 7.91667px; transform-origin: 25.2667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 339.533px 7.91667px; transform-origin: 339.533px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (mstart) the Starting state matrix of at least 40 puzzles all with perfect zero error solutions, [casenumber, 625 values]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.95px 7.91667px; transform-origin: 15.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHint:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 364.467px 7.91667px; transform-origin: 364.467px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e There are 40 non-trivial solutions for iterations 1 and 2 where a solving Start state has a single bit flip that is adjacent to a set bit or is a set bit. Cases where there are more than 40 set bits in the final state may consume significant time for no solutions. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function mstart = solveLife(mtest,numtosolve)\r\n  mstart=zeros(numtosolve,626)\r\nend","test_suite":"%%\r\n%'https://sites.google.com/site/razapor/matlab_cody/mtest.mat?attredirects=0\u0026d=1';\r\n%mtest format is [casenumer, iterations, start1:625,finish1:625] for 50K cases 0:49999\r\n%'https://sites.google.com/site/razapor/matlab_cody/mtrain.mat?attredirects=0\u0026d=1';\r\ntic\r\nfname='https://sites.google.com/site/razapor/matlab_cody/mtest.mat?attredirects=0\u0026d=1';\r\nurlwrite(fname,'mtest.mat') %1.22s\r\nload('mtest.mat'); %0.42s\r\ntoc\r\n\r\nnumtosolve=40;\r\nmstart = solveLife(mtest,numtosolve);\r\ntoc\r\nmstart=unique(mstart,'rows'); % remove exact duplicate solutions\r\n\r\n%Check for Trivial solutions; Life(mtest(case))==mtest(case)\r\nvalid=1;\r\nfor i=1:size(mstart,1)  % \r\n icase=mstart(i,1); %50000:99999\r\n iter=mtest(icase-49999,2); %Test cases start at 50000\r\n \r\n A=reshape(mtest(icase-49999,3:end),25,25);\r\n Abase=A;\r\n for j=1:iter\r\n  C=0;\r\n  for r=-1:1 % -1 Up   Using circshift to perform wrap convolution\r\n   Ar=circshift(A,r,1);\r\n   for c=-1:1 % -1 Left\r\n     Arc=circshift(Ar,c,2);\r\n     C=C+Arc;\r\n   end\r\n  end\r\n  A = C==3 | A\u0026C==4;\r\n end %j\r\n\r\n if isequal(Abase,A) % mtest [case, iter, data1:625]\r\n  valid=0; %Trivial solution entered\r\n  break;\r\n end\r\nend %main loop i\r\ntoc  % Trivial check timer\r\n\r\nLprocess=size(mstart,1)*valid;\r\nvalid=0; % Reset valid as counter for solutions\r\nfor i=1:Lprocess  % skip if any were trivial\r\n icase=mstart(i,1); %50000:99999\r\n iter=mtest(icase-49999,2); %Test cases start at 50000\r\n \r\n A=reshape(mstart(i,2:end),25,25);\r\n for j=1:iter\r\n  C=0;\r\n  for r=-1:1 % -1 Up   Using circshift to perform wrap convolution\r\n   Ar=circshift(A,r,1);\r\n   for c=-1:1 % -1 Left\r\n     Arc=circshift(Ar,c,2);\r\n     C=C+Arc;\r\n   end\r\n  end\r\n  A = C==3 | A\u0026C==4;\r\n end %j\r\n\r\n if ~isequal(A(:)',mtest(icase-49999,3:end)) % mtest [case, iter, data1:625]\r\n  valid=0; %Evolved does not match goal\r\n  break;\r\n else\r\n  valid=valid+1;\r\n end\r\nend %main loop i\r\ntoc\r\n\r\nassert(valid\u003e=40)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-06T18:14:45.000Z","updated_at":"2026-09-25T21:57:25.000Z","published_at":"2020-10-06T18:41:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.kaggle.com/c/conways-reverse-game-of-life-2020\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKaggle's Conway's Reverse Game of Life 2020 \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003econtest inspires this Life challenge. The kaggle contest runs from Oct-01-2020 thru Nov-30-2020. References:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://mathworld.wolfram.com/GameofLife.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGame of Life at Wolfram\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWiki Life\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The Kaggle event is 50K cases to solve for a state 1 to 5 iterations prior to a given state. Imperfect solutions are allowed but penalized. Input file to Kaggle is a csv so Matlab solutions can be posted at the Kaggle site for this event.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to Solve at least 40, excluding trivials, of the 50K puzzles per these revised Life Laws. Trivial solutions are where the Final state may match the Start State.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[1. Any live cell with fewer than two live neighbors dies, as if caused by under-population.\\n2. Any live cell with two or three live neighbors lives on to the next generation.\\n3. Any live cell with more than three live neighbors dies, as if by overcrowding.\\n4. Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.\\n5. Edges wrap around. Eight Neighbors. (Change to normal planar life)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: The edges wrap so the matrix represents the surface of a sphere.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (mtest,numtosolve) the Finish state matrix of 50K rows of [casenumber, iterations, 625 values], number of case to solve (40)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (mstart) the Starting state matrix of at least 40 puzzles all with perfect zero error solutions, [casenumber, 625 values]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHint:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e There are 40 non-trivial solutions for iterations 1 and 2 where a solving Start state has a single bit flip that is adjacent to a set bit or is a set bit. Cases where there are more than 40 set bits in the final state may consume significant time for no solutions. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42396,"title":"the proud tradition of zero scores in Cody","description":"The short version is: *_your function should return a zero and also have a zero score/size_*\r\n\r\nThe long version comes with a little history:\r\n\r\nThere is a long tradition of attempting to modify the scoring function in Cody to be able to create problems that score solutions, for example, based on the solution running-time instead of the solution code-complexity. There is, of course, a parallel tradition of Cody players trying to \"game\" the system into getting the lowest possible score for their solutions.\r\n \r\nCody players are a very resourceful crowd, and very early into the game they found that overwriting the solution file (after it was evaluated) did the trick: Cody would then evaluate your solution size/code-complexity from the contents of the overwritten file so problem creators could overwrite the solutions with specially-crafted files that would return the desired solution score. Also solvers could overwrite their own files to get a 0 score if they so wished, simply adding\r\n\r\n  !echo \"%\" \u003e my_fcn_name.m\r\n\r\nto their solutions. \r\n\r\nThat state of affairs, naturally, perhaps sadly, did not last long, and Cody machinery was modified to score the solutions _before_ the testsuite was run. \r\n\r\nOf course this fix lasted even shorter, and Cody players found that the variable where that score was being stored could be accessed from the testsuite code using evalin('caller',...) or assignin('caller',...) syntax (yes, that variable was very amicably named _score_). So cody creators could now add the line\r\n\r\n  assignin('caller','score',0);\r\n\r\nto their testsuite to give players a 0 (or any arbitrary) score. \r\n\r\nThis new scenario lasted for quite some time, probably because while problem creators could still modify the scoring function as they wish and create all forms of problems that departed from the size/complexity-based scoring, problem solvers could not do the same to get any arbitrary score. From the solution function perspective the variable _score_ was two(!) steps up in the stack, and there is simply no way to use evalin('caller',...) syntax recursively along the lines of\r\n\r\n  evalin('caller','assignin(''caller'',''score'',0)');\r\n \r\nSomewhat recently this situation changed again and Cody started using the Unit Testing framework to run solutions. That put _a lot_ of layers between the testsuite and the coveted workspace where the _score_ variable lived, making the assignin trick obsolete. In addition key Cody functionality was hidden into .p files, which added a small burden to exploring the inner workings of Cody, and the old _score_ variable was nowhere to be found in those new functions.\r\n\r\nYour job in this problem, following this proud tradition, is to get a zero score. Also your solution function should return a 0 as well, just to make it _do_ something. \r\n\r\nA few pointers to get you started would be:\r\n\r\n* the now somewhat obsolete \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1769-singularity-2-0-easier singularity\u003e series\r\n* the folder ~/+cody\r\n* \u003chttp://www.mathworks.com/help/matlab/ref/dbstack.html dbstack\u003e\r\n\r\nGood luck and please hack responsibly!\r\n\r\nps1. if you are thinking of submitting an empty solution, no, that does not count (that is not a function and that is not returning any number).\r\n\r\nps2. if you are thinking of copy/pasting my own _SetSolutionScore_ trick, that will not work here, sorry! (it is protected so that it only works when the testsuite code uses it; if you manage to disable this protection and make it work from within your solution file I will accept that as well as a valid solution)\r\n\r\nps3. if you want to use _SetSolutionScore_ to be able to assign not-size-based scores in your own problems, simply copy/paste the relevant code in \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1192-say-something-funny/solutions/new#test_suite_body this problem testsuite\u003e. _SetSolutionScore_, like the old _assignin_ trick, will not interfere with other problems (solvers cannot copy/paste your testsuite code to get zero-scores in other problems)\r\n\r\n*note: please refrain from using this sort of Cody tricks to get leading scores in general non-hacking problems. That is just discorteous to other players* (add here rant about the regexp trick and how leading scores used to be worth pursuing).\r\n\r\n","description_html":"\u003cp\u003eThe short version is: \u003cb\u003e\u003ci\u003eyour function should return a zero and also have a zero score/size\u003c/i\u003e\u003c/b\u003e\u003c/p\u003e\u003cp\u003eThe long version comes with a little history:\u003c/p\u003e\u003cp\u003eThere is a long tradition of attempting to modify the scoring function in Cody to be able to create problems that score solutions, for example, based on the solution running-time instead of the solution code-complexity. There is, of course, a parallel tradition of Cody players trying to \"game\" the system into getting the lowest possible score for their solutions.\u003c/p\u003e\u003cp\u003eCody players are a very resourceful crowd, and very early into the game they found that overwriting the solution file (after it was evaluated) did the trick: Cody would then evaluate your solution size/code-complexity from the contents of the overwritten file so problem creators could overwrite the solutions with specially-crafted files that would return the desired solution score. Also solvers could overwrite their own files to get a 0 score if they so wished, simply adding\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e!echo \"%\" \u0026gt; my_fcn_name.m\r\n\u003c/pre\u003e\u003cp\u003eto their solutions.\u003c/p\u003e\u003cp\u003eThat state of affairs, naturally, perhaps sadly, did not last long, and Cody machinery was modified to score the solutions \u003ci\u003ebefore\u003c/i\u003e the testsuite was run.\u003c/p\u003e\u003cp\u003eOf course this fix lasted even shorter, and Cody players found that the variable where that score was being stored could be accessed from the testsuite code using evalin('caller',...) or assignin('caller',...) syntax (yes, that variable was very amicably named \u003ci\u003escore\u003c/i\u003e). So cody creators could now add the line\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eassignin('caller','score',0);\r\n\u003c/pre\u003e\u003cp\u003eto their testsuite to give players a 0 (or any arbitrary) score.\u003c/p\u003e\u003cp\u003eThis new scenario lasted for quite some time, probably because while problem creators could still modify the scoring function as they wish and create all forms of problems that departed from the size/complexity-based scoring, problem solvers could not do the same to get any arbitrary score. From the solution function perspective the variable \u003ci\u003escore\u003c/i\u003e was two(!) steps up in the stack, and there is simply no way to use evalin('caller',...) syntax recursively along the lines of\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eevalin('caller','assignin(''caller'',''score'',0)');\r\n\u003c/pre\u003e\u003cp\u003eSomewhat recently this situation changed again and Cody started using the Unit Testing framework to run solutions. That put \u003ci\u003ea lot\u003c/i\u003e of layers between the testsuite and the coveted workspace where the \u003ci\u003escore\u003c/i\u003e variable lived, making the assignin trick obsolete. In addition key Cody functionality was hidden into .p files, which added a small burden to exploring the inner workings of Cody, and the old \u003ci\u003escore\u003c/i\u003e variable was nowhere to be found in those new functions.\u003c/p\u003e\u003cp\u003eYour job in this problem, following this proud tradition, is to get a zero score. Also your solution function should return a 0 as well, just to make it \u003ci\u003edo\u003c/i\u003e something.\u003c/p\u003e\u003cp\u003eA few pointers to get you started would be:\u003c/p\u003e\u003cul\u003e\u003cli\u003ethe now somewhat obsolete \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1769-singularity-2-0-easier\"\u003esingularity\u003c/a\u003e series\u003c/li\u003e\u003cli\u003ethe folder ~/+cody\u003c/li\u003e\u003cli\u003e\u003ca href = \"http://www.mathworks.com/help/matlab/ref/dbstack.html\"\u003edbstack\u003c/a\u003e\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eGood luck and please hack responsibly!\u003c/p\u003e\u003cp\u003eps1. if you are thinking of submitting an empty solution, no, that does not count (that is not a function and that is not returning any number).\u003c/p\u003e\u003cp\u003eps2. if you are thinking of copy/pasting my own \u003ci\u003eSetSolutionScore\u003c/i\u003e trick, that will not work here, sorry! (it is protected so that it only works when the testsuite code uses it; if you manage to disable this protection and make it work from within your solution file I will accept that as well as a valid solution)\u003c/p\u003e\u003cp\u003eps3. if you want to use \u003ci\u003eSetSolutionScore\u003c/i\u003e to be able to assign not-size-based scores in your own problems, simply copy/paste the relevant code in \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1192-say-something-funny/solutions/new#test_suite_body\"\u003ethis problem testsuite\u003c/a\u003e. \u003ci\u003eSetSolutionScore\u003c/i\u003e, like the old \u003ci\u003eassignin\u003c/i\u003e trick, will not interfere with other problems (solvers cannot copy/paste your testsuite code to get zero-scores in other problems)\u003c/p\u003e\u003cp\u003e\u003cb\u003enote: please refrain from using this sort of Cody tricks to get leading scores in general non-hacking problems. That is just discorteous to other players\u003c/b\u003e (add here rant about the regexp trick and how leading scores used to be worth pursuing).\u003c/p\u003e","function_template":"function y = zeroscore(~)\r\ny = 0;\r\n","test_suite":"%%\r\n\r\n% gets expected output/score\r\nfh=fopen('zeroscore.m');str=fread(fh,'*char')'; fclose(fh);\r\nresults=scoringengine.verifyCode(str,'assert(isequal(zeroscore(),0))');\r\n\r\n% pass/fail\r\nstr={'Failed','Passed'};\r\nif results.pass\u0026results.score=='0'\u0026ischar(results.score), \r\n    fprintf('Congrats! Solution score: %s; Solution status: %s\\n',results.score, str{1+results.pass}); \r\nelse \r\n    fprintf('Sorry! Solution score: %s; Solution status: %s\\n',results.score, str{1+results.pass}); \r\n    [a,b]=1; \r\nend\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":43,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":"2017-10-28T00:51:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-06-19T20:20:19.000Z","updated_at":"2026-09-28T14:58:36.000Z","published_at":"2015-06-21T03:36:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe short version is:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eyour function should return a zero and also have a zero score/size\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe long version comes with a little history:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere is a long tradition of attempting to modify the scoring function in Cody to be able to create problems that score solutions, for example, based on the solution running-time instead of the solution code-complexity. There is, of course, a parallel tradition of Cody players trying to \\\"game\\\" the system into getting the lowest possible score for their solutions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCody players are a very resourceful crowd, and very early into the game they found that overwriting the solution file (after it was evaluated) did the trick: Cody would then evaluate your solution size/code-complexity from the contents of the overwritten file so problem creators could overwrite the solutions with specially-crafted files that would return the desired solution score. Also solvers could overwrite their own files to get a 0 score if they so wished, simply adding\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[!echo \\\"%\\\" \u003e my_fcn_name.m]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eto their solutions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThat state of affairs, naturally, perhaps sadly, did not last long, and Cody machinery was modified to score the solutions\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ebefore\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the testsuite was run.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOf course this fix lasted even shorter, and Cody players found that the variable where that score was being stored could be accessed from the testsuite code using evalin('caller',...) or assignin('caller',...) syntax (yes, that variable was very amicably named\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003escore\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e). So cody creators could now add the line\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[assignin('caller','score',0);]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eto their testsuite to give players a 0 (or any arbitrary) score.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis new scenario lasted for quite some time, probably because while problem creators could still modify the scoring function as they wish and create all forms of problems that departed from the size/complexity-based scoring, problem solvers could not do the same to get any arbitrary score. From the solution function perspective the variable\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003escore\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e was two(!) steps up in the stack, and there is simply no way to use evalin('caller',...) syntax recursively along the lines of\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[evalin('caller','assignin(''caller'',''score'',0)');]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSomewhat recently this situation changed again and Cody started using the Unit Testing framework to run solutions. That put\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea lot\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of layers between the testsuite and the coveted workspace where the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003escore\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e variable lived, making the assignin trick obsolete. In addition key Cody functionality was hidden into .p files, which added a small burden to exploring the inner workings of Cody, and the old\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003escore\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e variable was nowhere to be found in those new functions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour job in this problem, following this proud tradition, is to get a zero score. Also your solution function should return a 0 as well, just to make it\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edo\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e something.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA few pointers to get you started would be:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe now somewhat obsolete\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1769-singularity-2-0-easier\\\"\u003e\u003cw:r\u003e\u003cw:t\u003esingularity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e series\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe folder ~/+cody\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/help/matlab/ref/dbstack.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003edbstack\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood luck and please hack responsibly!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eps1. if you are thinking of submitting an empty solution, no, that does not count (that is not a function and that is not returning any number).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eps2. if you are thinking of copy/pasting my own\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSetSolutionScore\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e trick, that will not work here, sorry! (it is protected so that it only works when the testsuite code uses it; if you manage to disable this protection and make it work from within your solution file I will accept that as well as a valid solution)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eps3. if you want to use\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSetSolutionScore\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to be able to assign not-size-based scores in your own problems, simply copy/paste the relevant code in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1192-say-something-funny/solutions/new#test_suite_body\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ethis problem testsuite\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSetSolutionScore\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, like the old\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e trick, will not interfere with other problems (solvers cannot copy/paste your testsuite code to get zero-scores in other problems)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enote: please refrain from using this sort of Cody tricks to get leading scores in general non-hacking problems. That is just discorteous to other players\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (add here rant about the regexp trick and how leading scores used to be worth pursuing).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":907,"title":"Now! (Anticheating version 1)","description":"By now, _Problem 901. Now!_ has not been solved without the use of cheats or hacks.\r\n\r\n\u003chttp://www.mathworks.com/matlabcentral/cody/problems/901-now\u003e\r\n\r\nThe goal of this Problem is to progressively design an anticheating test suite by learning from the solutions proposed by solvers of previous problems in the Now! series.","description_html":"\u003cp\u003eBy now, \u003ci\u003eProblem 901. Now!\u003c/i\u003e has not been solved without the use of cheats or hacks.\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://www.mathworks.com/matlabcentral/cody/problems/901-now\"\u003ehttp://www.mathworks.com/matlabcentral/cody/problems/901-now\u003c/a\u003e\u003c/p\u003e\u003cp\u003eThe goal of this Problem is to progressively design an anticheating test suite by learning from the solutions proposed by solvers of previous problems in the Now! series.\u003c/p\u003e","function_template":"function ans = ISaidNow\r\n   now;\r\nend","test_suite":"%%\r\n%#######################################################################%\r\nclear matlabCode;\r\n[~]=urlwrite('http://files4codygame.appspot.com/files/game.p','game.p');\r\nrehash;\r\nprotected_objs={'assert','isequal','now','error'};\r\ngame.status(protected_objs{:});\r\n%#######################################################################%\r\n\r\nnow1=ISaidNow;\r\n\r\n%#######################################################################%\r\n\r\nprotected_objs={'assert','isequal','now','error'};\r\ns2=game.status(protected_objs{:});\r\nallowed_vars={'now1'};\r\ncheated=game.cheated(allowed_vars{:});\r\n\r\nfprintf('Cheated = %d\\n',cheated)\r\nif cheated\r\nwhile 1\r\n%TIMEOUT EXPIRATION\r\nend\r\nend\r\n%#######################################################################%\r\n\r\n[~]=fft(rand(1,1000000));\r\nassert(isequal(now1,1))\r\n\r\n\r\n%%\r\n%#######################################################################%\r\n\r\nclear matlabCode;\r\n[~]=urlwrite('http://files4codygame.appspot.com/files/game.p','game.p');\r\nrehash;\r\nprotected_objs={'assert','isequal','now','error'};\r\ngame.status(protected_objs{:});\r\n\r\n%#######################################################################%\r\n\r\nnow1=ISaidNow;\r\n\r\n%#######################################################################%\r\n\r\nprotected_objs={'assert','isequal','now','error'};\r\ns2=game.status(protected_objs{:});\r\nallowed_vars={'now1'};\r\ncheated=game.cheated(allowed_vars{:});\r\n\r\nfprintf('Cheated = %d\\n',cheated)\r\nif cheated\r\nwhile 1\r\n%TIMEOUT EXPIRATION\r\nend\r\nend\r\n\r\n%#######################################################################%\r\n\r\n[~]=fft(rand(1,1000000));\r\nnow2=now;\r\nassert(isequal(now1,now2),sprintf('now1 = %.11f, now2 = %.11f',now1,now2))","published":true,"deleted":false,"likes_count":2,"comments_count":9,"created_by":5925,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2012-08-16T07:18:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-08-12T19:17:48.000Z","updated_at":"2026-09-28T15:00:20.000Z","published_at":"2012-08-16T07:06:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBy now,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem 901. Now!\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has not been solved without the use of cheats or hacks.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/901-now\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://www.mathworks.com/matlabcentral/cody/problems/901-now\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe goal of this Problem is to progressively design an anticheating test suite by learning from the solutions proposed by solvers of previous problems in the Now! series.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44270,"title":"Assert yourself!  Hack the assert function to pass this test.","description":"Have you ever wanted to test out one of those hacks you have seen which \"games\" the problem by simply overwriting the assert method?  Perhaps you have held off in good conscience or in consideration of the difficulty it brings to others wanting to find an actual, correct solution that they can learn from.  Well, this question is for you!  Please use whatever method you can to pass this test, which is otherwise stacked completely and unfairly against you.\r\n\r\n*Example 1*\r\n\r\n  y = assertYourself(10,1);\r\n  % Test is assert(false);\r\n\r\n*Example 2*\r\n\r\n  [v,y] = assertYourself(rand(10,1), 'blah','eh?');\r\n  % Test is assert(false);\r\n\r\nSee, just not fair.  \r\n\r\nNote: More unfair test cases added.","description_html":"\u003cp\u003eHave you ever wanted to test out one of those hacks you have seen which \"games\" the problem by simply overwriting the assert method?  Perhaps you have held off in good conscience or in consideration of the difficulty it brings to others wanting to find an actual, correct solution that they can learn from.  Well, this question is for you!  Please use whatever method you can to pass this test, which is otherwise stacked completely and unfairly against you.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample 1\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ey = assertYourself(10,1);\r\n% Test is assert(false);\r\n\u003c/pre\u003e\u003cp\u003e\u003cb\u003eExample 2\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e[v,y] = assertYourself(rand(10,1), 'blah','eh?');\r\n% Test is assert(false);\r\n\u003c/pre\u003e\u003cp\u003eSee, just not fair.\u003c/p\u003e\u003cp\u003eNote: More unfair test cases added.\u003c/p\u003e","function_template":"function varargout = assertYourself(varargin)\r\n  \r\nend","test_suite":"%%\r\nx = 'Try this one';\r\ny_correct = rand(1);\r\nassert(isequal(assertYourself(x),y_correct))\r\n\r\n%%\r\nclear all;\r\nx = rand(10);\r\ny_correct = rand(1);\r\nassertYourself();\r\nassert(isequal(true,false))\r\n\r\n%%\r\nclear all;\r\nx = rand(10);\r\ny = assertYourself(x,'blah')\r\ny_correct = rand(1);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nclear all;\r\nx = randi(26,10);\r\ny_correct = rand(1);\r\n[v,z]= assertYourself(x,x,x);\r\nz;\r\nmsg = ['That is not even fair!  ',char(randi(26,1,10)+'A')]\r\nassert(isequal(x,y_correct));\r\n\r\n%% \r\nclear all;\r\n[v,z]= assertYourself();\r\nv;\r\nassert(false);","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":130819,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2017-07-30T04:46:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-07-28T03:49:16.000Z","updated_at":"2026-09-28T14:59:50.000Z","published_at":"2017-07-28T03:58:18.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHave you ever wanted to test out one of those hacks you have seen which \\\"games\\\" the problem by simply overwriting the assert method? Perhaps you have held off in good conscience or in consideration of the difficulty it brings to others wanting to find an actual, correct solution that they can learn from. Well, this question is for you! Please use whatever method you can to pass this test, which is otherwise stacked completely and unfairly against you.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[y = assertYourself(10,1);\\n% Test is assert(false);]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[[v,y] = assertYourself(rand(10,1), 'blah','eh?');\\n% Test is assert(false);]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee, just not fair.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: More unfair test cases added.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"errors":[],"facets":[[{"value":"Cody Challenge","count":15,"selected":false},{"value":"Advanced Cryptography Algorithms and Mathematics","count":12,"selected":false},{"value":"Algorithm I","count":12,"selected":false},{"value":"Computer Games II","count":12,"selected":false},{"value":"Tough Stuff","count":12,"selected":false},{"value":"Computer Games III","count":10,"selected":false},{"value":"Cody5:Hard","count":9,"selected":false},{"value":"The Complexity Paradigm","count":8,"selected":false},{"value":"Easy Sequences Volume VI","count":7,"selected":false},{"value":"Prime Numbers III","count":7,"selected":false},{"value":"Easy Sequences Volume I","count":6,"selected":false},{"value":"Easy Sequences Volume IV","count":6,"selected":false},{"value":"Easy Sequences Volume V:  Fibonacci Obsession","count":6,"selected":false},{"value":"Probability \u0026 Stats","count":6,"selected":false},{"value":"Water Pouring Series","count":6,"selected":false},{"value":"Computational Geometry II","count":5,"selected":false},{"value":"Easy Sequences Volume III","count":5,"selected":false},{"value":"Easy Sequences Volume VIII","count":5,"selected":false},{"value":"Number theory","count":5,"selected":false},{"value":"Paper-\u0026-pencil Games","count":5,"selected":false},{"value":"Randomness","count":5,"selected":false},{"value":"Classic Game Puzzles","count":4,"selected":false},{"value":"Computer Games I","count":4,"selected":false},{"value":"Easy Sequences Volume VII","count":4,"selected":false},{"value":"Functions II","count":4,"selected":false},{"value":"Project Euler III","count":4,"selected":false},{"value":"Board Games I","count":3,"selected":false},{"value":"Combinatorics II","count":3,"selected":false},{"value":"Generate a point cloud","count":3,"selected":false},{"value":"Groundwater","count":3,"selected":false},{"value":"Magic Numbers","count":3,"selected":false},{"value":"Magic Numbers III","count":3,"selected":false},{"value":"Master Regular Expression","count":3,"selected":false},{"value":"Matrix Patterns I","count":3,"selected":false},{"value":"Number Manipulation III","count":3,"selected":false},{"value":"Operations","count":3,"selected":false},{"value":"Project Euler IV","count":3,"selected":false},{"value":"Special Functions","count":3,"selected":false},{"value":"The Prime Directive","count":3,"selected":false},{"value":"Word Puzzles","count":3,"selected":false},{"value":"Basics - 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