{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","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":"2026-04-06T00:00:00.000Z","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":50447,"title":"Calculate Triangle Area, A, B and Gamma is given.","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: 359px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 179.5px; transform-origin: 407px 179.5px; 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=\"\"\u003eCalculate Triangle Area:\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; \"\u003e 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; \"\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; \"\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; \"\u003e\u003cspan style=\"\"\u003eand\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; \"\u003e Gamma\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 [degree] is given as follows:\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: 209px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 104.5px; text-align: left; transform-origin: 384px 104.5px; 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 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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-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=\"\"\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=\"\"\u003eRound the answer to four decimal places\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\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaTriangle(A, B, Gamma)\r\n\r\nend","test_suite":"%% \r\nA = 4; B = 6; Gamma = 56.45; % [degree]\r\ny_correct = 10.0008\r\nassert(isequal(AreaTriangle(A, B, Gamma),y_correct))\r\n\r\n%%\r\nA = 5.7; B = 8.9; Gamma = 132; % [degree]\r\n\r\ny_correct = 18.8499\r\nassert(isequal(AreaTriangle(A, B, Gamma),y_correct))\r\n\r\n%%\r\nA = 48.3; B = 643; Gamma = 8; % [degree]\r\n\r\ny_correct = 2161.1425\r\nassert(isequal(AreaTriangle(A, B, Gamma),y_correct))\r\n\r\n%%\r\nA = pi; B = 2*pi; Gamma = 43; % [degree]\r\n\r\ny_correct = 6.7311\r\nassert(isequal(AreaTriangle(A, B, Gamma),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-18T16:05:19.000Z","updated_at":"2026-03-21T09:29:10.000Z","published_at":"2021-02-18T16:05:19.000Z","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\u003eCalculate Triangle Area:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e 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\u003eB \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e Gamma\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [degree] is given as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003e 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of a triangle","description":"A triangle is given with base *'b'* ,vertical hight *'h'* . then find it's area.","description_html":"\u003cp\u003eA triangle is given with base \u003cb\u003e'b'\u003c/b\u003e ,vertical hight \u003cb\u003e'h'\u003c/b\u003e . then find it's area.\u003c/p\u003e","function_template":"function A = trg_area(b,h)\r\n A=f(b,h);\r\nend","test_suite":"%%\r\nb = 1;\r\nh=5\r\ny_correct = 2.5;\r\nassert(isequal(trg_area(b,h),y_correct))\r\n\r\n%%\r\nb = 1;\r\nh=10\r\ny_correct = 5;\r\nassert(isequal(trg_area(b,h),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":22553,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":982,"test_suite_updated_at":"2014-07-07T12:31:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-06-18T17:40:40.000Z","updated_at":"2026-02-13T06:59:31.000Z","published_at":"2014-06-18T17:40:40.000Z","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 triangle is given with base\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'b'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ,vertical hight\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'h'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e . then find it's area.\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":61070,"title":"Square area to triangle area","description":"Given the area, A, of a square with side length, c, if a right angle triangle has the same area A and the hypothenuse length 2c (two times the square side), then find the height, h, of the triangle.\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho","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: 163.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 81.875px; transform-origin: 408px 81.875px; 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=\"\"\u003eGiven the area, \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; \"\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=\"\"\u003e, of a square with side length, \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; \"\u003ec\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, if a right angle triangle has the same area \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; \"\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=\"\"\u003e and the hypothenuse length \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; \"\u003e2c \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(two times the square side), then find the height, \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; \"\u003eh\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 the triangle.\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=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.75px; 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: 392px 40.875px; transform-origin: 392px 40.875px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; 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: 364px 10.2125px; text-align: left; transform-origin: 364px 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=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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: 364px 10.2125px; text-align: left; transform-origin: 364px 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=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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: 364px 10.2125px; text-align: left; transform-origin: 364px 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=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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: 364px 10.2125px; text-align: left; transform-origin: 364px 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=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function h = find_height(A)\r\n h = A;\r\nend","test_suite":"%%\r\nA = 8;\r\nh_correct = 4;\r\nassert(isequal(find_height(A),h_correct))\r\n\r\n%%\r\nfiletext = fileread('find_height.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 9;\r\nh_correct = 3*sqrt(2);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 15;\r\nh_correct = sqrt(30);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 16;\r\nh_correct = 4*sqrt(2);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 18;\r\nh_correct = 6;\r\nassert(isequal(find_height(A),h_correct))\r\n\r\n%%\r\nA = 32;\r\nh_correct = 8;\r\nassert(isequal(find_height(A),h_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":5,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-09T16:09:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-09T13:39:12.000Z","updated_at":"2026-03-23T20:43:13.000Z","published_at":"2025-11-09T16:09:35.000Z","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\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a square with side length, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, if a right angle triangle has the same area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and the hypothenuse length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2c \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(two times the square side), then find the height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\u003eForbidden functions / expressions\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\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":45897,"title":" Volume of Equilateral Triangle Prism","description":"Find volume of equilateral triangle prism\r\nx = side of triangle\r\nl = length of prism","description_html":"\u003cp\u003eFind volume of equilateral triangle prism\r\nx = side of triangle\r\nl = length of prism\u003c/p\u003e","function_template":"function y = volumeofequilateraltriangleprism(x,l)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 2;\r\nl = 5;\r\ny_correct = ((x^2*sqrt(3))/4)*l;\r\nassert(isequal(volumeofequilateraltriangleprism(x,l),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":441903,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":86,"test_suite_updated_at":"2020-06-12T20:14:39.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-12T20:08:02.000Z","updated_at":"2026-02-12T12:18:43.000Z","published_at":"2020-06-12T20:08:53.000Z","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\u003eFind volume of equilateral triangle prism x = side of triangle l = length of prism\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":55895,"title":"Tipos de Triangulos","description":"Dados os tamanhos dos lados de um triangulos A, B e C. Retorne qual o tipo do triangulo: 'equilátero', 'escaleno' ou 'isósceles'.\r\nTipoTriangulo(1, 2, 3) = 'escaleno'","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: 72.4375px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36.2188px; transform-origin: 407px 36.2188px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eDados os tamanhos dos lados de um triangulos A, B e C. Retorne qual o tipo do triangulo: 'equilátero', 'escaleno' ou 'isósceles'.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4375px; 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 10.2188px; transform-origin: 404px 10.2188px; 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; \"\u003eTipoTriangulo(1, 2, 3) = \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); text-emphasis-color: rgb(170, 4, 249); \"\u003e'escaleno'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = TipoTriangulo(A, B, C)\r\n %faça a sua solução\r\nend","test_suite":"%%\r\nA = 1;\r\nB = 2;\r\nC = 3;\r\ny_correct = 'escaleno';\r\nassert(isequal(TipoTriangulo(A, B, C),y_correct))\r\n\r\n\r\n%%\r\nA = 2;\r\nB = 2;\r\nC = 3;\r\ny_correct = 'isósceles';\r\nassert(isequal(TipoTriangulo(A, B, C),y_correct))\r\n\r\n\r\n%%\r\nA = 2;\r\nB = 2;\r\nC = 2;\r\ny_correct = 'equilátero';\r\nassert(isequal(TipoTriangulo(A, B, C),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":2564100,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":32,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-17T17:43:31.000Z","updated_at":"2026-02-09T14:17:00.000Z","published_at":"2022-09-17T17:43:31.000Z","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\u003eDados os tamanhos dos lados de um triangulos A, B e C. Retorne qual o tipo do triangulo: 'equilátero', 'escaleno' ou 'isósceles'.\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[TipoTriangulo(1, 2, 3) = 'escaleno']]\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":45217,"title":"Find a common vertex","description":"First input is T, a triplet list of indices. Second input is i, a single index (positive integer). The goal of this function is to find and return the indices of the rows in the list which contain this particular index. Output format is indifferently a column or a row vector.\r\nFor example if inputs are\r\nT = [1 2 3;...\r\n 1 3 4;...\r\n 1 4 2;...\r\n 2 3 4]\r\nand\r\ni = 2\r\nthe output is the vector\r\nrow_idx = [1 3 4]\r\nsince 2 is contained in rows number 1, 3, and 4 of T. If the index is not in the list, the function must of course return the empty set. Each index is at most contained once per row / triplet.\r\n\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","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: 479.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 239.8px; transform-origin: 408px 239.8px; 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: 385px 31.5px; text-align: left; transform-origin: 385px 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: 375.725px 8px; transform-origin: 375.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFirst input is T, a triplet list of indices. Second input is i, a single index (positive integer). The goal of this function is to find and return the indices of the rows in the list which contain this particular index. Output format is indifferently a column or a row vector.\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: 77.0167px 8px; transform-origin: 77.0167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example if inputs are\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: 405px 40.8667px; transform-origin: 405px 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003eT = [1 2 3;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 1 3 4;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 1 4 2;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 42.35px 8.5px; tab-size: 4; transform-origin: 42.35px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 2 3 4]\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; 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: 405px 10.2167px; transform-origin: 405px 10.2167px; 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; text-wrap-mode: 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: 19.25px 8.5px; tab-size: 4; transform-origin: 19.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ei = 2\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 70.7833px 8px; transform-origin: 70.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe output is the vector\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; 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: 405px 10.2167px; transform-origin: 405px 10.2167px; 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; text-wrap-mode: 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: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003erow_idx = [1 3 4]\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; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; 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: 367.533px 8px; transform-origin: 367.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince 2 is contained in rows number 1, 3, and 4 of T. If the index is not in the list, the function must of course return the empty set. Each index is at most contained once per row / triplet.\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 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: 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function row_idx = find_common_vertex(T,i)\r\n row_idx = i;\r\nend","test_suite":"%% Tetrahedron\r\nT = [1 2 3;...\r\n 1 3 4;...\r\n 1 4 2;...\r\n 2 3 4];\r\n\r\ni = 2;\r\n\r\nrow_idx = [1 3 4];\r\n\r\nassert(isequal(find_common_vertex(T,i),row_idx) || isequal(find_common_vertex(T,i),row_idx'))\r\n\r\n%% Octahedron\r\nT = [1 2 3;...\r\n 1 3 4;...\r\n 1 4 5;...\r\n 1 5 2;...\r\n 6 3 2;...\r\n 6 4 3;...\r\n 6 5 4;...\r\n 6 2 5];\r\n\r\ni = 4;\r\n\r\nrow_idx = [2 3 6 7];\r\n\r\nassert(isequal(find_common_vertex(T,i),row_idx) || isequal(find_common_vertex(T,i),row_idx'))\r\n\r\n%% Triangulated cube\r\nT = [1 2 4;...\r\n 2 3 4;...\r\n 5 6 8;...\r\n 6 7 8;...\r\n 1 2 5;...\r\n 2 5 6;...\r\n 2 3 6;...\r\n 3 6 7;...\r\n 3 4 7;...\r\n 4 7 8;...\r\n 4 1 8;...\r\n 1 8 5];\r\n\r\ni = 6;\r\n\r\nrow_idx = [3 4 6 7 8];\r\n\r\nassert(isequal(find_common_vertex(T,i),row_idx) || isequal(find_common_vertex(T,i),row_idx'))\r\n\r\n%% Empty set test\r\nT = [2 3 5;...\r\n 3 5 7;...\r\n 5 7 11;...\r\n 7 11 13];\r\n\r\ni = 8;\r\n\r\nassert(isempty(find_common_vertex(T,i)))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('find_common_vertex.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:50:48.000Z","deleted_by":null,"deleted_at":null,"solvers_count":43,"test_suite_updated_at":"2025-07-09T05:47:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-12-01T16:22:33.000Z","updated_at":"2026-03-02T14:28:36.000Z","published_at":"2019-12-01T16:58:33.000Z","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\u003eFirst input is T, a triplet list of indices. Second input is i, a single index (positive integer). The goal of this function is to find and return the indices of the rows in the list which contain this particular index. Output format is indifferently a column or a row vector.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 if inputs are\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[T = [1 2 3;...\\n 1 3 4;...\\n 1 4 2;...\\n 2 3 4]]]\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\u003eand\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[i = 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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe output is the vector\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[row_idx = [1 3 4]]]\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 2 is contained in rows number 1, 3, and 4 of T. If the index is not in the list, the function must of course return the empty set. Each index is at most contained once per row / triplet.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\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:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\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":55905,"title":"Triangulo Semelhante","description":"Dados dois vetores A = (a1, a2, a3) e B = (b1, b2, b3) sendo referentes a arestas de triangulos. Verifique se os triangulos são semelhantes, retorne true ou false.\r\nTriangulosSemelhantes([6, 4, 2], [3, 2, 1]) = true;","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: 72.4375px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36.2188px; transform-origin: 407px 36.2188px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eDados dois vetores A = (a1, a2, a3) e B = (b1, b2, b3) sendo referentes a arestas de triangulos. Verifique se os triangulos são semelhantes, retorne true ou false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4375px; 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 10.2188px; transform-origin: 404px 10.2188px; 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; \"\u003eTriangulosSemelhantes([6, 4, 2], [3, 2, 1]) = true;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = TriangulosSemelhantes(A, B)\r\n % faça a sua solução aqui\r\nend","test_suite":"%%\r\nA = [6, 4, 2];\r\nB = [3, 2, 1];\r\ny_correct = true;\r\nassert(isequal(TriangulosSemelhantes(A, B), y_correct))\r\n\r\n%%\r\nA = [7, 6, 2];\r\nB = [3, 2, 1];\r\ny_correct = false;\r\nassert(isequal(TriangulosSemelhantes(A, B), y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":2564100,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":33,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-17T18:36:29.000Z","updated_at":"2026-02-12T12:21:15.000Z","published_at":"2022-09-17T18:36:29.000Z","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\u003eDados dois vetores A = (a1, a2, a3) e B = (b1, b2, b3) sendo referentes a arestas de triangulos. Verifique se os triangulos são semelhantes, retorne true ou false.\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[TriangulosSemelhantes([6, 4, 2], [3, 2, 1]) = true;]]\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":60855,"title":"What kind of triangle?","description":"Write a function named check_triangle that receives three positive integers as input: a, b, and c.\r\nThese three numbers are intended to represent the sides of a triangle.\r\nThe function should return in the variable t one of the following four strings:\r\na. Not a triangle – The numbers cannot represent the sides of a triangle because they do not satisfy the triangle inequality rule: the sum of any two sides must be greater than the third side.\r\n(Example: the triple 2, 3, 20 does not satisfy the rule because 2 + 3 is not greater than 20.)\r\nb. Equilateral – The numbers represent the sides of an equilateral triangle (example: 4, 4, 4).\r\nc. Isosceles – The numbers represent the sides of an isosceles triangle (example: 5, 5, 4).\r\nd. Scalene – The numbers represent the sides of a scalene triangle (a triangle that is neither equilateral nor isosceles) (example: 4, 8, 5).\r\nHint: use the if ... else if ... structure.\r\nAssume that the input always consists of three positive integers (greater than zero).\r\nImportant:\r\nYou must return only the most accurate conclusion regarding the triple a, b, c.\r\nFor example, if the triangle is equilateral, return only the corresponding string \"Equilateral\" and not \"Isosceles\"or \"Scalene\".\r\n\r\nTerms: \r\nEquilateral – all three sides are equal\r\nIsosceles – two sides are equal\r\nScalene – all sides are different\r\nNot a triangle – the numbers cannot form a triangle","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: 624px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 312px; transform-origin: 408px 312px; 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: 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 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; font-weight: 700; \"\u003echeck_triangle\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 receives three positive integers as input: \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; \"\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=\"\"\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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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, 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ec\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; 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=\"\"\u003eThese three numbers are intended to represent the sides of a triangle.\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=\"\"\u003eThe function should return in the variable \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; \"\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 one of the following four strings:\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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-weight: 700; \"\u003eNot a triangle\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 – The numbers cannot represent the sides of a triangle because they do not satisfy the triangle inequality rule: the sum of any two sides must be greater than the third side.\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=\"\"\u003e(Example: the triple \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; \"\u003e2, 3, 20\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 does not satisfy the rule because \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; \"\u003e2 + 3\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 is not greater than \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; \"\u003e20\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; 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=\"\"\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=\"font-weight: 700; \"\u003eEquilateral\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 – The numbers represent the sides of an equilateral triangle (example: \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; \"\u003e4, 4, 4\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; 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=\"\"\u003ec. \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; \"\u003eIsosceles\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 – The numbers represent the sides of an isosceles triangle (example: \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; \"\u003e5, 5, 4\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; 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=\"\"\u003ed. \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; \"\u003eScalene\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 – The numbers represent the sides of a scalene triangle (a triangle that is neither equilateral nor isosceles) (example: \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; \"\u003e4, 8, 5\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; 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=\"\"\u003eHint: use the \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; \"\u003eif ... else if ... \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=\"\"\u003estructure.\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=\"\"\u003eAssume that the input always consists of three positive integers (greater than zero).\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=\"font-weight: 700; \"\u003eImportant:\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=\"\"\u003eYou must return \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; \"\u003eonly the most accurate conclusion\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 regarding the triple \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; \"\u003ea, b, c\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; 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=\"\"\u003eFor example, if the triangle is equilateral, return only the corresponding string \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; \"\u003e\"Equilateral\" \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=\"\"\u003eand not \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; \"\u003e\"Isosceles\"\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=\"\"\u003eor \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; \"\u003e\"Scalene\"\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; 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=\"\"\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=\"font-weight: 700; \"\u003eTerms:\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; 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=\"font-weight: 700; \"\u003eEquilateral\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 – all three sides are equal\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=\"font-weight: 700; \"\u003eIsosceles\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 – two sides are equal\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=\"font-weight: 700; \"\u003eScalene\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 – all sides are different\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=\"font-weight: 700; \"\u003eNot a triangle\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 – the numbers cannot form a triangle\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = check_triangle(a,b,c)\r\n t = 'Not a triangle';\r\nend","test_suite":"%%\r\na=4;\r\nb=6;\r\nc=4;\r\nt_correct = 'Isosceles';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n\r\n\r\n%%\r\na=4;\r\nb=4;\r\nc=4;\r\nt_correct = 'Equilateral';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n\r\n\r\n%%\r\na=3;\r\nb=4;\r\nc=5;\r\nt_correct = 'Scalene';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n\r\n%%\r\na=3;\r\nb=14;\r\nc=15;\r\nt_correct = 'Scalene';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n\r\n%%\r\na=1;\r\nb=1;\r\nc=1;\r\nt_correct = 'Equilateral';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n\r\n\r\n\r\n%%\r\na=4;\r\nb=5;\r\nc=30;\r\nt_correct = 'Not a triangle';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n\r\n%%\r\na=4;\r\nb=2;\r\nc=6;\r\nt_correct = 'Not a triangle';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n\r\n%%\r\na=40;\r\nb=5;\r\nc=3;\r\nt_correct = 'Not a triangle';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n\r\n%%\r\na=4;\r\nb=50;\r\nc=3;\r\nt_correct = 'Not a triangle';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n\r\n%%\r\na=4;\r\nb=4;\r\nc=7;\r\nt_correct = 'Isosceles';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n\r\n%%\r\na=8;\r\nb=8;\r\nc=5;\r\nt_correct = 'Isosceles';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":2710538,"edited_by":2710538,"edited_at":"2025-04-27T18:25:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":70,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-04-27T17:26:20.000Z","updated_at":"2026-03-04T22:12:48.000Z","published_at":"2025-04-27T17:26:19.000Z","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 named \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\u003echeck_triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that receives three positive integers as input: \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\u003ea\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\u003eb\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\u003ec\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\u003eThese three numbers are intended to represent the sides of a triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 should return in the variable \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\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e one of the following four strings:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNot a triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e – The numbers cannot represent the sides of a triangle because they do not satisfy the triangle inequality rule: the sum of any two sides must be greater than the third side.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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(Example: the triple \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\u003e2, 3, 20\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e does not satisfy the rule because \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\u003e2 + 3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is not greater than \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\u003e20\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\u003eb. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEquilateral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e – The numbers represent the sides of an equilateral triangle (example: \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, 4, 4\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\u003ec. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIsosceles\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e – The numbers represent the sides of an isosceles triangle (example: \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\u003e5, 5, 4\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\u003ed. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScalene\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e – The numbers represent the sides of a scalene triangle (a triangle that is neither equilateral nor isosceles) (example: \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, 8, 5\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\u003eHint: use the \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\u003eif ... else if ... \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003estructure.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssume that the input always consists of three positive integers (greater than 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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eImportant:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 must return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eonly the most accurate conclusion\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e regarding the triple \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\u003ea, b, c\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\u003eFor example, if the triangle is equilateral, return only the corresponding string \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\\\"Equilateral\\\" \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand not \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\\\"Isosceles\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eor \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\\\"Scalene\\\"\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\u003eTerms:\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEquilateral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e – all three sides are equal\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\u003eIsosceles\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e – two sides are equal\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\u003eScalene\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e – all sides are different\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\u003eNot a triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e – the numbers cannot form a triangle\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":50452,"title":"Calculate Triangle Area: A, B and Beta is given","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: 275px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 137.5px; transform-origin: 407px 137.5px; 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=\"\"\u003eCalculate Triangle Area: \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; \"\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; \"\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; \"\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; \"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBeta\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 [degree] is given as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 215px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 107.5px; text-align: left; transform-origin: 384px 107.5px; 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\u003cimg class=\"imageNode\" width=\"269\" height=\"209\" style=\"vertical-align: baseline;width: 269px;height: 209px\" 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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-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=\"\"\u003e Round the answer to four decimal places\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaTriangle(A, B, Beta)\r\n\r\nend","test_suite":"%% \r\nA = 4; B = 4; Beta = 45; % [degree]\r\n\r\ny_correct = 8\r\nassert(isequal(AreaTriangle(A, B, Beta),y_correct))\r\n\r\n%%\r\nA = 6.39; B = 4.9; Beta = 32.9; % [degree]\r\n\r\ny_correct = 15.3134\r\nassert(isequal(AreaTriangle(A, B, Beta),y_correct))\r\n\r\n%%\r\nA = 257; B = 567; Beta = 23.8; % [degree]\r\n\r\ny_correct = 41099.6329\r\nassert(isequal(AreaTriangle(A, B, Beta),y_correct))\r\n\r\n%%\r\nA = 2*pi; B = 3*pi; Beta = 56.3; % [degree]\r\n\r\ny_correct = 29.6088\r\nassert(isequal(AreaTriangle(A, B, Beta),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-18T16:37:21.000Z","updated_at":"2026-03-14T18:27:52.000Z","published_at":"2021-02-18T16:44:29.000Z","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\u003eCalculate Triangle Area: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\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 and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBeta\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [degree] is given as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"209\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"269\\\"/\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\u003c/w:p\u003e\u003cw:p\u003e\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 Round the answer to four decimal 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60982,"title":"Mesh the square with triangles","description":"Problem statement\r\n\r\nAn square is a regular polygon with 4 vertices and 4 edges.\r\nA triangulated mesh T (stands for triangles here) -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh, that is to say give one triangulation T of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\r\n\r\nExample\r\nThe first triangle here can be [1, 2, 3] if counterclockwise oriented.\r\n\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","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: 995.233px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 497.617px; transform-origin: 408px 497.617px; 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: 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: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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: 183.608px 8px; transform-origin: 183.608px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn square is a regular polygon with 4 vertices and 4 edges.\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.1833px 8px; transform-origin: 64.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh \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: 4.275px 8px; transform-origin: 4.275px 8px; 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: 176.983px 8px; transform-origin: 176.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (stands for triangles here) -or a triangulation- is simply 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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 132.633px 8px; transform-origin: 132.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \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 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: 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: 192.275px 8px; transform-origin: 192.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh, that is to say give one triangulation \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: 4.275px 8px; transform-origin: 4.275px 8px; 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: 183.583px 8px; transform-origin: 183.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\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: 92.9583px 8px; transform-origin: 92.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle here can 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: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 3]\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: 89.8583px 8px; transform-origin: 89.8583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented.\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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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 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: 340.5px; 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: 385px 170.25px; text-align: left; transform-origin: 385px 170.25px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"447\" height=\"335\" style=\"vertical-align: baseline;width: 447px;height: 335px\" 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margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\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; 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 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: 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_square()\r\n T = 1;\r\nend","test_suite":"%% Test every possible solutions\r\nT_correct1 = [1 2 3;\r\n 3 4 1];\r\n\r\nT_correct2 = [2 3 4;\r\n 1 2 4];\r\n\r\nassert(isequal(sortrows(sort(mesh_the_square(),2)),sortrows(sort(T_correct1,2)))...\r\n | isequal(sortrows(sort(mesh_the_square(),2)),sortrows(sort(T_correct2,2))))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_square.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:45:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T16:29:27.000Z","updated_at":"2026-02-10T17:10:21.000Z","published_at":"2025-07-23T16:40:49.000Z","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\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\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\u003eAn square is a regular polygon with 4 vertices and 4 edges.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 triangulated mesh \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 (stands for triangles here) -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eYour task here is to mesh, that is to say give one triangulation \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 of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\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\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 first triangle here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"335\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"447\\\"/\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\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\u003eForbidden functions / expressions\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation 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triangles from edge","description":"First input is T, a Triplet list of indices -whom each row actually contains the three indices of a triangle vertices-. size(T) = [nb_triangles, 3]. Second input is e = [e1, e2], a row vector, couple of indices. Output S is the triplet list of indices which Share the edge e. For instance, if\r\ne = [2, 4]\r\nand T a tetrahedron\r\nT = [1, 2, 3;...\r\n 1, 3, 4;...\r\n 1, 2, 4;...\r\n 2, 3, 4]\r\nthen the output of the function is\r\nS = [1, 2, 4;...\r\n 2, 3, 4]\r\nsince both triangles [1, 2, 4] and [2, 3, 4] contain the edge [2, 4].\r\nConditions :\r\nIf the edge is not part of any triangle in the list, the function must of course return the empty set, [].\r\nEdges are symmetric : [e1, e2] is the same edge as [e2, e1]\r\nOrder of rows / edges in the output doesn't matter.\r\nTriangle indices are assumed always to be sorted in ascending order, T = [t1, t2, t3] with t1 \u003c t2 \u003c t3.\r\nEvery indices are positive, distinct integers.\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","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: 572.2px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 286.1px; transform-origin: 408px 286.1px; 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: 385px 31.5px; text-align: left; transform-origin: 385px 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: 374.5px 8px; transform-origin: 374.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFirst input is T, a Triplet list of indices -whom each row actually contains the three indices of a triangle vertices-. size(T) = [nb_triangles, 3]. Second input is e = [e1, e2], a row vector, couple of indices. Output S is the triplet list of indices which Share the edge e. For instance, if\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; 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: 405px 10.2167px; transform-origin: 405px 10.2167px; 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; text-wrap-mode: 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: 38.5px 8.5px; tab-size: 4; transform-origin: 38.5px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ee = [2, 4]\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 61.4583px 8px; transform-origin: 61.4583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand T a tetrahedron\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: 405px 40.8667px; transform-origin: 405px 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003eT = [1, 2, 3;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 1, 3, 4;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 1, 2, 4;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 50.05px 8.5px; tab-size: 4; transform-origin: 50.05px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 2, 3, 4]\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 99.5667px 8px; transform-origin: 99.5667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen the output of the function is\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: 405px 20.4333px; transform-origin: 405px 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003eS = [1, 2, 4;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 50.05px 8.5px; tab-size: 4; transform-origin: 50.05px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 2, 3, 4]\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 197.567px 8px; transform-origin: 197.567px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince both triangles [1, 2, 4] and [2, 3, 4] contain the edge [2, 4].\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: 40.8167px 8px; transform-origin: 40.8167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConditions :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.167px; 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: 392px 51.0833px; transform-origin: 392px 51.0833px; 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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 302.95px 8px; transform-origin: 302.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf the edge is not part of any triangle in the list, the function must of course return the empty set, [].\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 69.6167px 8px; transform-origin: 69.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEdges are symmetric :\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\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: 118.233px 8px; transform-origin: 118.233px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e[e1, e2] is the same edge as [e2, e1]\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 167.692px 8px; transform-origin: 167.692px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOrder of rows / edges in the output doesn't matter.\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 330.342px 8px; transform-origin: 330.342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTriangle indices are assumed always to be sorted in ascending order, T = [t1, t2, t3] with t1 \u0026lt; t2 \u0026lt; t3.\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 17.8917px 8px; transform-origin: 17.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEvery\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\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: 124.817px 8px; transform-origin: 124.817px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eindices are positive, distinct integers.\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; 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function S = find_triangles_from_edge(T,e)\r\n S = [];\r\nend","test_suite":"%% Tetrahedron\r\nT = [1, 2, 3;...\r\n 1, 3, 4;...\r\n 1, 2, 4;...\r\n 2, 3, 4];\r\n\r\ne = [2, 4];\r\n\r\nS = [1, 2, 4;...\r\n 2, 3, 4];\r\n\r\nassert(isequal(sortrows(find_triangles_from_edge(T,e)),S))\r\n\r\n%% Filled octahedron (two pyramids stuck together via their square bases)\r\nT = [1, 2, 3;...\r\n 1, 3, 4;...\r\n 1, 4, 5;...\r\n 1, 2, 5;...\r\n 2, 3, 6;...\r\n 3, 4, 6;...\r\n 4, 5, 6;...\r\n 2, 5, 6;...\r\n 2, 3, 4;...\r\n 2, 4, 5;...\r\n 1, 2, 4;...\r\n 2, 4, 6];\r\n\r\ne = [2, 4];\r\n\r\nS = [1, 2, 4;...\r\n 2, 3, 4;...\r\n 2, 4, 5;...\r\n 2, 4, 6];\r\n\r\nassert(isequal(sortrows(find_triangles_from_edge(T,e)),S))\r\n\r\n%% Triangulated cube\r\nT = [1, 2, 4;...\r\n 2, 3, 4;...\r\n 5, 6, 8;...\r\n 6, 7, 8;...\r\n 1, 2, 5;...\r\n 2, 5, 6;...\r\n 2, 3, 6;...\r\n 3, 6, 7;...\r\n 3, 4, 7;...\r\n 4, 7, 8;...\r\n 1, 4, 8;...\r\n 1, 5, 8];\r\n\r\ne = [3, 7];\r\n\r\nS = [3, 4, 7;...\r\n 3, 6, 7];\r\n\r\nassert(isequal(sortrows(find_triangles_from_edge(T,e)),S))\r\n\r\n%% Empty set test\r\nT = [2, 3, 5;...\r\n 3, 5, 7;...\r\n 5, 7, 11;...\r\n 7, 11, 13];\r\n\r\ne = [6, 8];\r\n\r\nassert(isempty(find_triangles_from_edge(T,e)))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('find_triangles_from_edge.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:51:41.000Z","deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":"2025-07-09T05:48:39.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-12-03T18:46:56.000Z","updated_at":"2025-12-18T17:15:46.000Z","published_at":"2019-12-03T20:30:58.000Z","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\u003eFirst input is T, a Triplet list of indices -whom each row actually contains the three indices of a triangle vertices-. size(T) = [nb_triangles, 3]. Second input is e = [e1, e2], a row vector, couple of indices. Output S is the triplet list of indices which Share the edge e. For instance, 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[e = [2, 4]]]\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\u003eand T a tetrahedron\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[T = [1, 2, 3;...\\n 1, 3, 4;...\\n 1, 2, 4;...\\n 2, 3, 4]]]\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\u003ethen the output of the function 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[S = [1, 2, 4;...\\n 2, 3, 4]]]\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 both triangles [1, 2, 4] and [2, 3, 4] contain the edge [2, 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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConditions :\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 the edge is not part of any triangle in the list, the function must of course return the empty set, [].\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\u003eEdges are symmetric :\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[e1, e2] is the same edge as [e2, e1]\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOrder of rows / edges in the output doesn't matter.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTriangle indices are assumed always to be sorted in ascending order, T = [t1, t2, t3] with t1 \u0026lt; t2 \u0026lt; t3.\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\u003eEvery\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\u003eindices are positive, distinct integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\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:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\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":44085,"title":"Can the given sides form a triangle?","description":"Can the three given sides form a triangle?","description_html":"\u003cp\u003eCan the three given sides form a triangle?\u003c/p\u003e","function_template":"function y = isTriangle(sides)\r\n y = false;\r\nend","test_suite":"%%\r\nx = [3 4 5];\r\ny_correct = true;\r\nassert(isequal(isTriangle(x),y_correct))\r\n\r\n%%\r\nx = [1 3 5];\r\ny_correct = false;\r\nassert(isequal(isTriangle(x),y_correct))\r\n\r\n%%\r\nx = [6 5 3];\r\ny_correct = true;\r\nassert(isequal(isTriangle(x),y_correct))\r\n\r\n%%\r\nx = [3 3 3];\r\ny_correct = true;\r\nassert(isequal(isTriangle(x),y_correct))\r\n\r\n%%\r\nx = [4 7 5];\r\ny_correct = true;\r\nassert(isequal(isTriangle(x),y_correct))\r\n\r\n%%\r\nx = [5 8 3];\r\ny_correct = false;\r\nassert(isequal(isTriangle(x),y_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":63069,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":140,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-03-13T19:09:28.000Z","updated_at":"2026-03-14T18:36:17.000Z","published_at":"2017-03-13T19:15:30.000Z","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\",\"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\u003eCan the three given sides form a triangle?\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":45179,"title":"The length of the equal sides of an isoceles triangle is 'a'.For all the possible (integer) values of the remaining side,find the associated angles between the two equal sides.","description":"the remaining side may have many possible values.only assume integer ones for simplicity.","description_html":"\u003cp\u003ethe remaining side may have many possible values.only assume integer ones for simplicity.\u003c/p\u003e","function_template":"function y = isoceles(a)\r\n y = a;\r\nend","test_suite":"%%\r\na = 2;\r\ny_correct = [ 28.9550 97.1808];\r\nassert(isequal(isoceles(a),y_correct))\r\n%%\r\na = 3;\r\ny_correct = [ 19.1881\t38.9424\t83.6206\t112.8854];\r\nassert(isequal(isoceles(a),y_correct))\r\n%%\r\na = 1;\r\ny_correct = [];\r\nassert(isequal(isoceles(a),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":4,"created_by":363598,"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":1,"created_at":"2019-10-19T16:23:25.000Z","updated_at":"2026-01-18T13:33:34.000Z","published_at":"2019-10-19T17:45:07.000Z","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\u003ethe remaining side may have many possible values.only assume integer ones for simplicity.\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":45218,"title":"Find a common edge","description":"First input is T, a triplet list of indices. Second input is e = [e1 e2], a row vector, couple of indices (positive distinct integers always sorted in ascending order, ie e1 \u003c e2 ). The goal of this function is to find and return the indices of the rows in the list which contain this particular edge. Output format can be either a column or a row vector.\r\nFor example if inputs are\r\nT = [1 2 3 ;\r\n 1 3 4 ;\r\n 1 4 2 ;\r\n 2 3 4]\r\nand\r\ne = [2 3]\r\nthe output is the vector\r\nrow_idx = [1 4]\r\nsince [2 3] is contained in rows number 1 and 4 of T. With the same input T, but with e = [2 4] this time, the output is the vector row_idx = [3 4], since [2 4] is contained in rows number 3 and 4 of T (Note that edge [b a] is the same as edge [a b] so must be the corresponding outputs). If the edge is not in the list, the function must of course return the empty set.\r\n\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","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: 500.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 250.3px; transform-origin: 408px 250.3px; 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: 385px 31.5px; text-align: left; transform-origin: 385px 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: 377.083px 8px; transform-origin: 377.083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFirst input is T, a triplet list of indices. Second input is e = [e1 e2], a row vector, couple of indices (positive distinct integers always sorted in ascending order, ie\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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 23.5417px 8px; transform-origin: 23.5417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ee1 \u0026lt; e2\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: 247.358px 8px; transform-origin: 247.358px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ). The goal of this function is to find and return the indices of the rows in the list which contain this particular edge. Output format can be either a column or a row vector.\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: 77.0167px 8px; transform-origin: 77.0167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example if inputs are\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: 405px 40.8667px; transform-origin: 405px 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 46.2px 8.5px; tab-size: 4; transform-origin: 46.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eT = [1 2 3 ;\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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 46.2px 8.5px; tab-size: 4; transform-origin: 46.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 3 4 ;\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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 46.2px 8.5px; tab-size: 4; transform-origin: 46.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 4 2 ;\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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 42.35px 8.5px; tab-size: 4; transform-origin: 42.35px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 2 3 4]\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; 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: 405px 10.2167px; transform-origin: 405px 10.2167px; 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; text-wrap-mode: 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: 34.65px 8.5px; tab-size: 4; transform-origin: 34.65px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ee = [2 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; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 70.7833px 8px; transform-origin: 70.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe output is the vector\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; 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: 405px 10.2167px; transform-origin: 405px 10.2167px; 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; text-wrap-mode: 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: 57.75px 8.5px; tab-size: 4; transform-origin: 57.75px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003erow_idx = [1 4]\u003c/span\u003e\u003c/span\u003e\u003c/div\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: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; 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: 369.667px 8px; transform-origin: 369.667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince [2 3] is contained in rows number 1 and 4 of T. With the same input T, but with e = [2 4] this time, the output is the vector row_idx = [3 4], since [2 4] is contained in rows number 3 and 4 of T (Note that\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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 117.825px 8px; transform-origin: 117.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eedge [b a] is the same as edge [a b]\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: 1.725px 8px; transform-origin: 1.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e so must be the corresponding outputs). If the edge is not in the list, the function must of course return the empty set.\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 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: 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function row_idx = find_common_edge(T,e)\r\n row_idx = e;\r\nend","test_suite":"%% Tetrahedron 1\r\nT = [1 2 3;...\r\n 1 3 4;...\r\n 1 4 2;...\r\n 2 3 4];\r\n\r\ne = [2 3];\r\nrow_idx = [1 4];\r\n\r\nassert(isequal(find_common_edge(T,e),row_idx) || isequal(find_common_edge(T,e),row_idx'))\r\n\r\n%% Tetrahedron 2\r\nT = [1 2 3;...\r\n 1 3 4;...\r\n 1 4 2;...\r\n 2 3 4];\r\n\r\ne = [2 4];\r\nrow_idx = [3 4];\r\n\r\nassert(isequal(find_common_edge(T,e),row_idx) || isequal(find_common_edge(T,e),row_idx'))\r\n\r\n%% Octahedron\r\nT = [1 2 3;...\r\n 1 3 4;...\r\n 1 4 5;...\r\n 1 5 2;...\r\n 6 3 2;...\r\n 6 4 3;...\r\n 6 5 4;...\r\n 6 2 5];\r\n\r\ne = [1 5];\r\nrow_idx = [3 4];\r\n\r\nassert(isequal(find_common_edge(T,e),row_idx) || isequal(find_common_edge(T,e),row_idx'))\r\n\r\n%% Triangulated cube\r\nT = [1 2 4;...\r\n 2 3 4;...\r\n 5 6 8;...\r\n 6 7 8;...\r\n 1 2 5;...\r\n 2 5 6;...\r\n 2 3 6;...\r\n 3 6 7;...\r\n 3 4 7;...\r\n 4 7 8;...\r\n 4 1 8;...\r\n 1 8 5];\r\n\r\ne = [6 7];\r\nrow_idx = [4 8];\r\n\r\nassert(isequal(find_common_edge(T,e),row_idx) || isequal(find_common_edge(T,e),row_idx'))\r\n\r\n%% Empty set test\r\nT = [2 3 5;...\r\n 3 5 7;...\r\n 5 7 11;...\r\n 7 11 13];\r\n\r\ne = [6 28];\r\n\r\nassert(isempty(find_common_edge(T,e)))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('find_common_edge.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:50:32.000Z","deleted_by":null,"deleted_at":null,"solvers_count":42,"test_suite_updated_at":"2025-07-09T05:45:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-12-01T17:21:36.000Z","updated_at":"2026-03-14T18:58:02.000Z","published_at":"2019-12-01T18:01:01.000Z","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\u003eFirst input is T, a triplet list of indices. Second input is e = [e1 e2], a row vector, couple of indices (positive distinct integers always sorted in ascending order, ie\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\u003ee1 \u0026lt; e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ). The goal of this function is to find and return the indices of the rows in the list which contain this particular edge. Output format can be either a column or a row vector.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 if inputs are\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[T = [1 2 3 ;\\n 1 3 4 ;\\n 1 4 2 ;\\n 2 3 4]]]\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\u003eand\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[e = [2 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\u003ethe output is the vector\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[row_idx = [1 4]]]\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 [2 3] is contained in rows number 1 and 4 of T. With the same input T, but with e = [2 4] this time, the output is the vector row_idx = [3 4], since [2 4] is contained in rows number 3 and 4 of T (Note that\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\u003eedge [b a] is the same as edge [a b]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e so must be the corresponding outputs). If the edge is not in the list, the function must of course return the empty set.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\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:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\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":60166,"title":"Recursive triangle area","description":"Given triangle 1 with sides of length a, b, and c. Triangle 2 is constructed within triangle 1 by bisecting each side. Triangle 3 is constructed within triangle 2 by bisecting each of triangle 2's sides. And so on. \r\nFind the area of triangle n.","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: 71.9661px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 359.492px 35.9766px; transform-origin: 359.499px 35.9831px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 41.9792px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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: 336.497px 20.9896px; text-align: left; transform-origin: 336.497px 20.9896px; 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=\"\"\u003eGiven triangle 1 with sides of length a, b, and c. Triangle 2 is constructed within triangle 1 by bisecting each side. Triangle 3 is constructed within triangle 2 by bisecting each of triangle 2's sides. And so on. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9896px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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: 336.497px 10.4948px; text-align: left; transform-origin: 336.497px 10.4948px; 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=\"\"\u003eFind the area of triangle n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = your_fcn_name(a,b,c,n)\r\n area = a+b+c+n;\r\nend","test_suite":"%%\r\na=1;b=1;c=sqrt(2);n=1;\r\ny_correct = 0.50;\r\nassert(your_fcn_name(a,b,c,n) - y_correct \u003c y_correct/1000)\r\n\r\n\r\n%%\r\na=100;b=100;c=100;n=2;\r\ny_correct = 1082.53;\r\nassert(your_fcn_name(a,b,c,n) - y_correct \u003c y_correct/1000)\r\n\r\n\r\n%%\r\na=13;b=33;c=44;n=4;\r\ny_correct = 2.0540;\r\nassert(your_fcn_name(a,b,c,n) - y_correct \u003c y_correct/1000)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":3293343,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-30T18:08:43.000Z","updated_at":"2026-03-11T15:33:11.000Z","published_at":"2024-04-30T18:08:43.000Z","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:t\u003eGiven triangle 1 with sides of length a, b, and c. Triangle 2 is constructed within triangle 1 by bisecting each side. Triangle 3 is constructed within triangle 2 by bisecting each of triangle 2's sides. 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\u003eFind the area of triangle n.\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":60980,"title":"Mesh the tetrahedron","description":"Problem statement\r\n\r\nAn tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five well known platonic solids.\r\nA triangulated mesh -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh this tetrahedron. To do so, you will list the triangles/rows in a matrix of triangles, T. You will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles [1, 2, 3] and [3, 2, 1] are distinct).\r\nOn the other hand [1, 2, 3], [2, 3, 1] and [3, 1, 2] are one same unique triangle.\r\nThe row order of the triangles in the list doesn't matter.\r\n \r\nEdit / update\r\nTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\r\n\r\nExample\r\nThe first triangle (X \u003e 0 and Y \u003e 0) here can be [1, 2, 4] if counterclockwise oriented (normals outward).\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","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: 1194.73px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 597.367px; transform-origin: 408px 597.367px; 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: 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: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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; 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: 374.592px 8px; transform-origin: 374.592px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five well known platonic solids.\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.542px 8px; transform-origin: 157.542px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh -or a triangulation- is simply 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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 206.533px 8px; transform-origin: 206.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \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 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: 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: 385px 31.5px; text-align: left; transform-origin: 385px 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: 328.017px 8px; transform-origin: 328.017px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh this tetrahedron. To do so, you will list the triangles/rows in a matrix of triangles, \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: 7.51667px 8px; transform-origin: 7.51667px 8px; 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: 49.4667px 8px; transform-origin: 49.4667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles \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: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3]\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 8px; transform-origin: 15.5583px 8px; 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: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[3, 2, 1]\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: 40.0583px 8px; transform-origin: 40.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are distinct).\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: 58.3417px 8px; transform-origin: 58.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the other hand \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: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3]\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 8px; transform-origin: 3.88333px 8px; 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: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[2, 3, 1]\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 8px; transform-origin: 15.5583px 8px; 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: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[3, 1, 2]\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: 94.5333px 8px; transform-origin: 94.5333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are one same unique triangle.\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: 168.575px 8px; transform-origin: 168.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe row order of the triangles in the list doesn't matter.\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: 13.5917px 8px; transform-origin: 13.5917px 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: 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: 41.9833px 8px; transform-origin: 41.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEdit / update\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: 351.75px 8px; transform-origin: 351.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\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 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: 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: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\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: 52.1167px 8px; transform-origin: 52.1167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle \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: 53.2917px 8px; transform-origin: 53.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(X \u0026gt; 0 and Y \u0026gt; 0)\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: 42.7833px 8px; transform-origin: 42.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e here can 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: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 4]\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: 148.208px 8px; transform-origin: 148.208px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented (normals outward).\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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan 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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: 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 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: 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: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; 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: 392px 40.8667px; transform-origin: 392px 40.8667px; 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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\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; 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 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: 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_tetrahedron()\r\n T = 1;\r\nend","test_suite":"%%\r\nT_correct = [1 2 4;\r\n 2 3 4;\r\n 3 1 4;\r\n 1 3 2];\r\n\r\n% Check every possible solutions\r\nassert(isequal(sortrows(sort(mesh_the_tetrahedron(),2)),sortrows(sort(T_correct,2))))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_tetrahedron.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:43:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":39,"test_suite_updated_at":"2025-07-23T16:17:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T11:03:01.000Z","updated_at":"2026-03-31T18:44:34.000Z","published_at":"2025-07-23T11:11:01.000Z","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\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\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\u003eAn tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five well known platonic solids.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 triangulated mesh -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eYour task here is to mesh this tetrahedron. To do so, you will list the triangles/rows in a matrix of triangles, \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\u003eYou will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 3]\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3, 2, 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are distinct).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the other hand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 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[2, 3, 1]\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3, 1, 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are one same unique triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eEdit / update\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 first triangle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(X \u0026gt; 0 and Y \u0026gt; 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented (normals outward).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"378\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"504\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\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\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\u003eForbidden functions / expressions\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 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Numbers Below N","description":"This is an offshoot of \u003chttp://www.mathworks.com/matlabcentral/cody/problems/5-triangle-numbers Cody Problem 5: Triangle Numbers\u003e.\r\n\r\nTriangle numbers are the sums of successive integers. So 6 is a triangle number because\r\n\r\n 6 = 1 + 2 + 3\r\n\r\nwhich can be displayed in a triangular shape like so\r\n\r\n *\r\n * *\r\n * * * \r\n\r\nReturn all triangle numbers below _N_.","description_html":"\u003cp\u003eThis is an offshoot of \u003ca href=\"http://www.mathworks.com/matlabcentral/cody/problems/5-triangle-numbers\"\u003eCody Problem 5: Triangle Numbers\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eTriangle numbers are the sums of successive integers. So 6 is a triangle number because\u003c/p\u003e\u003cpre\u003e 6 = 1 + 2 + 3\u003c/pre\u003e\u003cp\u003ewhich can be displayed in a triangular shape like so\u003c/p\u003e\u003cpre\u003e *\r\n * *\r\n * * * \u003c/pre\u003e\u003cp\u003eReturn all triangle numbers below \u003ci\u003eN\u003c/i\u003e.\u003c/p\u003e","function_template":"function y = TriBeNum(num)\r\n y = 1:num;\r\nend","test_suite":"%%\r\nx = 100;\r\ny_correct = cumsum(1:13);\r\nassert(isequal(TriBeNum(x),y_correct))\r\n\r\n%%\r\nx = 1000;\r\ny_correct = cumsum(1:44);\r\nassert(isequal(TriBeNum(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":134,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":237,"test_suite_updated_at":"2012-02-08T23:52:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-08T23:52:34.000Z","updated_at":"2026-03-14T18:52:07.000Z","published_at":"2012-02-08T23:54:52.000Z","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 is an offshoot 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.mathworks.com/matlabcentral/cody/problems/5-triangle-numbers\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 5: Triangle Numbers\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\u003eTriangle numbers are the sums of successive integers. So 6 is a triangle number because\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[ 6 = 1 + 2 + 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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhich can be displayed in a triangular shape like so\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[ *\\n * *\\n * * *]]\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\u003eReturn all triangle numbers below\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\u003eN\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\"},{\"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":45259,"title":"Build edges list","description":"Input T is a triangulation connectivity indices list (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\r\nThe purpose of this function is to query the list E of all the edges.\r\nFor instance if T = [1, 2, 3; 4, 5, 6; 7, 8, 9], then the output of the function must be E = [1, 2; 1, 3; 2, 3; 4, 5; 4, 6; 5, 6; 7, 8; 7, 9; 8, 9] (all the 3 possible combination of the 3 vertices of a triangle / row, for every triangle / row of the list).\r\nHypothesis on output E :\r\nsize(E) = [N, 2], with N the number of edges\r\nE doesn't need to be ordered neither following dimension 1 (rows) nor dimension 2 (columns), but must not contain duplicated edges\r\nEdges are symmetric : [e1, e2] is the same edge as [e2, e1]\r\nEvery indices are positive, distinct integers.\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","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: 366.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 183.083px; transform-origin: 408px 183.083px; 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: 367.967px 8px; transform-origin: 367.967px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInput T is a triangulation connectivity indices list (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\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: 200.692px 8px; transform-origin: 200.692px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe purpose of this function is to query the list E of all the edges.\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384.55px 8px; transform-origin: 384.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor instance if T = [1, 2, 3; 4, 5, 6; 7, 8, 9], then the output of the function must be E = [1, 2; 1, 3; 2, 3; 4, 5; 4, 6; 5, 6; 7, 8; 7, 9; 8, 9] (all the 3 possible combination of the 3 vertices of a triangle / row, for every triangle / row of the list).\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: 82.8083px 8px; transform-origin: 82.8083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHypothesis on output E :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.167px; 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: 392px 51.0833px; transform-origin: 392px 51.0833px; 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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 135.933px 8px; transform-origin: 135.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esize(E) = [N, 2], with N the number of edges\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; 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: 364px 20.4333px; text-align: left; transform-origin: 364px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 318.758px 8px; transform-origin: 318.758px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eE doesn't need to be ordered neither following dimension 1 (rows) nor dimension 2 (columns), but must\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\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: 39.65px 8px; transform-origin: 39.65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003enot contain duplicated edges\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 194.858px 8px; transform-origin: 194.858px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEdges are symmetric : [e1, e2] is the same edge as [e2, e1]\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 133.808px 8px; transform-origin: 133.808px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEvery indices are positive, distinct integers.\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; 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function E = query_edges_list(T)\r\n E = T;\r\nend","test_suite":"%% Description example\r\nT = [1, 2, 3;...\r\n 4, 5, 6;...\r\n 7, 8, 9];\r\n \r\nE = [1, 2;...\r\n 1, 3;...\r\n 2, 3;...\r\n 4, 5;...\r\n 4, 6;...\r\n 5, 6;...\r\n 7, 8;...\r\n 7, 9;...\r\n 8, 9];\r\n\r\nassert(isequal(sortrows(sort(query_edges_list(T),2)),E))\r\n\r\n%% Another test\r\nT = [2, 3, 5;...\r\n 7, 11, 13;...\r\n 17, 19, 23];\r\n \r\nE = [2, 3;...\r\n 2, 5;...\r\n 3, 5;...\r\n 7, 11;...\r\n 7, 13;...\r\n 11, 13;...\r\n 17, 19;...\r\n 17, 23;...\r\n 19, 23];\r\n\r\nassert(isequal(sortrows(sort(query_edges_list(T),2)),E))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('query_edges_list.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:49:28.000Z","deleted_by":null,"deleted_at":null,"solvers_count":40,"test_suite_updated_at":"2025-07-09T05:51:51.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-08T15:52:04.000Z","updated_at":"2025-12-07T21:53:51.000Z","published_at":"2020-01-08T17:13:08.000Z","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\u003eInput T is a triangulation connectivity indices list (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 purpose of this function is to query the list E of all the edges.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 instance if T = [1, 2, 3; 4, 5, 6; 7, 8, 9], then the output of the function must be E = [1, 2; 1, 3; 2, 3; 4, 5; 4, 6; 5, 6; 7, 8; 7, 9; 8, 9] (all the 3 possible combination of the 3 vertices of a triangle / row, for every triangle / row of the list).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\u003eHypothesis on output E :\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\u003esize(E) = [N, 2], with N the number of edges\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\u003eE doesn't need to be ordered neither following dimension 1 (rows) nor dimension 2 (columns), but must\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\u003enot contain duplicated edges\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEdges are symmetric : [e1, e2] is the same edge as [e2, e1]\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\u003eEvery indices are positive, distinct integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\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:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\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":60984,"title":"Mesh the icosahedron","description":"Problem statement\r\n\r\nAn icosahedron is a regular polyhedron with 12 vertices and 20 triangular faces. It is also one of the five well known platonic solids. \r\nA triangulation, or triangulated mesh, is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh this icosahedron. To do so, you will list the triangles/rows in a matrix of triangles, T.\r\nThe row order of the triangles in the list doesn't matter.\r\n\r\nTip\r\nVertex indices are written on the figure below; use it to help you visualize;\r\nYou can start with the triangles of the top cap and bottom cap, they are the easiest ones to identify here.\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","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: 996.1px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 498.05px; transform-origin: 408px 498.05px; 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: 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: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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; 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: 384.717px 8px; transform-origin: 384.717px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn icosahedron is a regular polyhedron with 12 vertices and 20 triangular faces. It is also one of the five well known platonic solids. \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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 150.925px 8px; transform-origin: 150.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulation, or triangulated mesh, is simply 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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 229.017px 8px; transform-origin: 229.017px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \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 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: 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: 334.633px 8px; transform-origin: 334.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh this icosahedron. To do so, you will list the triangles/rows in a matrix of triangles, T\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: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 168.575px 8px; transform-origin: 168.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe row order of the triangles in the list doesn't matter.\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 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: 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: 10.3667px 8px; transform-origin: 10.3667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTip\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; 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: 392px 20.4333px; transform-origin: 392px 20.4333px; 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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 226.783px 8px; transform-origin: 226.783px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eVertex indices are written on the figure below; use it to help you visualize;\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 321.4px 8px; transform-origin: 321.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou can start with the triangles of the top cap and bottom cap, they are the easiest ones to identify here.\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; 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 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: 339.5px; font-family: Helvetica, Arial, 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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: 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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; 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: 392px 40.8667px; transform-origin: 392px 40.8667px; 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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\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; 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_icosahedron()\r\n T = 1;\r\nend","test_suite":"%%\r\nT_correct = [1 2 3;\r\n 1 3 4;\r\n 1 4 5;\r\n 1 5 6;\r\n 1 6 2; \r\n 8 7 9;\r\n 7 10 9;\r\n 7 11 10;\r\n 7 12 11;\r\n 7 8 12; \r\n 2 11 3;\r\n 3 11 12\r\n 3 12 4;\r\n 4 12 8;\r\n 4 8 5;\r\n 5 8 9;\r\n 5 9 6;\r\n 6 9 10;\r\n 2 6 10;\r\n 2 10 11];\r\n\r\n% Check every possible solutions\r\nassert(isequal(sortrows(sort(mesh_the_icosahedron(),2)),sortrows(sort(T_correct,2))))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_icosahedron.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:46:02.000Z","deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T20:09:09.000Z","updated_at":"2026-02-13T17:44:47.000Z","published_at":"2025-07-24T14:11:48.000Z","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\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\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\u003eAn icosahedron is a regular polyhedron with 12 vertices and 20 triangular faces. It is also one of the five well known platonic solids. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 triangulation, or triangulated mesh, is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eYour task here is to mesh this icosahedron. To do so, you will list the triangles/rows in a matrix of triangles, T\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\u003c/w:p\u003e\u003cw:p\u003e\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 row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eTip\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\u003eVertex indices are written on the figure below; use it to help you visualize;\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\u003eYou can start with the triangles of the top cap and bottom cap, they are the easiest ones to identify here.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"334\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"446\\\"/\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\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\u003eForbidden functions / expressions\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\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 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and wrong","description":"Given a vector of lengths [a b c], determines whether a triangle with those sides lengths is a right triangle: \u003chttp://en.wikipedia.org/wiki/Right_triangle\u003e.\r\n\r\nExamples:\r\n\r\n[3 4 5] ---\u003e true\r\n\r\n[5 12 13] ---\u003e true\r\n\r\n[5 5 5] ---\u003e false","description_html":"\u003cp\u003eGiven a vector of lengths [a b c], determines whether a triangle with those sides lengths is a right triangle: \u003ca href=\"http://en.wikipedia.org/wiki/Right_triangle\"\u003ehttp://en.wikipedia.org/wiki/Right_triangle\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cp\u003e[3 4 5] ---\u003e true\u003c/p\u003e\u003cp\u003e[5 12 13] ---\u003e true\u003c/p\u003e\u003cp\u003e[5 5 5] ---\u003e false\u003c/p\u003e","function_template":"function y = right(sides)\r\n y = sides;\r\nend","test_suite":"%%\r\nsides = [3 4 5];\r\ntf_correct = true;\r\nassert(isequal(right(sides),tf_correct))\r\n%%\r\nsides = [3 5 4];\r\ntf_correct = true;\r\nassert(isequal(right(sides),tf_correct))\r\n%%\r\nsides = [5 12 13];\r\ntf_correct = true;\r\nassert(isequal(right(sides),tf_correct))\r\n%%\r\nsides = [5 5 5];\r\ntf_correct = false;\r\nassert(isequal(right(sides),tf_correct))\r\n%%\r\nsides = [113 112 15];\r\ntf_correct = true;\r\nassert(isequal(right(sides),tf_correct))\r\n%%\r\nsides = [113 110 15];\r\ntf_correct = false;\r\nassert(isequal(right(sides),tf_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":11,"comments_count":3,"created_by":39,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1440,"test_suite_updated_at":"2013-05-25T12:43:14.000Z","rescore_all_solutions":false,"group_id":17,"created_at":"2012-01-29T15:17:31.000Z","updated_at":"2026-02-27T10:50:39.000Z","published_at":"2012-02-17T20:59:33.000Z","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 vector of lengths [a b c], determines whether a triangle with those sides lengths is a right triangle:\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/Right_triangle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://en.wikipedia.org/wiki/Right_triangle\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\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[3 4 5] ---\u0026gt; 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\u003e[5 12 13] ---\u0026gt; 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\u003e[5 5 5] ---\u0026gt; false\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":45230,"title":"Remove duplicated triangles","description":"Input T is a triangulation (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\r\nIt sometimes happens a triangle may be duplicated several times. The goal of this problem is to remove all the duplicated triangles of T, and to keep only one.\r\nFor instance if :\r\nT_in = [1 2 3;...\r\n 4 5 6;...\r\n 1 2 3;...\r\n 7 8 9;...\r\n 6 4 5;...\r\n 10 11 12;...\r\n 2 1 3;...\r\n 8 7 9;...\r\n 10 11 12]\r\nthen the output must be :\r\nT_out = [1 2 3;...\r\n 4 5 6;...\r\n 7 8 9;...\r\n 10 11 12]\r\nsince rows [1 2 3], [6 4 5], [2 1 3], [8 7 9], and [10 11 12] are just duplicata. Indeed triangle [i2 i1 i3] is the same as triangle [i1 i2 i3] for example.\r\nHypothesis :\r\nT is always a N x 3 integer matrix with N \u003e 0 (non empty matrix)\r\nEach row / triangle of T always contains three distinct integers\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","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: 673.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 336.75px; transform-origin: 408px 336.75px; 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: 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: 380.425px 8px; transform-origin: 380.425px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInput T is a triangulation (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.533px 8px; transform-origin: 376.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIt sometimes happens a triangle may be duplicated several times. The goal of this problem is to remove all the duplicated triangles of T, and to keep only one.\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: 47.8333px 8px; transform-origin: 47.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor instance if :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 183.9px; 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: 405px 91.95px; transform-origin: 405px 91.95px; 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 53.9px 8.5px; transform-origin: 53.9px 8.5px; \"\u003eT_in = [1 2 3;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 53.9px 8.5px; transform-origin: 53.9px 8.5px; \"\u003e 4 5 6;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 53.9px 8.5px; transform-origin: 53.9px 8.5px; \"\u003e 1 2 3;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 53.9px 8.5px; transform-origin: 53.9px 8.5px; \"\u003e 7 8 9;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 53.9px 8.5px; transform-origin: 53.9px 8.5px; \"\u003e 6 4 5;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 77px 8.5px; tab-size: 4; transform-origin: 77px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 65.45px 8.5px; transform-origin: 65.45px 8.5px; \"\u003e 10 11 12;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 53.9px 8.5px; transform-origin: 53.9px 8.5px; \"\u003e 2 1 3;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 53.9px 8.5px; transform-origin: 53.9px 8.5px; \"\u003e 8 7 9;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 10 11 12]\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 77.3917px 8px; transform-origin: 77.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen the output must be :\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: 405px 40.8667px; transform-origin: 405px 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 69.3px 8.5px; tab-size: 4; transform-origin: 69.3px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 57.75px 8.5px; transform-origin: 57.75px 8.5px; \"\u003eT_out = [1 2 3;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 69.3px 8.5px; tab-size: 4; transform-origin: 69.3px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 57.75px 8.5px; transform-origin: 57.75px 8.5px; \"\u003e 4 5 6;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 69.3px 8.5px; tab-size: 4; transform-origin: 69.3px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 57.75px 8.5px; transform-origin: 57.75px 8.5px; \"\u003e 7 8 9;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 69.3px 8.5px; tab-size: 4; transform-origin: 69.3px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 10 11 12]\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; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; 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: 385px 8px; transform-origin: 385px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince rows [1 2 3], [6 4 5], [2 1 3], [8 7 9], and [10 11 12] are just duplicata. Indeed triangle [i2 i1 i3] is the same as triangle [i1 i2 i3] for example.\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: 38.5083px 8px; transform-origin: 38.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHypothesis :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; 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: 392px 20.4333px; transform-origin: 392px 20.4333px; 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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 209.408px 8px; transform-origin: 209.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eT is always a N x 3 integer matrix with N \u0026gt; 0 (non empty matrix)\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 191.758px 8px; transform-origin: 191.758px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach row / triangle of T always contains three distinct integers\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; 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T_out = remove_duplicated_triangles(T_in)\r\n T_out = T_in;\r\nend","test_suite":"%% Intro example\r\nT_in = [1 2 3;...\r\n 4 5 6;...\r\n 1 2 3;...\r\n 7 8 9;...\r\n 6 4 5;...\r\n 10 11 12;...\r\n 2 1 3;...\r\n 8 7 9;...\r\n 10 11 12];\r\n \r\nT_out = [1 2 3;...\r\n 4 5 6;...\r\n 7 8 9;...\r\n 10 11 12];\r\n\r\nassert(isequal(remove_duplicated_triangles(T_in),T_out))\r\n\r\n%% Single triangle\r\nT_in = [3 5 7];\r\nT_out = T_in;\r\nassert(isequal(remove_duplicated_triangles(T_in),T_out))\r\n\r\n%% One duplicated triangle\r\nT_in = [2 11 13;...\r\n 2 13 11;...\r\n 11 2 13;...\r\n 11 13 2;...\r\n 13 2 11;...\r\n 13 11 2];\r\n\r\nT_out = [2 11 13];\r\nassert(isequal(remove_duplicated_triangles(T_in),T_out))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('remove_duplicated_triangles.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:50:13.000Z","deleted_by":null,"deleted_at":null,"solvers_count":50,"test_suite_updated_at":"2025-07-09T05:52:22.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-12-11T10:22:14.000Z","updated_at":"2025-11-16T17:58:55.000Z","published_at":"2019-12-11T10:37:52.000Z","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\u003eInput T is a triangulation (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 sometimes happens a triangle may be duplicated several times. The goal of this problem is to remove all the duplicated triangles of T, and to keep only one.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 instance 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[T_in = [1 2 3;...\\n 4 5 6;...\\n 1 2 3;...\\n 7 8 9;...\\n 6 4 5;...\\n 10 11 12;...\\n 2 1 3;...\\n 8 7 9;...\\n 10 11 12]]]\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\u003ethen the output must be :\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[T_out = [1 2 3;...\\n 4 5 6;...\\n 7 8 9;...\\n 10 11 12]]]\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 rows [1 2 3], [6 4 5], [2 1 3], [8 7 9], and [10 11 12] are just duplicata. Indeed triangle [i2 i1 i3] is the same as triangle [i1 i2 i3] for 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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHypothesis :\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT is always a N x 3 integer matrix with N \u0026gt; 0 (non empty matrix)\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\u003eEach row / triangle of T always contains three distinct integers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\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:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\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":61076,"title":"Covering rectangle area of a four-pointed star polygon","description":"Given the four-pointed star polygon formed by the rectangle, with dimensions l1xl2, and four triangles, with height, h, from their bases to the apices, find the rectangle, with dimensions y1xy2, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). Given x=[l1 l2 h], return y=[y1 y2].\r\n\r\n","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: 520.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 260.4px; transform-origin: 408px 260.4px; 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: 385px 31.5px; text-align: left; transform-origin: 385px 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=\"\"\u003eGiven the four-pointed star polygon formed by the rectangle, with dimensions \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; \"\u003el1xl2\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, and four triangles, with height, \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; \"\u003eh,\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 from their bases to the apices, find the rectangle, with dimensions \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; \"\u003ey1xy2\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, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). Given \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; \"\u003ex=[l1 l2 h]\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, return \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; \"\u003ey=[y1 y2]\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: 418.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 209.4px; text-align: left; transform-origin: 385px 209.4px; white-space-collapse: preserve; 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: 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=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = covering(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = [2 7 4];\r\ny_correct = [5 10];\r\nassert(isequal(covering(x),y_correct))\r\n\r\n%%\r\nx = [7 2 1];\r\ny_correct = [2.5 -2.5] + 1.5*sqrt(13);\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nx = [5 2 1];\r\ny_correct = [3 -3]/2 + sqrt(77)/2;\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nfiletext = fileread('covering.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = [7 9 5];\r\ny_correct = [11 13];\r\nassert(isequal(covering(x),y_correct))\r\n\r\n%%\r\nx = [7 9 1];\r\ny_correct = [-1 1] + 4*sqrt(5);\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-16T14:03:25.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-15T16:57:30.000Z","updated_at":"2026-03-27T12:50:09.000Z","published_at":"2025-11-16T14:03:25.000Z","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\u003eGiven the four-pointed star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1xl2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the apices, find the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey1xy2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). Given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex=[l1 l2 h]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey=[y1 y2]\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"413\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"508\\\"/\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 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the hypotenuse of a right triangle without using ^ and sqrt ()","description":"Find out the hypotenuse of right triangle.\r\n\r\n\r\nSay a = 4, b = 3 then c = 5 \r\n\r\n\r\nPlease don't use ^ and sqrt() function. ","description_html":"\u003cp\u003eFind out the hypotenuse of right triangle.\u003c/p\u003e\u003cp\u003eSay a = 4, b = 3 then c = 5\u003c/p\u003e\u003cp\u003ePlease don't use ^ and sqrt() function.\u003c/p\u003e","function_template":"function y = hypotenuse(a,b)\r\n y = sqrt(a^2+b^2)\r\nend","test_suite":"%%\r\na = 3;\r\nb= 4;\r\ny_correct = 5;\r\nassert(abs(hypotenuse(a,b)-y_correct)\u003c0.0001)\r\n\r\n%%\r\na = 2;\r\nb = pi * 2;\r\ny_correct = sqrt(a^2+b^2);\r\nassert(abs(hypotenuse(a,b)-y_correct)\u003c0.0001)\r\n\r\n%%\r\na = randi(10);\r\nb = randi(13);\r\ny_correct = sqrt(a^2+b^2);\r\nassert(abs(hypotenuse(a,b)-y_correct)\u003c0.0001)\r\n\r\n%%\r\nuser_solution = fileread('hypotenuse.m');\r\nassert(isempty(strfind(user_solution,'^')));\r\n\r\n%%\r\nassessFunctionAbsence({'sqrt'}, 'FileName', 'hypotenuse.m');\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":14644,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":104,"test_suite_updated_at":"2016-11-30T19:36:02.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-16T08:20:00.000Z","updated_at":"2026-04-03T02:50:47.000Z","published_at":"2016-10-16T08:20:07.000Z","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\u003eFind out the hypotenuse of right triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSay a = 4, b = 3 then c = 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\u003ePlease don't use ^ and sqrt() function.\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":43601,"title":"Find the sines of an isosceles triangle when given its area and height","description":"Find the sines of an isosceles triangle when given its area and height.\r\nFor example, when A=12 and h=4, the result is [0.8 0.8 0.96].","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: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; 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: 219.5px 8px; transform-origin: 219.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the sines of an isosceles triangle when given its area and height.\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: 192.5px 8px; transform-origin: 192.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, when A=12 and h=4, the result is [0.8 0.8 0.96].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = theSineOfAnglesOfATriangle(A,h)\r\n y = x;\r\nend","test_suite":"%%\r\nA = 12;\r\nh = 4;\r\ny_correct = [0.8, 0.8, 0.96];\r\ny = theSineOfAnglesOfATriangle(A,h);\r\ntolerance = 1e-4;\r\nassert(abs(y(1)-y_correct(1))\u003ctolerance)\r\nassert(abs(y(2)-y_correct(2))\u003ctolerance)\r\nassert(abs(y(3)-y_correct(3))\u003ctolerance)\r\n\r\n%%\r\nA = 48;\r\nh = 8;\r\ny_correct = [0.8, 0.8, 0.96];\r\ny = theSineOfAnglesOfATriangle(A,h);\r\ntolerance = 1e-4;\r\nassert(abs(y(1)-y_correct(1))\u003ctolerance)\r\nassert(abs(y(2)-y_correct(2))\u003ctolerance)\r\nassert(abs(y(3)-y_correct(3))\u003ctolerance)\r\n\r\n%%\r\nA = 40;\r\nh = 10;\r\ny_correct = [0.9285, 0.9285, 0.6897];\r\ny = theSineOfAnglesOfATriangle(A,h);\r\ntolerance = 1e-4;\r\nassert(abs(y(1)-y_correct(1))\u003ctolerance)\r\nassert(abs(y(2)-y_correct(2))\u003ctolerance)\r\nassert(abs(y(3)-y_correct(3))\u003ctolerance)\r\n\r\n%%\r\nA = 11;\r\nh = 7;\r\ny_correct = [0.9757, 0.9757, 0.4274];\r\ny = theSineOfAnglesOfATriangle(A,h);\r\ntolerance = 1e-4;\r\nassert(abs(y(1)-y_correct(1))\u003ctolerance)\r\nassert(abs(y(2)-y_correct(2))\u003ctolerance)\r\nassert(abs(y(3)-y_correct(3))\u003ctolerance)\r\n\r\n%%\r\nA = 10;\r\nh = 7;\r\ny_correct = [0.9798, 0.9798, 0.3918];\r\ny = theSineOfAnglesOfATriangle(A,h);\r\ntolerance = 1e-4;\r\nassert(abs(y(1)-y_correct(1))\u003ctolerance)\r\nassert(abs(y(2)-y_correct(2))\u003ctolerance)\r\nassert(abs(y(3)-y_correct(3))\u003ctolerance)\r\n\r\n%%\r\nA = 100;\r\nh = 90;\r\ny_correct = [0.9999, 0.9999, 0.0247];\r\ny = theSineOfAnglesOfATriangle(A,h);\r\ntolerance = 1e-4;\r\nassert(abs(y(1)-y_correct(1))\u003ctolerance)\r\nassert(abs(y(2)-y_correct(2))\u003ctolerance)\r\nassert(abs(y(3)-y_correct(3))\u003ctolerance)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":15,"created_by":90467,"edited_by":223089,"edited_at":"2023-02-04T06:18:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":57,"test_suite_updated_at":"2023-02-04T06:18:22.000Z","rescore_all_solutions":false,"group_id":37,"created_at":"2016-10-23T10:38:22.000Z","updated_at":"2026-02-08T11:35:41.000Z","published_at":"2016-10-23T10:38:22.000Z","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\u003eFind the sines of an isosceles triangle when given its area and height.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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, when A=12 and h=4, the result is [0.8 0.8 0.96].\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":60978,"title":"Mesh the octahedron","description":"Problem statement\r\n\r\nAn octahedron is a regular polyhedron with 6 vertices and 8 triangular faces. It is also one of the five well known platonic solids.\r\nA triangulated mesh -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh this octahedron. To do so, you will list the triangles/rows in a matrix of triangles, T. You will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles [1, 2, 3] and [3, 2, 1] are distinct).\r\nOn the other hand [1, 2, 3], [2, 3, 1] and [3, 1, 2] are one same unique triangle.\r\nThe row order of the triangles in the list doesn't matter.\r\n\r\nEdit / update\r\nTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\r\n\r\nExample\r\nThe first triangle (X \u003e 0, Y \u003e 0, and Z \u003e 0) here can be [1, 2, 5] if counterclockwise oriented (normals are outward oriented).\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","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: 1200.23px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 600.117px; transform-origin: 408px 600.117px; 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: 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: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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; 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: 373.817px 8px; transform-origin: 373.817px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn octahedron is a regular polyhedron with 6 vertices and 8 triangular faces. It is also one of the five well known platonic solids.\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.542px 8px; transform-origin: 157.542px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh -or a triangulation- is simply 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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 206.533px 8px; transform-origin: 206.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \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 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: 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: 385px 31.5px; text-align: left; transform-origin: 385px 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: 327.242px 8px; transform-origin: 327.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh this octahedron. To do so, you will list the triangles/rows in a matrix of triangles, \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: 7.51667px 8px; transform-origin: 7.51667px 8px; 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: 49.9333px 8px; transform-origin: 49.9333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles \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: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3]\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 8px; transform-origin: 15.5583px 8px; 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: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[3, 2, 1]\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: 40.0583px 8px; transform-origin: 40.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are distinct).\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: 58.3417px 8px; transform-origin: 58.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the other hand \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: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3]\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 8px; transform-origin: 3.88333px 8px; 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: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[2, 3, 1]\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 8px; transform-origin: 15.5583px 8px; 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: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[3, 1, 2]\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: 94.5333px 8px; transform-origin: 94.5333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are one same unique triangle.\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: 168.575px 8px; transform-origin: 168.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe row order of the triangles in the list doesn't matter.\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 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: 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: 41.9833px 8px; transform-origin: 41.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEdit / update\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: 351.75px 8px; transform-origin: 351.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\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 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: 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: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\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: 52.1167px 8px; transform-origin: 52.1167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle \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: 75.2583px 8px; transform-origin: 75.2583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(X \u0026gt; 0, Y \u0026gt; 0, and Z \u0026gt; 0)\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: 42.7833px 8px; transform-origin: 42.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e here can 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: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 5]\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: 187.5px 8px; transform-origin: 187.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented (normals are outward oriented).\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 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: 383.5px; 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: 385px 191.75px; text-align: left; transform-origin: 385px 191.75px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"504\" height=\"378\" style=\"vertical-align: baseline;width: 504px;height: 378px\" 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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: 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 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: 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: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; 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: 392px 40.8667px; transform-origin: 392px 40.8667px; 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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\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; 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 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: 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_octahedron()\r\n T = 1;\r\nend","test_suite":"%%\r\nT_correct = [1 2 5;\r\n 2 3 5;\r\n 3 4 5;\r\n 4 1 5;\r\n 2 1 6;\r\n 3 2 6;\r\n 4 3 6;\r\n 1 4 6];\r\n\r\n% Check every possible solutions\r\nassert(isequal(sortrows(sort(mesh_the_octahedron(),2)),sortrows(sort(T_correct,2))))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_octahedron.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:44:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":50,"test_suite_updated_at":"2025-07-23T16:11:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T08:24:47.000Z","updated_at":"2026-03-31T18:40:36.000Z","published_at":"2025-07-23T09:23:40.000Z","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\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\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\u003eAn octahedron is a regular polyhedron with 6 vertices and 8 triangular faces. It is also one of the five well known platonic solids.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 triangulated mesh -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eYour task here is to mesh this octahedron. To do so, you will list the triangles/rows in a matrix of triangles, \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\u003eYou will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 3]\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3, 2, 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are distinct).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the other hand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 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[2, 3, 1]\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3, 1, 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are one same unique triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eEdit / update\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 first triangle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(X \u0026gt; 0, Y \u0026gt; 0, and Z \u0026gt; 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented (normals are outward oriented).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"378\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"504\\\"/\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\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 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neighbor triangle indices","description":"First input T is a triangulation (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\r\nGiven a second input t (a certain triangle row index), one would like to query the list L of all its triangle neighbor indices. A triangle is neighbor to another triangle if they share exactly one edge.\r\nFor instance if\r\nT = [1 2 4;...\r\n 2 3 4;...\r\n 5 6 8;...\r\n 6 7 8;...\r\n 1 2 5;...\r\n 2 5 6;...\r\n 2 3 6;...\r\n 3 6 7;...\r\n 3 4 7;...\r\n 4 7 8;...\r\n 4 1 8;...\r\n 1 8 5]\r\nand t = 3, then the function should return\r\nL = [4, 6, 12]'\r\nsince rows / (triangles of T) 4, 6, and 12 contain an edge in common with triangle / row 3.edge [6 8] for the first, edge [5 6] for the second, and edge [8 5] for the third.\r\nHypothesis :\r\n- Since a triangle is not considered neighbor of itself, t should not be part of L.\r\n- Order doesn't matter, but T must be a column vector containing all the neighbor triangle -row- indices (except itself then) once only. No duplicata is admitted.\r\n- Edges are symmetric : [e1, e2] is the same edge as [e2, e1]\r\n- Every indices are positive, distinct integers.\r\n\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","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: 782.633px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 391.317px; transform-origin: 408px 391.317px; 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: 349.292px 8px; transform-origin: 349.292px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFirst input T is a triangulation (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.767px 8px; transform-origin: 368.767px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a second input t (a certain triangle row index), one would like to query the list L of all its triangle neighbor indices.\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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 7px 8px; transform-origin: 7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eA triangle is neighbor to another triangle if they share exactly one edge.\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: 43.95px 8px; transform-origin: 43.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor instance if\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 245.2px; 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: 405px 122.6px; transform-origin: 405px 122.6px; 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003eT = [1 2 4;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 2 3 4;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 5 6 8;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 6 7 8;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 1 2 5;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 2 5 6;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 2 3 6;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 3 6 7;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 3 4 7;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 4 7 8;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 4 1 8;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 42.35px 8.5px; tab-size: 4; transform-origin: 42.35px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 8 5]\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 125.833px 8px; transform-origin: 125.833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand t = 3, then the function should return\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; 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: 405px 10.2167px; transform-origin: 405px 10.2167px; 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; text-wrap-mode: 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: 57.75px 8.5px; tab-size: 4; transform-origin: 57.75px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eL = [4, 6, 12]'\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; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; 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: 378.042px 8px; transform-origin: 378.042px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince rows / (triangles of T) 4, 6, and 12 contain an edge in common with triangle / row 3.edge [6 8] for the first, edge [5 6] for the second, and edge [8 5] for the third.\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: 38.5083px 8px; transform-origin: 38.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHypothesis :\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: 162.6px 8px; transform-origin: 162.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e- Since a triangle is not considered neighbor of itself,\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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 82.0167px 8px; transform-origin: 82.0167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003et should not be part of L.\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.4417px 8px; transform-origin: 81.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e- Order doesn't matter, but\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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 180.008px 8px; transform-origin: 180.008px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eT must be a column vector containing all the neighbor\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: 109.692px 8px; transform-origin: 109.692px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e triangle -row- indices (except itself then) once only.\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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 82.8167px 8px; transform-origin: 82.8167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNo duplicata is admitted.\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: 2.33333px 8px; transform-origin: 2.33333px 8px; 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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 194.858px 8px; transform-origin: 194.858px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEdges are symmetric : [e1, e2] is the same edge as [e2, e1]\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: 138.083px 8px; transform-origin: 138.083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e- Every indices are positive, distinct integers.\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 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: 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function L = find_neighbor_triangles_indices(T,t);\r\n L = t;\r\nend","test_suite":"%% Tetrahedron, all triangles have all the other 3 neighbor triangles \r\nT = [1, 2, 3;...\r\n 1, 3, 4;...\r\n 1, 2, 4;...\r\n 2, 3, 4];\r\n \r\nt = 2;\r\n\r\nL = [1, 3, 4]';\r\nassert(isequal(sort(find_neighbor_triangles_indices(T,t)),L))\r\n\r\n%% Triangulated cube (same as problem description)\r\nT = [1, 2, 4;...\r\n 2, 3, 4;...\r\n 5, 6, 8;...\r\n 6, 7, 8;...\r\n 1, 2, 5;...\r\n 2, 5, 6;...\r\n 2, 3, 6;...\r\n 3, 6, 7;...\r\n 3, 4, 7;...\r\n 4, 7, 8;...\r\n 1, 4, 8;...\r\n 1, 5, 8];\r\n \r\nt = 3;\r\n\r\nL = [4, 6, 12]';\r\nassert(isequal(sort(find_neighbor_triangles_indices(T,t)),L))\r\n\r\n%% Filled octahedron (two pyramids stuck together via their square bases)\r\nT = [1, 2, 3;...\r\n 1, 3, 4;...\r\n 1, 4, 5;...\r\n 1, 2, 5;...\r\n 2, 3, 6;...\r\n 3, 4, 6;...\r\n 4, 5, 6;...\r\n 2, 5, 6;...\r\n 2, 3, 4;...\r\n 2, 4, 5;...\r\n 1, 2, 4;...\r\n 2, 4, 6];\r\n\r\nt = 6;\r\n\r\nL = [2, 5, 7, 9, 12]';\r\nassert(isequal(sort(find_neighbor_triangles_indices(T,t)),L))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('find_neighbor_triangles_indices.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:49:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":"2025-07-09T05:52:10.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-07T12:33:20.000Z","updated_at":"2025-11-16T17:50:56.000Z","published_at":"2020-01-07T13:06:47.000Z","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\u003eFirst input T is a triangulation (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 second input t (a certain triangle row index), one would like to query the list L of all its triangle neighbor indices.\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\u003eA triangle is neighbor to another triangle if they share exactly one edge.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 instance 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[T = [1 2 4;...\\n 2 3 4;...\\n 5 6 8;...\\n 6 7 8;...\\n 1 2 5;...\\n 2 5 6;...\\n 2 3 6;...\\n 3 6 7;...\\n 3 4 7;...\\n 4 7 8;...\\n 4 1 8;...\\n 1 8 5]]]\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\u003eand t = 3, then the function should return\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[L = [4, 6, 12]']]\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 rows / (triangles of T) 4, 6, and 12 contain an edge in common with triangle / row 3.edge [6 8] for the first, edge [5 6] for the second, and edge [8 5] for the third.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHypothesis :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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- Since a triangle is not considered neighbor of itself,\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\u003et should not be part of L.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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- Order doesn't matter, but\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\u003eT must be a column vector containing all the neighbor\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e triangle -row- indices (except itself then) once 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\u003eNo duplicata is admitted.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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: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\u003eEdges are symmetric : [e1, e2] is the same edge as [e2, e1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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- Every indices are positive, distinct integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\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:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\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":60986,"title":"Mesh the convex hull of a random 3D point cloud","description":"Problem statement\r\n\r\nThe convex hull of a 3D point set is actually a first -though rough- triangulation of it.\r\nA triangulation, or triangulated mesh, is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\nUse Matlab functions to compute the convex hull of the random point clouds given in the tests here below.\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","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: 795.233px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 397.617px; transform-origin: 408px 397.617px; 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: 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: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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: 256.717px 8px; transform-origin: 256.717px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe convex hull of a 3D point set is actually a first -though rough- triangulation of 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; 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: 150.925px 8px; transform-origin: 150.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulation, or triangulated mesh, is simply 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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 229.017px 8px; transform-origin: 229.017px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \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: 327.125px 8px; transform-origin: 327.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUse Matlab functions to compute the convex hull of the random point clouds given in the tests here below.\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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 341.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; 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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: 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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; 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: 392px 40.8667px; transform-origin: 392px 40.8667px; 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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\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; 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_convex_hull(V)\r\n T = V;\r\nend","test_suite":"%% Point set #1\r\nV = [0.7253 -0.3789 0.5520\r\n 0.4471 -0.3044 0.8245\r\n 0.8241 0.6916 0.2092\r\n -0.7553 -0.5126 0.2692\r\n -0.2179 -0.8765 -0.3024\r\n -0.0984 0.3260 0.8808\r\n -0.9354 -0.0462 0.2274\r\n 0.2122 -0.6391 0.6226\r\n -0.0248 -0.1993 -0.8833\r\n 0.0772 0.9644 -0.2436\r\n -0.1098 -0.0333 -0.9851\r\n -0.6662 0.0466 0.7499\r\n -0.6866 0.5290 -0.5468\r\n 0.0357 0.0086 -0.9728\r\n 0.0829 -0.2777 -1.0373\r\n -0.3445 0.5795 0.6257];\r\n\r\nT_correct = [1 2 8;\r\n 1 3 2;\r\n 1 5 15;\r\n 1 8 5;\r\n 1 15 3;\r\n 2 3 6;\r\n 2 6 12;\r\n 2 12 8;\r\n 3 10 16;\r\n 3 14 10;\r\n 3 15 14;\r\n 3 16 6;\r\n 4 5 8;\r\n 4 7 13;\r\n 4 8 12;\r\n 4 12 7;\r\n 4 13 5;\r\n 5 11 15;\r\n 5 13 11;\r\n 6 16 12;\r\n 7 12 16;\r\n 7 16 13;\r\n 10 13 16;\r\n 10 14 13;\r\n 11 13 14;\r\n 11 14 15];\r\n\r\nassert(isequal(mesh_the_convex_hull(V),T_correct))\r\n\r\n\r\n%% Point set #2\r\nV = [-0.0775 -0.4239 0.9421;\r\n -0.8154 0.0299 -0.4279;\r\n 0.6777 -0.4686 -0.6602;\r\n -0.2960 -0.8871 0.5367;\r\n -0.0034 -0.0899 0.9352;\r\n 0.8245 -0.5624 0.0630;\r\n 0.6048 -0.7364 -0.3692;\r\n 0.4215 0.9403 -0.2533;\r\n 0.3255 0.0593 -0.8884;\r\n 0.4979 -0.0671 0.8623;\r\n -1.0254 0.1883 -0.0015;\r\n 0.7398 0.2020 -0.4934;\r\n 0.7488 0.5209 -0.0621;\r\n -0.0994 -0.5682 -0.8936;\r\n -0.8099 -0.0951 -0.4470;\r\n 0.3038 -0.9284 -0.4938];\r\n\r\nT_correct = [1 4 6;\r\n 1 5 11;\r\n 1 6 10;\r\n 1 10 5;\r\n 1 11 4;\r\n 2 8 9;\r\n 2 9 14;\r\n 2 11 8;\r\n 2 14 15;\r\n 2 15 11;\r\n 3 6 7;\r\n 3 7 16;\r\n 3 9 12;\r\n 3 12 6;\r\n 3 14 9;\r\n 3 16 14;\r\n 4 11 15;\r\n 4 14 16;\r\n 4 15 14;\r\n 4 16 6;\r\n 5 8 11;\r\n 5 10 8;\r\n 6 12 13;\r\n 6 13 10;\r\n 6 16 7;\r\n 8 10 13;\r\n 8 12 9;\r\n 8 13 12];\r\n\r\nassert(isequal(mesh_the_convex_hull(V),T_correct))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_convex_hull.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:46:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T20:10:16.000Z","updated_at":"2026-02-13T17:40:03.000Z","published_at":"2025-07-24T18:00:49.000Z","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\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\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 convex hull of a 3D point set is actually a first -though rough- triangulation of 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\u003eA triangulation, or triangulated mesh, is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUse Matlab functions to compute the convex hull of the random point clouds given in the tests here below.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"336\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"448\\\"/\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\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\u003eForbidden functions / expressions\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\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 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for everyone!","description":"Accordingly to the \u003chttp://nl.mathworks.com/matlabcentral/cody/problems/42460-the-cake-is-a-lie problem 42460\u003e. All the children have eaten the cake and they were playing in the garden. You was trying to make barbecue, but someone spoken \"maybe pancakes?\" and all the children want pancakes. They want it now! Grab a frying pan and make a big pancake, then use minimum number of cuts to serve pancake to all the children at the same time.","description_html":"\u003cp\u003eAccordingly to the \u003ca href = \"http://nl.mathworks.com/matlabcentral/cody/problems/42460-the-cake-is-a-lie\"\u003eproblem 42460\u003c/a\u003e. All the children have eaten the cake and they were playing in the garden. You was trying to make barbecue, but someone spoken \"maybe pancakes?\" and all the children want pancakes. They want it now! Grab a frying pan and make a big pancake, then use minimum number of cuts to serve pancake to all the children at the same time.\u003c/p\u003e","function_template":"function y = pancake(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 1;y_correct = 0;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 2;y_correct = 1;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 4;y_correct = 2;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 7;y_correct = 3;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 12;y_correct = 5;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 27;y_correct = 7;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 127;y_correct = 16;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 2015;y_correct = 63;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 4060225;y_correct = 2850;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 1234567890;y_correct = 49690;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 1362067890;y_correct = 52193;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 2030000;y_correct = 2015;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 11581428900;y_correct = 152193;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 9007199187632129; y_correct = 134217727;\r\nassert(isequal(pancake(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":"2015-08-07T07:58:07.000Z","rescore_all_solutions":false,"group_id":37,"created_at":"2015-08-06T09:41:35.000Z","updated_at":"2026-03-14T18:55:26.000Z","published_at":"2015-08-06T09:44:29.000Z","restored_at":"2018-02-06T15:11:34.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"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\u003eAccordingly to 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=\\\"http://nl.mathworks.com/matlabcentral/cody/problems/42460-the-cake-is-a-lie\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eproblem 42460\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. All the children have eaten the cake and they were playing in the garden. You was trying to make barbecue, but someone spoken \\\"maybe pancakes?\\\" and all the children want pancakes. They want it now! Grab a frying pan and make a big pancake, then use minimum number of cuts to serve pancake to all the children at the same 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":163,"title":"Love triangles","description":"Given a vector of lengths [a b c], determines whether a triangle with non-zero area (in two-dimensional Euclidean space, smarty!) could have sides of those lengths.\r\n\r\nExamples:\r\n\r\n[1 2 1000] ---\u003e false\r\n\r\n[3 4 5] ---\u003e true\r\n\r\n[5 5 5] ---\u003e true","description_html":"\u003cp\u003eGiven a vector of lengths [a b c], determines whether a triangle with non-zero area (in two-dimensional Euclidean space, smarty!) could have sides of those lengths.\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cp\u003e[1 2 1000] ---\u003e false\u003c/p\u003e\u003cp\u003e[3 4 5] ---\u003e true\u003c/p\u003e\u003cp\u003e[5 5 5] ---\u003e true\u003c/p\u003e","function_template":"function tf = triangle(sides)\r\n tf = true;\r\nend","test_suite":"%%\r\nsides = [1 2 1000];\r\ny_correct = false;\r\nassert(isequal(triangle(sides),y_correct))\r\n\r\n%%\r\nsides = [3 4 5];\r\ny_correct = true;\r\nassert(isequal(triangle(sides),y_correct))\r\n\r\n%%\r\nsides = [5 5 5];\r\ny_correct = true;\r\nassert(isequal(triangle(sides),y_correct))\r\n\r\n%%\r\nsides = [6 6 6];\r\ny_correct = true;\r\nassert(isequal(triangle(sides),y_correct))\r\n\r\n%%\r\nsides = [1 1 1];\r\ny_correct = true;\r\nassert(isequal(triangle(sides),y_correct))\r\n\r\n%%\r\nsides = [1 2 2];\r\ny_correct = true;\r\nassert(isequal(triangle(sides),y_correct))\r\n\r\n%%\r\nsides = [2 2 5];\r\ny_correct = false;\r\nassert(isequal(triangle(sides),y_correct))\r\n\r\n%%\r\nsides = [5 2 2];\r\ny_correct = false;\r\nassert(isequal(triangle(sides),y_correct))\r\n\r\n\r\n%%\r\nsides = [1 3 1];\r\ny_correct = false;\r\nassert(isequal(triangle(sides),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":39,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":591,"test_suite_updated_at":"2013-03-09T04:38:31.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-29T15:07:57.000Z","updated_at":"2026-03-29T20:34:50.000Z","published_at":"2012-01-29T15:07:57.000Z","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 vector of lengths [a b c], determines whether a triangle with non-zero area (in two-dimensional Euclidean space, smarty!) could have sides of those lengths.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003e[1 2 1000] ---\u003e 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\u003e[3 4 5] ---\u003e 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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[5 5 5] ---\u003e true\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":45256,"title":"List one vertex neighbors","description":"First input T is a triangulation connectivity indices list (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\r\nSecond input i is a vertex index (positive integer).\r\nThe purpose of this function is to query the list L of all i neighbor indices.\r\nFor instance if\r\nT = [1 2 4;...\r\n 2 3 4;...\r\n 5 6 8;...\r\n 6 7 8;...\r\n 1 2 5;...\r\n 2 5 6;...\r\n 2 3 6;...\r\n 3 6 7;...\r\n 3 4 7;...\r\n 4 7 8;...\r\n 4 1 8;...\r\n 1 8 5]\r\nand i = 3, then the function should return\r\nL = [2, 4, 6, 7]\r\nsince 2, 4, 6, and 7 are all part of triangles / rows in which 3 is also a vertex member.\r\nHypothesis :\r\n- Output L doesn't need to be ordered, but must not contain duplicated index.\r\n- Output L is a row vector , and if the vertex index is not in the list , the function must of course return the empty set, [].\r\n\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","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: 710.633px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 355.317px; transform-origin: 408px 355.317px; 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: 383.133px 8px; transform-origin: 383.133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFirst input T is a triangulation connectivity indices list (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\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: 152.483px 8px; transform-origin: 152.483px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSecond input i is a vertex index (positive integer).\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: 223.658px 8px; transform-origin: 223.658px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe purpose of this function is to query the list L of all i neighbor indices.\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; 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\"\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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003eT = [1 2 4;\u003c/span\u003e\u003cspan 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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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 5 6 8;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 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min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 6 7 8;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 1 2 5;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 2 5 6;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 2 3 6;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 3 6 7;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 3 4 7;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 4 7 8;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 4 1 8;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 42.35px 8.5px; tab-size: 4; transform-origin: 42.35px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 8 5]\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 125.45px 8px; transform-origin: 125.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand i = 3, then the function should return\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; 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: 405px 10.2167px; transform-origin: 405px 10.2167px; 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; text-wrap-mode: 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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eL = [2, 4, 6, 7]\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 261.758px 8px; transform-origin: 261.758px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince 2, 4, 6, and 7 are all part of triangles / rows in which 3 is also a vertex member.\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: 38.5083px 8px; transform-origin: 38.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHypothesis :\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: 2.33333px 8px; transform-origin: 2.33333px 8px; 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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 29.15px 8px; transform-origin: 29.15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput L\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: 116.075px 8px; transform-origin: 116.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e doesn't need to be ordered, but must\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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 96.8px 8px; transform-origin: 96.8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003enot contain duplicated index.\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.33333px 8px; transform-origin: 2.33333px 8px; 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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 80.0917px 8px; transform-origin: 80.0917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput L is a row 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: 17.5px 8px; transform-origin: 17.5px 8px; 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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 112.75px 8px; transform-origin: 112.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eif the vertex index is not in the list\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: 42px 8px; transform-origin: 42px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e , 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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 119.392px 8px; transform-origin: 119.392px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003emust of course return the empty set\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 8px; transform-origin: 3.88333px 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: 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 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: 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function L = query_vertex_neighbors(T,i)\r\n L = i;\r\nend","test_suite":"%% triangulated cube\r\nT = [1 2 4;...\r\n 2 3 4;...\r\n 5 6 8;...\r\n 6 7 8;...\r\n 1 2 5;...\r\n 2 5 6;...\r\n 2 3 6;...\r\n 3 6 7;...\r\n 3 4 7;...\r\n 4 7 8;...\r\n 4 1 8;...\r\n 1 8 5];\r\n \r\ni = 3;\r\nL = [2 4 6 7];\r\nassert(isequal(sort(query_vertex_neighbors(T,i),2),L))\r\n\r\n%% Octahedron\r\nT = [1 2 3;...\r\n 1 3 4;...\r\n 1 4 5;...\r\n 1 5 2;...\r\n 6 3 2;...\r\n 6 4 3;...\r\n 6 5 4;...\r\n 6 2 5];\r\n \r\ni = 5;\r\nL = [1 2 4 6];\r\nassert(isequal(sort(query_vertex_neighbors(T,i),2),L))\r\n\r\n%% Empty set test\r\nT = [2 3 5;...\r\n 3 5 7;...\r\n 5 7 11;...\r\n 7 11 13];\r\n\r\ni = 6;\r\n\r\nassert(isempty(query_vertex_neighbors(T,i)))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('query_vertex_neighbors.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:51:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":27,"test_suite_updated_at":"2025-07-09T05:47:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-07T09:24:11.000Z","updated_at":"2025-11-18T16:44:59.000Z","published_at":"2020-01-07T09:56:23.000Z","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\u003eFirst input T is a triangulation connectivity indices list (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 input i is a vertex index (positive integer).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 purpose of this function is to query the list L of all i neighbor indices.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 instance 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[T = [1 2 4;...\\n 2 3 4;...\\n 5 6 8;...\\n 6 7 8;...\\n 1 2 5;...\\n 2 5 6;...\\n 2 3 6;...\\n 3 6 7;...\\n 3 4 7;...\\n 4 7 8;...\\n 4 1 8;...\\n 1 8 5]]]\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\u003eand i = 3, then the function should return\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[L = [2, 4, 6, 7]]]\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 2, 4, 6, and 7 are all part of triangles / rows in which 3 is also a vertex member.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHypothesis :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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: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\u003eOutput L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e doesn't need to be ordered, but must\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\u003enot contain duplicated index.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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: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\u003eOutput L is a row vector\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\u003eif the vertex index is not in the list\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e , 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:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emust of course return the empty set\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\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\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:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\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":2021,"title":"Is this triangle right-angled?","description":"Given three positive numbers a, b, c, where c is the largest number, return true if the triangle with sides a, b and c is right-angled. Otherwise, return false.","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: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; 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 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: 233.5px 8px; transform-origin: 233.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven three positive numbers a, b, c, where c is the largest number, return\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-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=\"font-weight: 700; \"\u003etrue\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: 118px 8px; transform-origin: 118px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if the triangle with sides a, b and c is right-angled. Otherwise, return\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003efalse\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\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function flag = isRightAngled(a, b, c)\r\n flag = false;\r\nend","test_suite":"%%\r\na = 3;\r\nb = 4;\r\nc = 5;\r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 2;\r\nb = 3;\r\nc = 4;\r\nflag_correct = false; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5;\r\nb = 12;\r\nc = 13;\r\nflag_correct = true; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n\r\n%%\r\na = 17;\r\nb = 19;\r\nc = 23;\r\nflag_correct = false; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n\r\n%%\r\na = 12;\r\nb = 35;\r\nc = 37;\r\nflag_correct = true; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n\r\n%%\r\na = 10*rand;\r\nb = a;\r\nc = a;\r\nflag_correct = false; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))","published":true,"deleted":false,"likes_count":38,"comments_count":7,"created_by":974,"edited_by":223089,"edited_at":"2023-05-04T07:40:55.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6418,"test_suite_updated_at":"2023-05-04T07:40:55.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:28:55.000Z","updated_at":"2026-04-06T22:39:36.000Z","published_at":"2013-11-28T17:12:28.000Z","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\u003eGiven three positive numbers a, b, c, where c is the largest number, return\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\u003etrue\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if the triangle with sides a, b and c is right-angled. Otherwise, return\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\u003efalse\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":61088,"title":"Covering a four-pointed star polygon by circles","description":"Given the area, A, of a star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).\r\nGiven (A,h), return the 2x2 matrix M = [A1/π a1; A2/π a2], where\r\nin the first row (i=1), A1 stands for the area of the circle that covers the minimum distance (cf. left figure), and a1 stands for the logical 1 if A1 is smaller than or reaches the area A or a1 stands for the logical 0 if A1 surpasses A;\r\nin the second row (i=2), A2 stands for the area of the circle that covers the maximum distance (cf. right figure), and a2 has the same previous false-true meaning relative to the areas A2 and A. Obviously, that A2 \u003e A holds true, then a2 = 0.\r\ninput: (A, h)\r\noutput: M = [A1/π a1; A2/π 0]\r\n","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: 748.987px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 374.487px; transform-origin: 408px 374.494px; 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=\"\"\u003eGiven the area, \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; \"\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=\"\"\u003e, of a star polygon formed by the rectangle, with dimensions \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×\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; \"\u003e2L\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, and four triangles, with height \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; \"\u003eh\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 from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).\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=\"\"\u003eGiven \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(A,h)\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, return the \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; \"\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=\"\"\u003ex\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; \"\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=\"\"\u003e 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=\"font-style: italic; \"\u003eM = [A1/π a1; A2/π a2]\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, where\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.188px; 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 51.0875px; transform-origin: 391px 51.0938px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.875px; 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 20.4375px; text-align: left; transform-origin: 363px 20.4375px; 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=\"\"\u003ein the first row \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=1)\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; unicode-bidi: normal; \"\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of the circle that covers the minimum distance (cf. left figure), 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is smaller than or reaches the area \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e0\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e surpasses \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 61.3125px; 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 30.65px; text-align: left; transform-origin: 363px 30.6562px; 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=\"\"\u003ein the second row \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=2)\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; unicode-bidi: normal; \"\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of the circle that covers the maximum distance (cf. right figure), 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea2\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has the same previous false-true meaning relative to the areas \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\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; unicode-bidi: normal; \"\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Obviously, that A2 \u0026gt; A holds true, then \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea2 = 0\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\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=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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 \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(A, h)\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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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 \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 = [A1/π a1; A2/π 0]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 484.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 242.4px; text-align: left; transform-origin: 384px 242.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"601\" height=\"479\" style=\"vertical-align: baseline;width: 601px;height: 479px\" 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\" alt=\"Covering by circles\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = covering_by_circles(A,h)\r\n M = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nh = 1;\r\nM_correct = [6.25 1; 16 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nA = 36;\r\nh = 2;\r\nM_correct = [12.25 0; 25 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nA = 56;\r\nh = 2;\r\nM_correct = [16 1; 36 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nfiletext = fileread('covering_by_circles.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 68;\r\nh = 1.2;\r\nM_correct = [13.69 1; 38.44 0];\r\nassert(all(isapprox(covering_by_circles(A,h),M_correct), 'all'))\r\n\r\n%%\r\nA = 89;\r\nh = 2.6;\r\nM_correct = [26.01 1; 57.76 0];\r\nassert(all(isapprox(covering_by_circles(A,h),M_correct), 'all'))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-30T13:14:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-29T14:26:03.000Z","updated_at":"2026-03-22T14:02:11.000Z","published_at":"2025-11-30T13:14:56.000Z","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:t\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a star polygon formed by the rectangle, with dimensions \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×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A,h)\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1/π a1; A2/π a2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\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\u003ein the first row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=1)\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\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of the circle that covers the minimum distance (cf. left figure), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is smaller than or reaches the area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e surpasses \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\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=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the second row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of the circle that covers the maximum distance (cf. right figure), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has the same previous false-true meaning relative to the areas \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Obviously, that A2 \u0026gt; A holds true, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2 = 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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\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(A, h)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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:rFonts 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":5,"title":"Triangle Numbers","description":"Triangle numbers are the sums of successive integers. So 6 is a triangle number because\r\n 6 = 1 + 2 + 3\r\nwhich can be displayed in a triangular shape like so\r\n *\r\n * *\r\n * * *\r\nThus 6 = triangle(3). Given n, return t, the triangular number for n.\r\nExample:\r\n Input n = 4\r\n Output t is 10","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: 265.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 132.8px; transform-origin: 407px 132.8px; 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: 282px 8px; transform-origin: 282px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTriangle numbers are the sums of successive integers. So 6 is a triangle number because\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; 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 10.2167px; transform-origin: 404px 10.2167px; 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: 56px 8.5px; tab-size: 4; transform-origin: 56px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 6 = 1 + 2 + 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; 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: 162px 8px; transform-origin: 162px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhich can be displayed in a triangular shape like so\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: 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 *\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: 32px 8.5px; tab-size: 4; transform-origin: 32px 8.5px; 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: 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: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; 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\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: 208.5px 8px; transform-origin: 208.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThus 6 = triangle(3). Given n, return t, the triangular number for 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: 28.5px 8px; transform-origin: 28.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample:\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: 52px 8.5px; tab-size: 4; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003e Input \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: 20px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 20px 8.5px; \"\u003en = 4\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: 60px 8.5px; tab-size: 4; transform-origin: 60px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003e Output \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: 28px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 28px 8.5px; \"\u003et is 10\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = triangle(n)\r\n t = n;\r\nend","test_suite":"%%\r\nfiletext = fileread('triangle.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'if') || contains(filetext, 'switch'); \r\nassert(~illegal)\r\n\r\n%%\r\nn = 1;\r\nt = 1;\r\nassert(isequal(triangle(n),t))\r\n\r\n%%\r\nn = 3;\r\nt = 6;\r\nassert(isequal(triangle(n),t))\r\n\r\n%%\r\nn = 5;\r\nt = 15;\r\nassert(isequal(triangle(n),t))\r\n\r\n%%\r\nn = 30;\r\nt = 465;\r\nassert(isequal(triangle(n),t))\r\n\r\n%%\r\nn = 30;\r\nt = 465;\r\nassert(isequal(triangle(n),t))","published":true,"deleted":false,"likes_count":143,"comments_count":27,"created_by":1,"edited_by":223089,"edited_at":"2022-12-21T10:26:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":30174,"test_suite_updated_at":"2022-12-21T10:26:58.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:17.000Z","updated_at":"2026-04-06T14:52:51.000Z","published_at":"2012-01-18T01:00:17.000Z","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\u003eTriangle numbers are the sums of successive integers. So 6 is a triangle number because\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[ 6 = 1 + 2 + 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\u003ewhich can be displayed in a triangular shape like so\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[ *\\n * *\\n * * *]]\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\u003eThus 6 = triangle(3). Given n, return t, the triangular number for 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\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 n = 4\\n Output t is 10]]\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":45261,"title":"List every vertices neighbor indices","description":"Input T is a triangulation.\r\nThe purpose of this function is to query at once the cell array N of all vertex neighbor indices... of every vertices, nothing less (!)\r\nOutput N must be a cell array since of course each vertex may have a different number of neighbors.\r\nFor example, for an input filled octahedron whom triangulation is\r\nT = [1, 2, 3;...\r\n 1, 3, 4;...\r\n 1, 4, 5;...\r\n 1, 2, 5;...\r\n 2, 3, 6;...\r\n 3, 4, 6;...\r\n 4, 5, 6;...\r\n 2, 5, 6;...\r\n 2, 3, 4;...\r\n 2, 4, 5;...\r\n 1, 2, 4;...\r\n 2, 4, 6],\r\nthen the output N is a 6x1 cell array of integers row vectors, such that :\r\nN(1,1) = {[2, 3, 4, 5]};\r\nN(2,1) = {[1, 3, 4, 5, 6]};\r\nN(3,1) = {[1, 2, 4, 6]};\r\nN(4,1) = {[1, 2, 3, 5, 6]};\r\nN(5,1) = {[1, 2, 4, 6]};\r\nN(6,1) = {[2, 3, 4, 5]};\r\nIndeed vertex #2 is part of triangles [1, 2, 3], [1, 2, 5], [2, 3, 6], [2, 5, 6], [2, 3, 4], [2, 4, 5], [1, 2, 4], and [2, 4, 6], it then admit all the other vertices as neighbors ([1, 3, 4, 5, 6]).\r\nHypothesis / conditions :\r\na vertex is the neighbor of another if they are linked with an edge in at least one same triangle. A vertex is not neighbor of itself.\r\nOutput N row order is crucial since row number actually corresponds to the vertex id / index.\r\nOutput N cells content order doesn't matter, but it doesn't admit any duplicated index / value.\r\nTip : solving my previous problems, and especially query_vertex_neighbors will help you to fully understand and solve this one.\r\nNB : the question of unreferenced vertices is not tacled here. We just supposed there are not.\r\n\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","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: 936.533px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 468.267px; transform-origin: 408px 468.267px; 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: 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: 34.6083px 8px; transform-origin: 34.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInput T is 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: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/help/matlab/ref/triangulation.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003etriangulation\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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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; 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: 372.617px 8px; transform-origin: 372.617px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe purpose of this function is to query at once the cell array N of all vertex neighbor indices... of every vertices, nothing less (!)\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: 311.425px 8px; transform-origin: 311.425px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOutput N must be a cell array since of course each vertex may have a different number of neighbors.\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: 198.783px 8px; transform-origin: 198.783px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, for an input filled octahedron whom triangulation is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 245.2px; 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: 405px 122.6px; transform-origin: 405px 122.6px; 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003eT = [1, 2, 3;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 1, 3, 4;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 1, 4, 5;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 1, 2, 5;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 2, 3, 6;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 3, 4, 6;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 4, 5, 6;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 2, 5, 6;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 2, 3, 4;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 2, 4, 5;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 1, 2, 4;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 2, 4, 6],\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 218.575px 8px; transform-origin: 218.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen the output N is a 6x1 cell array of integers row vectors, such that :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 122.6px; 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: 405px 61.3px; transform-origin: 405px 61.3px; 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 92.4px 8.5px; tab-size: 4; transform-origin: 92.4px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eN(1,1) = {[2, 3, 4, 5]};\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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 103.95px 8.5px; tab-size: 4; transform-origin: 103.95px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eN(2,1) = {[1, 3, 4, 5, 6]};\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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 92.4px 8.5px; tab-size: 4; transform-origin: 92.4px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eN(3,1) = {[1, 2, 4, 6]};\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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 103.95px 8.5px; tab-size: 4; transform-origin: 103.95px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eN(4,1) = {[1, 2, 3, 5, 6]};\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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 92.4px 8.5px; tab-size: 4; transform-origin: 92.4px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eN(5,1) = {[1, 2, 4, 6]};\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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 92.4px 8.5px; tab-size: 4; transform-origin: 92.4px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eN(6,1) = {[2, 3, 4, 5]};\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; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; 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: 382.583px 8px; transform-origin: 382.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIndeed vertex #2 is part of triangles [1, 2, 3], [1, 2, 5], [2, 3, 6], [2, 5, 6], [2, 3, 4], [2, 4, 5], [1, 2, 4], and [2, 4, 6], it then admit all the other vertices as neighbors ([1, 3, 4, 5, 6]).\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: 83.2px 8px; transform-origin: 83.2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHypothesis / conditions :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; 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: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.8667px; 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: 364px 20.4333px; text-align: left; transform-origin: 364px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\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: 108.875px 8px; transform-origin: 108.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003evertex is the neighbor of another\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 94.525px 8px; transform-origin: 94.525px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if they are linked with an edge\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\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: 93.7167px 8px; transform-origin: 93.7167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ein at least one same triangle\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 50.1583px 8px; transform-origin: 50.1583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. A vertex is not neighbor of itself.\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 96.425px 8px; transform-origin: 96.425px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput N row order is crucial\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 18.2833px 8px; transform-origin: 18.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e since\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\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: 190.142px 8px; transform-origin: 190.142px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003erow number actually corresponds to the vertex id / index.\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 285.433px 8px; transform-origin: 285.433px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOutput N cells content order doesn't matter, but it doesn't admit any duplicated index / value.\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: 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: 14.6417px 8px; transform-origin: 14.6417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTip :\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: 23.7333px 8px; transform-origin: 23.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e solving\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: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/players/8668631-nicolas-douillet/created\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003emy previous problems\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: 48.2417px 8px; transform-origin: 48.2417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and especially\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: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/problems/45256-query-a-vertex-neighbors\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003equery_vertex_neighbors\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: 145.875px 8px; transform-origin: 145.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will help you to fully understand and solve this one.\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: 288.867px 8px; transform-origin: 288.867px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNB : the question of unreferenced vertices is not tacled here. We just supposed there are not.\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 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: 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function N = query_every_vertices_neighbor_indices(T)\r\n N = num2cell(T);\r\nend","test_suite":"%% Filled octahedron\r\nT = [1, 2, 3;...\r\n 1, 3, 4;...\r\n 1, 4, 5;...\r\n 1, 2, 5;...\r\n 2, 3, 6;...\r\n 3, 4, 6;...\r\n 4, 5, 6;...\r\n 2, 5, 6;...\r\n 2, 3, 4;...\r\n 2, 4, 5;...\r\n 1, 2, 4;...\r\n 2, 4, 6];\r\n \r\nN = cell(6,1);\r\n\r\nN(1,1) = {[2, 3, 4, 5]};\r\nN(2,1) = {[1, 3, 4, 5, 6]};\r\nN(3,1) = {[1, 2, 4, 6]};\r\nN(4,1) = {[1, 2, 3, 5, 6]};\r\nN(5,1) = {[1, 2, 4, 6]};\r\nN(6,1) = {[2, 3, 4, 5]};\r\n\r\nassert(isequal(query_every_vertices_neighbor_indices(T),N))\r\n\r\n%% Triangulated cube\r\nT = [1, 2, 4;...\r\n 2, 3, 4;...\r\n 5, 6, 8;...\r\n 6, 7, 8;...\r\n 1, 2, 5;...\r\n 2, 5, 6;...\r\n 2, 3, 6;...\r\n 3, 6, 7;...\r\n 3, 4, 7;...\r\n 4, 7, 8;...\r\n 1, 4, 8;...\r\n 1, 5, 8];\r\n\r\nN = cell(8,1);\r\n\r\nN(1,1) = {[2, 4, 5, 8]};\r\nN(2,1) = {[1, 3, 4, 5, 6]};\r\nN(3,1) = {[2, 4, 6, 7]};\r\nN(4,1) = {[1, 2, 3, 7, 8]};\r\nN(5,1) = {[1, 2, 6, 8]};\r\nN(6,1) = {[2, 3, 5, 7, 8]};\r\nN(7,1) = {[3, 4, 6, 8]};\r\nN(8,1) = {[1 4 5 6 7]};\r\n\r\nassert(isequal(query_every_vertices_neighbor_indices(T),N))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('query_every_vertices_neighbor_indices.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:49:16.000Z","deleted_by":null,"deleted_at":null,"solvers_count":27,"test_suite_updated_at":"2025-07-09T05:51:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-10T08:35:13.000Z","updated_at":"2025-11-16T17:45:29.000Z","published_at":"2020-01-10T09:24:12.000Z","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\u003eInput T 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://fr.mathworks.com/help/matlab/ref/triangulation.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003etriangulation\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\u003eThe purpose of this function is to query at once the cell array N of all vertex neighbor indices... of every vertices, nothing less (!)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 N must be a cell array since of course each vertex may have a different number of neighbors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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, for an input filled octahedron whom triangulation 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[T = [1, 2, 3;...\\n 1, 3, 4;...\\n 1, 4, 5;...\\n 1, 2, 5;...\\n 2, 3, 6;...\\n 3, 4, 6;...\\n 4, 5, 6;...\\n 2, 5, 6;...\\n 2, 3, 4;...\\n 2, 4, 5;...\\n 1, 2, 4;...\\n 2, 4, 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\u003ethen the output N is a 6x1 cell array of integers row vectors, such that :\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[N(1,1) = {[2, 3, 4, 5]};\\nN(2,1) = {[1, 3, 4, 5, 6]};\\nN(3,1) = {[1, 2, 4, 6]};\\nN(4,1) = {[1, 2, 3, 5, 6]};\\nN(5,1) = {[1, 2, 4, 6]};\\nN(6,1) = {[2, 3, 4, 5]};]]\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\u003eIndeed vertex #2 is part of triangles [1, 2, 3], [1, 2, 5], [2, 3, 6], [2, 5, 6], [2, 3, 4], [2, 4, 5], [1, 2, 4], and [2, 4, 6], it then admit all the other vertices as neighbors ([1, 3, 4, 5, 6]).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\u003eHypothesis / conditions :\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\u003ea\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\u003evertex is the neighbor of another\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if they are linked with an edge\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 at least one same triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. A vertex is not neighbor of itself.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput N row order is crucial\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e since\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\u003erow number actually corresponds to the vertex id / index.\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\u003eOutput N cells content order doesn't matter, but it doesn't admit any duplicated index / value.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\u003eTip :\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e solving\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://fr.mathworks.com/matlabcentral/cody/players/8668631-nicolas-douillet/created\\\"\u003e\u003cw:r\u003e\u003cw:t\u003emy previous problems\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and especially\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://fr.mathworks.com/matlabcentral/cody/problems/45256-query-a-vertex-neighbors\\\"\u003e\u003cw:r\u003e\u003cw:t\u003equery_vertex_neighbors\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e will help you to fully understand and solve this one.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNB : the question of unreferenced vertices is not tacled here. We just supposed there are not.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\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:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\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":45379,"title":"3rd side of a Triangle","description":"Given two sides of a triangle, find the minimum and maximum possible area of the triangle.\r\n\r\nthe length of the third side has to be of integer-valued.","description_html":"\u003cp\u003eGiven two sides of a triangle, find the minimum and maximum possible area of the triangle.\u003c/p\u003e\u003cp\u003ethe length of the third side has to be of integer-valued.\u003c/p\u003e","function_template":"function [max,min]=tri_side(a1,a2)","test_suite":"%%\r\n[mx,mn]=tri_side(20,10);\r\nassert(abs(mx-99.9199)\u003c.001)\r\nassert(abs(mn- 31.9756)\u003c.001)\r\n\r\n%%\r\n[mx,mn]=tri_side(50,50);\r\nassert(abs(mx-1249.9579)\u003c.001)\r\nassert(abs(mn-24.9987)\u003c.001)\r\n\r\n%%\r\n[mx,mn]=tri_side(1,3);\r\nassert(abs(mx-1.479)\u003c.001)\r\nassert(abs(mn- 1.479)\u003c.001)\r\n\r\n%%\r\n[mx,mn]=tri_side(1000,30);\r\nassert(abs(mx-14998.3124)\u003c.001)\r\nassert(abs(mn-3784.4461)\u003c.001)","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2020-03-24T18:55:45.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-03-23T14:24:55.000Z","updated_at":"2026-01-29T12:45:10.000Z","published_at":"2020-03-23T14:34:12.000Z","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 two sides of a triangle, find the minimum and maximum possible area of the triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 length of the third side has to be of integer-valued.\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":45271,"title":"Calculate triangle area","description":"Imagine that you want to calculate the areas of some triangles given in matrix form. First the coordinates of the vertices of the triangles are in a matrix called coords where the line number represents the vertex number and the column number is the dimension, in this case it is equal to 2 (x, y). The way the nodes connect are found in the lnods matrix where the line number is the triangle number and the column number is the vertex number that makes up each triangle (v_i, v_j, v_k).","description_html":"\u003cp\u003eImagine that you want to calculate the areas of some triangles given in matrix form. First the coordinates of the vertices of the triangles are in a matrix called coords where the line number represents the vertex number and the column number is the dimension, in this case it is equal to 2 (x, y). The way the nodes connect are found in the lnods matrix where the line number is the triangle number and the column number is the vertex number that makes up each triangle (v_i, v_j, v_k).\u003c/p\u003e","function_template":"function y =areas(coords,lnods)\r\n y = ?;\r\nend","test_suite":"%%\r\ncoords=[0 0;1 0; 1 1; 0 1];\r\nlnods=[ 1 2 4; 2 3 4];\r\ny_correct = [0.500;0.500];\r\nassert(isequal(areas(coords,lnods),y_correct))\r\n%%\r\ncoords=[0 0;1 0; 1 1; 0 1; 0.5 0.5];\r\nlnods=[ 1 2 5; 2 3 5;3 4 5;4 1 5];\r\ny_correct = [0.2500;0.2500;0.2500;0.2500];\r\nassert(isequal(areas(coords,lnods),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":396229,"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":"2020-01-19T02:12:33.000Z","updated_at":"2026-03-14T18:54:18.000Z","published_at":"2020-01-19T02:17:46.000Z","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\u003eImagine that you want to calculate the areas of some triangles given in matrix form. First the coordinates of the vertices of the triangles are in a matrix called coords where the line number represents the vertex number and the column number is the dimension, in this case it is equal to 2 (x, y). The way the nodes connect are found in the lnods matrix where the line number is the triangle number and the column number is the vertex number that makes up each triangle (v_i, v_j, v_k).\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":44037,"title":"Pascal's triangle","description":"\u003chttps://en.wikipedia.org/wiki/Pascal%27s_triangle\u003e\r\nif the order is: x = 3; the output will be:\r\n\r\n\r\n output = [0 0 0 1 0 0 0;\r\n 0 0 1 0 1 0 0;\r\n 0 1 0 2 0 1 0;\r\n 1 0 3 0 3 0 1]","description_html":"\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Pascal%27s_triangle\"\u003ehttps://en.wikipedia.org/wiki/Pascal%27s_triangle\u003c/a\u003e\r\nif the order is: x = 3; the output will be:\u003c/p\u003e\u003cpre\u003e output = [0 0 0 1 0 0 0;\r\n 0 0 1 0 1 0 0;\r\n 0 1 0 2 0 1 0;\r\n 1 0 3 0 3 0 1]\u003c/pre\u003e","function_template":"function y = stg_Pascal(x)\r\n y = [];\r\nend","test_suite":"%%\r\nx = 3;\r\ny_correct = [0 0 0 1 0 0 0;\r\n 0 0 1 0 1 0 0;\r\n 0 1 0 2 0 1 0;\r\n 1 0 3 0 3 0 1];\r\nassert(isequal(stg_Pascal(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = [0 0 0 0 1 0 0 0 0;\r\n 0 0 0 1 0 1 0 0 0;\r\n 0 0 1 0 2 0 1 0 0;\r\n 0 1 0 3 0 3 0 1 0;\r\n 1 0 4 0 6 0 4 0 1];\r\nassert(isequal(stg_Pascal(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = [0 0 1 0 0;\r\n 0 1 0 1 0;\r\n 1 0 2 0 1];\r\nassert(isequal(stg_Pascal(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":108804,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":38,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-01-23T15:05:29.000Z","updated_at":"2026-03-14T18:48:45.000Z","published_at":"2017-01-23T15:05:29.000Z","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/Pascal%27s_triangle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://en.wikipedia.org/wiki/Pascal%27s_triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt; if the order is: x = 3; the output will be:\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[ output = [0 0 0 1 0 0 0;\\n 0 0 1 0 1 0 0;\\n 0 1 0 2 0 1 0;\\n 1 0 3 0 3 0 1]]]\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":61086,"title":"Covering a four-pointed star polygon by rectangles","description":"Given the area, A, of a star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, find the rectangles that have the same area, A, and cover the distance between opposite vertices (cf. figure below).\r\nGiven (A, L), return the 2x2 matrix M, where \r\nthe first row returns the dimensions, y1×y2, of the rectangle that covers the minimum distance (cf. left figure);\r\nthe second row returns the dimensions, z1×z2, of the rectangle that covers the maximum distance (cf. right figure).\r\ninput: (A, L)\r\noutput: M = [y1 y2; z1 z2]\r\n","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: 635.675px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 317.837px; transform-origin: 408px 317.837px; 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; 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=\"\"\u003eGiven the area, \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; \"\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=\"\"\u003e, of a star polygon formed by the rectangle, with dimensions \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×\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; \"\u003e2L\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, and four triangles, with height \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; \"\u003eh\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 from their bases to the vertices, find the rectangles that have the same area, \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; \"\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=\"\"\u003e, and cover the distance between opposite vertices (cf. figure below).\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=\"\"\u003eGiven \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(A, L)\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, return the \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; \"\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=\"\"\u003ex\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; \"\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=\"\"\u003e 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=\"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, where \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; 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 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; 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=\"\"\u003ethe first row returns the dimensions, y\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\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; unicode-bidi: normal; \"\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey2\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of the rectangle that covers the minimum distance (cf. left figure);\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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=\"\"\u003ethe second row returns the dimensions, \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ez1\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×z\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of the rectangle that covers the maximum distance (cf. right figure).\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=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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 \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(A, L)\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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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 \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 = [y1 y2; z1 z2]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 411.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 205.9px; text-align: left; transform-origin: 384px 205.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"508\" height=\"406\" style=\"vertical-align: baseline;width: 508px;height: 406px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = covering_polygon(A,L)\r\n M = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nL = 3;\r\nM_correct = [5 5.4; 3.375 8];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nA = 36;\r\nL = 3;\r\nM_correct = [7 36/7; 3.6 10];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nfiletext = fileread('covering_polygon.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 48;\r\nL = 4;\r\nM_correct = [20/3 36/5; 4.5 32/3];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nA = 56;\r\nL = 4;\r\nM_correct = [8 7; 14/3 12];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-28T15:21:25.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-27T15:06:59.000Z","updated_at":"2026-03-21T13:41:00.000Z","published_at":"2025-11-28T15:21:25.000Z","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\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a star polygon formed by the rectangle, with dimensions \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×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, find the rectangles that have the same area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and cover the distance between opposite vertices (cf. figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, L)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the 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\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×z\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the rectangle that covers the maximum distance (cf. right figure).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\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(A, L)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":985,"title":"Make a Star Pyramid","description":"Create a star pyramid. First line will have 1 star, second will have two stars and so on... a basic program which is easily done in c programming.\r\n\r\nExample\r\n\r\n n = 3\r\n p = pyramid(n)\r\n\r\nreturns this string matrix in p\r\n\r\n '* '\r\n '** '\r\n '***'\r\n\r\nThe output p is an n-by-n string matrix with spaces (ASCII=32) in the blank spots and '*' as shown. ","description_html":"\u003cp\u003eCreate a star pyramid. First line will have 1 star, second will have two stars and so on... a basic program which is easily done in c programming.\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cpre\u003e n = 3\r\n p = pyramid(n)\u003c/pre\u003e\u003cp\u003ereturns this string matrix in p\u003c/p\u003e\u003cpre\u003e '* '\r\n '** '\r\n '***'\u003c/pre\u003e\u003cp\u003eThe output p is an n-by-n string matrix with spaces (ASCII=32) in the blank spots and '*' as shown.\u003c/p\u003e","function_template":"function p = pyramid(n)\r\n p = '*';\r\nend","test_suite":"%%\r\nn = 2;\r\np = ['* ';'**'];\r\nassert(isequal(pyramid(n),p));\r\n\r\n%%\r\nn = 3;\r\np = ['* ';'** ';'***'];\r\nassert(isequal(pyramid(n),p));\r\n\r\n%%\r\nn = 4;\r\np = ['* ';'** ';'*** ';'****'];\r\nassert(isequal(pyramid(n),p));\r\n\r\n%%\r\nn = 10;\r\np = ['* ';\r\n '** ';\r\n '*** ';\r\n '**** ';\r\n '***** ';\r\n '****** ';\r\n '******* ';\r\n '******** ';\r\n '********* ';\r\n '**********'];\r\nassert(isequal(pyramid(n),p));\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":7262,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":219,"test_suite_updated_at":"2012-10-12T14:45:22.000Z","rescore_all_solutions":false,"group_id":18,"created_at":"2012-10-10T08:06:01.000Z","updated_at":"2026-03-31T18:12:10.000Z","published_at":"2012-10-10T08:08:21.000Z","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\u003eCreate a star pyramid. First line will have 1 star, second will have two stars and so on... a basic program which is easily done in c programming.\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[ n = 3\\n p = pyramid(n)]]\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\u003ereturns this string matrix in p\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[ '* '\\n '** '\\n '***']]\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 output p is an n-by-n string matrix with spaces (ASCII=32) in the blank spots and '*' as shown.\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":49918,"title":"Splitting Triangle - Problem the first","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: 368px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 184px; transform-origin: 407px 184px; 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=\"\"\u003eConsider an equilateral triangle sitting in Quadrant I as depicted in an example below:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 245px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 122.5px; text-align: left; transform-origin: 384px 122.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"247\" height=\"239\" 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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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis triangle is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the triangle, determine the x coordinate of the line that splits the regions. The ratio between the regions (red to blue) is presented through the first two entries of the input. For example, if the ratio is 2 and 5, then these two numbers will be the first two numbers in the input. The last entry is the side of the triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = ratio_polygon(s)\r\n y = s;\r\nend","test_suite":"%%\r\ns=[1 1 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.5;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[1 3 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.3536;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[1 0 1];\r\ny=ratio_polygon(s);\r\ny_correct=1;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[3 1 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.6464;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[1 pi 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.3475;\r\nassert(abs(y-y_correct)\u003ceps)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-21T22:16:27.000Z","updated_at":"2025-12-04T15:18:46.000Z","published_at":"2021-01-21T22:18:44.000Z","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\u003eConsider an equilateral triangle sitting in Quadrant I as depicted in an example below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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=\\\"239\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"247\\\"/\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\u003eThis triangle is to be split into two regions (e.g., red and blue). 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of a four-pointed star polygon","description":"Given the area A, of a rectangle with dimensions l1xl2, where the side lengths are integers and form the smallest possible perimeter, and given the total area A_t of the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, h, from their bases to the apices, find the vector [l1 l2 h] such that l1\u003cl2.\r\n","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: 490.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 245.4px; transform-origin: 408px 245.4px; 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: 385px 31.5px; text-align: left; transform-origin: 385px 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=\"\"\u003eGiven the area \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; \"\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=\"\"\u003e, of a rectangle with dimensions \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; \"\u003el1xl2\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, where the side lengths are integers and form the smallest possible perimeter, and given the total area \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; \"\u003eA_t\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 the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, \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; \"\u003eh\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, from their bases to the apices, find 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[l1 l2 h]\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 such that \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; \"\u003el1\u0026lt;l2\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: 418.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 209.4px; text-align: left; transform-origin: 385px 209.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"508\" height=\"413\" style=\"vertical-align: baseline;width: 508px;height: 413px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = star_polygon(A,A_t)\r\n y = A;\r\nend","test_suite":"%%\r\nA = 10;\r\nA_t = 24;\r\ny_correct = [2 5 2];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 11;\r\nA_t = 23;\r\ny_correct = [1 11 1];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 72;\r\nA_t = 106;\r\ny_correct = [8 9 2];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nfiletext = fileread('star_polygon.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 156;\r\nA_t = 180;\r\ny_correct = [12 13 0.96];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 168;\r\nA_t = 190;\r\ny_correct = [12 14 11/13];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-14T17:36:31.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-13T17:02:46.000Z","updated_at":"2026-01-15T09:17:29.000Z","published_at":"2025-11-14T17:36:31.000Z","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\u003eGiven the area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a rectangle with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1xl2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where the side lengths are integers and form the smallest possible perimeter, and given the total area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_t\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, from their bases to the apices, find the vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[l1 l2 h]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1\u0026lt;l2\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"413\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"508\\\"/\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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the centroid of triangle","description":"Imagine that you want to calculate the *centroid* of some _triangles_ given in matrix form. First the coordinates of the vertices of the triangles are in a matrix called coords where the line number represents the vertex number and the column number is the dimension, in this case it is equal to 2 (x, y). The way the nodes connect are found in the lnods matrix where the line number is the triangle number and the column number is the vertex number that makes up each triangle (v_i, v_j, v_k).","description_html":"\u003cp\u003eImagine that you want to calculate the \u003cb\u003ecentroid\u003c/b\u003e of some \u003ci\u003etriangles\u003c/i\u003e given in matrix form. First the coordinates of the vertices of the triangles are in a matrix called coords where the line number represents the vertex number and the column number is the dimension, in this case it is equal to 2 (x, y). The way the nodes connect are found in the lnods matrix where the line number is the triangle number and the column number is the vertex number that makes up each triangle (v_i, v_j, v_k).\u003c/p\u003e","function_template":"function c = your_fcn_name(coords,lnods)\r\n c = x;\r\nend","test_suite":"%%\r\ncoords=[0 0;1 0; 1 1; 0 1];\r\nlnods=[ 1 2 4; 2 3 4];\r\ny_correct =[1/3 1/3;2/3 2/3];\r\nassert(isequal(your_fcn_name(coords,lnods),y_correct))\r\n%%\r\ncoords=[0 0;1 0; 1 1; 0 1; 0.5 0.5];\r\nlnods=[ 1 2 5; 2 3 5;3 4 5;4 1 5];\r\ny_correct =[1/2 1/6; 5/6 1/2 ;1/2 5/6;1/6 1/2];\r\nassert(isequal(your_fcn_name(coords,lnods),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":396229,"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":1,"created_at":"2020-01-19T13:43:13.000Z","updated_at":"2026-03-14T18:42:54.000Z","published_at":"2020-01-19T13:51:41.000Z","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\u003eImagine that you want to calculate 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\u003ecentroid\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of some\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\u003etriangles\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e given in matrix form. First the coordinates of the vertices of the triangles are in a matrix called coords where the line number represents the vertex number and the column number is the dimension, in this case it is equal to 2 (x, y). The way the nodes connect are found in the lnods matrix where the line number is the triangle number and the column number is the vertex number that makes up each triangle (v_i, v_j, v_k).\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":61071,"title":"Generalizing square area to triangle area","description":"Cody Problem 61070 asked for the height, h, of a right triangle that had the same area, A, of a square with side length, c, and the hypothenuse length was correlated to the square side by x = 2. \r\nNow, find the height, h, of the right triangle that has the same area, A, of a square with side length, c, and the hypothenuse length is xc, for an arbitrary number x \u003e 2. Here, the height stands for the smallest cathetus.\r\n","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: 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\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/61070-square-area-to-triangle-area\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 61070\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 asked for the height, \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; \"\u003eh\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 a right triangle that had the same area, \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; \"\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=\"\"\u003e, of a square with side length, \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; \"\u003ec\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, and the hypothenuse length was correlated to the square side by \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; \"\u003ex = 2\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; 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=\"\"\u003eNow, find the height, \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; \"\u003eh\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 the right triangle that has the same area, \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; \"\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=\"\"\u003e, of a square with side length, \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; \"\u003ec\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, and the hypothenuse length is \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; \"\u003exc\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, for an arbitrary number \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; \"\u003ex \u0026gt; 2\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. Here, the height stands for the smallest cathetus.\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=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function h = find_height(A,x)\r\n h = x;\r\nend","test_suite":"%%\r\nA = 9;\r\nx = sqrt(5);\r\nh_correct = 3;\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A,x)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 10;\r\nx = 3;\r\nh_correct = sqrt(5*(9-sqrt(65)));\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A,x)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 16;\r\nx = sqrt(5);\r\nh_correct = 4;\r\nassert(isequal(find_height(A,x),h_correct))\r\n\r\n%%\r\nfiletext = fileread('find_height.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 16;\r\nx = 3; \r\nh_correct = 4*sqrt((9-sqrt(65))/2);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A,x)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 16;\r\nx = 5; \r\nh_correct = 4*sqrt((25 - sqrt(609))/2);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A,x)-h_correct)\u003ctolerance)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":7,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-13T10:09:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":"2025-11-13T10:09:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-10T14:44:15.000Z","updated_at":"2026-03-23T21:14:52.000Z","published_at":"2025-11-12T17:58:52.000Z","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:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/61070-square-area-to-triangle-area\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 61070\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asked for the height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a right triangle that had the same area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a square with side length, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and the hypothenuse length was correlated to the square side by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex = 2\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\u003eNow, find the height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the right triangle that has the same area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a square with side length, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and the hypothenuse length is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003exc\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, for an arbitrary number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex \u0026gt; 2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Here, the height stands for the smallest cathetus.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\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":43599,"title":"Find the sides of an isosceles triangle when given its area and height from its base to apex","description":"Find the sides of an isosceles triangle when given its area and the height from its base to apex.\r\nFor example, with A=12 and h=4, the result will be [5 5 6].","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: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; 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: 299px 8px; transform-origin: 299px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the sides of an isosceles triangle when given its area and the height from its base to apex.\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: 180px 8px; transform-origin: 180px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, with A=12 and h=4, the result will be [5 5 6].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = sidesOfTheTriangle(A,h)\r\n y = h;\r\nend","test_suite":"filetext = fileread('sidesOfTheTriangle.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'assert') || ...\r\n contains(filetext, 'elseif');\r\nassert(~illegal)\r\n\r\n%%\r\nA = 12;\r\nh = 4;\r\ny_correct = [5 5 6];\r\nassert(sum(abs(sidesOfTheTriangle(A,h)-y_correct))\u003c1e-3)\r\n\r\n%%\r\nA = 60;\r\nh = 5;\r\ny_correct = [13 13 24];\r\nassert(sum(abs(sidesOfTheTriangle(A,h)-y_correct))\u003c1e-3)\r\n\r\n%%\r\nA = 120;\r\nh = 8;\r\ny_correct = [17 17 30];\r\nassert(sum(abs(sidesOfTheTriangle(A,h)-y_correct))\u003c1e-3)\r\n\r\n%%\r\nA = 50;\r\nh = 11;\r\ny_correct = [11.9021492607341 11.9021492607341 9.09090909090909];\r\nassert(sum(abs(sidesOfTheTriangle(A,h)-y_correct))\u003c1e-3)\r\n\r\n%%\r\nA = 5;\r\nh = 3;\r\ny_correct = [3.43187671366233 3.43187671366233 10/3];\r\nassert(sum(abs(sidesOfTheTriangle(A,h)-y_correct))\u003c1e-3)\r\n\r\n%%\r\nA = 150;\r\nh = 10;\r\ny_correct = [18.0277563773199 18.0277563773199 30];\r\nassert(sum(abs(sidesOfTheTriangle(A,h)-y_correct))\u003c1e-3)\r\n\r\n%%\r\nA = 5;\r\nh = 0.5;\r\ny_correct = [10.0124921972504 10.0124921972504 20];\r\nassert(sum(abs(sidesOfTheTriangle(A,h)-y_correct))\u003c1e-3)\r\n\r\n%%\r\nA = 42;\r\nh = pi;\r\ny_correct = [13.7331777948941 13.7331777948941 26.7380304394384];\r\nassert(sum(abs(sidesOfTheTriangle(A,h)-y_correct))\u003c1e-3)\r\n","published":true,"deleted":false,"likes_count":12,"comments_count":3,"created_by":90467,"edited_by":223089,"edited_at":"2023-02-02T06:57:50.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2147,"test_suite_updated_at":"2023-02-02T06:57:50.000Z","rescore_all_solutions":false,"group_id":37,"created_at":"2016-10-22T23:50:43.000Z","updated_at":"2026-04-04T19:12:10.000Z","published_at":"2016-12-02T18:59:27.000Z","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\u003eFind the sides of an isosceles triangle when given its area and the height from its base to apex.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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, with A=12 and h=4, the result will be [5 5 6].\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":49933,"title":"Splitting Triangle - Problem the second","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: 369px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 184.5px; transform-origin: 407px 184.5px; 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=\"\"\u003eConsider an equilateral triangle sitting in Quadrant I as depicted in an example below:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 225px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 112.5px; text-align: left; transform-origin: 384px 112.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"268\" height=\"219\" style=\"vertical-align: baseline;width: 268px;height: 219px\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 52.5px; text-align: left; transform-origin: 384px 52.5px; 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=\"\"\u003eThis equilateral triangle is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the equilateral triangle, determine the angle between the red line splitting the regions and the positive x-axis (in degrees). The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 11 to 12, then these two numbers will be the first two numbers in the input. The last entry is the side of the triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = ratio_polygon(s)\r\n y = s;\r\nend","test_suite":"%%\r\ns=[1 1 1];\r\ny=ratio_polygon(s);\r\ny_correct=30;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[1 0 1];\r\ny=ratio_polygon(s);\r\ny_correct=60;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[0 1 1];\r\ny=ratio_polygon(s);\r\ny_correct=0;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[pi 17 1];\r\ny=ratio_polygon(s);\r\ny_correct=8.3348;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[3 2 1];\r\ny=ratio_polygon(s);\r\ny_correct=36.5868;\r\nassert(abs(y-y_correct)\u003ceps)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":"2021-01-22T02:14:20.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-22T01:43:29.000Z","updated_at":"2025-12-04T16:12:19.000Z","published_at":"2021-01-22T02:14:20.000Z","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\u003eConsider an equilateral triangle sitting in Quadrant I as depicted in an example below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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=\\\"219\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"268\\\"/\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\u003eThis equilateral triangle is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the equilateral triangle, determine the angle between the red line splitting the regions and the positive x-axis (in degrees). The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 11 to 12, then these two numbers will be the first two numbers in the input. The last entry is the side of the 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edges from a vertex","description":"First input is T, a triplet list of indices. Second input is i, a single index (positive integer). The goal of this function is to find and return all the edges [e1 e2] this vertex belong to.\r\nFor example if inputs are\r\nT = [1 2 3 ;...\r\n 1 3 4 ;...\r\n 1 4 2 ;...\r\n 2 3 4]\r\nand\r\ni = 4\r\nthen the output is the 3 x 2\r\nmatrix edg_list= [1 4;...\r\n 3 4;...\r\n 2 4]\r\nsince vertex number 4 is linked with vertices number 1, 2, and 3 and then part of edges [1 4], [2 4], and [3 4]. Format of the output must be the following :\r\nsize(edg_list) = [number of edges, 2]\r\nEvery row of it is an edge at the format [e1, e2], sorted in ascending order, i.e. e1 \u003c e2, and e1, e2 positive integers.\r\nEach edge is present once and only once, no duplicated edge admitted\r\nOrder of rows / edges in the output doesn't matter .\r\nIf the vertex is not in the list, the function must of course return the empty set.\r\n\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","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: 632.2px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 316.1px; transform-origin: 408px 316.1px; 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: 375.725px 8px; transform-origin: 375.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFirst input is T, a triplet list of indices. Second input is i, a single index (positive integer). The goal of this function is to find and return all the edges [e1 e2] this vertex belong to.\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: 77.0167px 8px; transform-origin: 77.0167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example if inputs are\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: 405px 40.8667px; transform-origin: 405px 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 57.75px 8.5px; tab-size: 4; transform-origin: 57.75px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 46.2px 8.5px; transform-origin: 46.2px 8.5px; \"\u003eT = [1 2 3 ;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 57.75px 8.5px; tab-size: 4; transform-origin: 57.75px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 46.2px 8.5px; transform-origin: 46.2px 8.5px; \"\u003e 1 3 4 ;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 57.75px 8.5px; tab-size: 4; transform-origin: 57.75px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 46.2px 8.5px; transform-origin: 46.2px 8.5px; \"\u003e 1 4 2 ;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 42.35px 8.5px; tab-size: 4; transform-origin: 42.35px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 2 3 4]\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; 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: 405px 10.2167px; transform-origin: 405px 10.2167px; 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; text-wrap-mode: 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: 19.25px 8.5px; tab-size: 4; transform-origin: 19.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ei = 4\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 82.45px 8px; transform-origin: 82.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen the output is the 3 x 2\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: 405px 30.65px; transform-origin: 405px 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 96.25px 8.5px; tab-size: 4; transform-origin: 96.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 26.95px 8.5px; transform-origin: 26.95px 8.5px; \"\u003ematrix \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 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 53.9px 8.5px; \"\u003eedg_list= [1 4\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 3.85px 8.5px; transform-origin: 3.85px 8.5px; \"\u003e;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 96.25px 8.5px; tab-size: 4; transform-origin: 96.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 84.7px 8.5px; transform-origin: 84.7px 8.5px; \"\u003e 3 4;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 84.7px 8.5px; tab-size: 4; transform-origin: 84.7px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 2 4]\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; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; 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: 380.75px 8px; transform-origin: 380.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince vertex number 4 is linked with vertices number 1, 2, and 3 and then part of edges [1 4], [2 4], and [3 4]. Format of the output must be the following :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; 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: 392px 40.8667px; transform-origin: 392px 40.8667px; 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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 113.392px 8px; transform-origin: 113.392px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esize(edg_list) = [number of edges, 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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 240.742px 8px; transform-origin: 240.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEvery row of it is an edge at the format [e1, e2], sorted in ascending order, i.e.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\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: 23.5417px 8px; transform-origin: 23.5417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ee1 \u0026lt; e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 91.4083px 8px; transform-origin: 91.4083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and e1, e2 positive integers.\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 236.008px 8px; transform-origin: 236.008px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEach edge is present once and only once, no duplicated edge admitted\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 166.133px 8px; transform-origin: 166.133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOrder of rows / edges in the output doesn't matter\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e .\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; 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: 238.775px 8px; transform-origin: 238.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf the vertex is not in the list, the function must of course return the empty set.\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 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: 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function edg_list = find_edges_from_vertex(T,i)\r\n edg_list = T;\r\nend","test_suite":"%% Tetrahedron\r\nT = [1 2 3;...\r\n 1 3 4;...\r\n 1 4 2;...\r\n 2 3 4];\r\n \r\ni = 4;\r\n\r\nedg_list = [1 4;...\r\n 2 4;...\r\n 3 4];\r\n \r\nassert(isequal(sortrows(find_edges_from_vertex(T,i)),edg_list))\r\n \r\n%% Triangulated cube\r\nT = [1 2 4;...\r\n 2 3 4;...\r\n 5 6 8;...\r\n 6 7 8;...\r\n 1 2 5;...\r\n 2 5 6;...\r\n 2 3 6;...\r\n 3 6 7;...\r\n 3 4 7;...\r\n 4 7 8;...\r\n 4 1 8;...\r\n 1 8 5];\r\n\r\ni = 7;\r\n\r\nedg_list = [3 7;...\r\n 4 7;...\r\n 6 7;...\r\n 7 8];\r\n\r\nassert(isequal(sortrows(find_edges_from_vertex(T,i)),edg_list)); \r\n\r\n%% Empty set test\r\nT = [2 3 5;...\r\n 3 5 7;...\r\n 5 7 11;...\r\n 7 11 13];\r\n \r\ni = 8;\r\n\r\nassert(isempty(find_edges_from_vertex(T,i)))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('find_edges_from_vertex.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:51:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":"2025-07-09T05:49:14.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-12-02T15:54:28.000Z","updated_at":"2025-11-18T16:58:11.000Z","published_at":"2019-12-03T07:32:15.000Z","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\u003eFirst input is T, a triplet list of indices. Second input is i, a single index (positive integer). The goal of this function is to find and return all the edges [e1 e2] this vertex belong to.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 if inputs are\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[T = [1 2 3 ;...\\n 1 3 4 ;...\\n 1 4 2 ;...\\n 2 3 4]]]\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\u003eand\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[i = 4]]\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\u003ethen the output is the 3 x 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[matrix edg_list= [1 4;...\\n 3 4;...\\n 2 4]]]\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 vertex number 4 is linked with vertices number 1, 2, and 3 and then part of edges [1 4], [2 4], and [3 4]. Format of the output must be the following :\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\u003esize(edg_list) = [number of edges, 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\u003eEvery row of it is an edge at the format [e1, e2], sorted in ascending order, i.e.\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\u003ee1 \u0026lt; e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and e1, e2 positive integers.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEach edge is present once and only once, no duplicated edge admitted\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOrder of rows / edges in the output doesn't matter\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\u003eIf the vertex is not in the list, the function must of course return the empty set.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\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:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\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":43294,"title":"Can we make a triangle?","description":"Given three positive number, check whether a triangle can be made with these sides length or not. remember that in a triangle sum of two sides should be greater than the third one. So with the lengths of 2,3 and 6 we can not make a triangle","description_html":"\u003cp\u003eGiven three positive number, check whether a triangle can be made with these sides length or not. remember that in a triangle sum of two sides should be greater than the third one. So with the lengths of 2,3 and 6 we can not make a triangle\u003c/p\u003e","function_template":"function flag = Is_Triangle(a, b, c)\r\n flag=false;\r\nend","test_suite":"%%\r\nassert(isequal(Is_Triangle(3,4,6),true))\r\n%%\r\nassert(isequal(Is_Triangle(6,4,3),true))\r\n%%\r\nassert(isequal(Is_Triangle(3,7,4),false))\r\n%%\r\nassert(isequal(Is_Triangle(4,3,7),false))\r\n%%\r\nassert(isequal(Is_Triangle(3,3,4),true))\r\n\r\n","published":true,"deleted":false,"likes_count":16,"comments_count":3,"created_by":94830,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2256,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-10T06:51:56.000Z","updated_at":"2026-04-04T19:14:04.000Z","published_at":"2016-10-10T06:51:56.000Z","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 three positive number, check whether a triangle can be made with these sides length or not. remember that in a triangle sum of two sides should be greater than the third one. So with the lengths of 2,3 and 6 we can not make a triangle\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":58354,"title":"Find the circle inscribed in 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 center and radius of a circle inscribed in the triangle (i.e., tangent to each of the three sides).","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: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; 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 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: 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 center and radius of a circle inscribed in the triangle (i.e., tangent to each of the three sides).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [x0,y0,r] = incircle(x,y)\r\n% x = vector of x-coordinates of the triangle's vertices\r\n% y = vector of y-coordinates of the triangle's vertices\r\n% (x0,y0) = coordinates of the incircle's center\r\n% r = radius of the incircle\r\n [x0,y0,r] = Delaunay(something(x),something(y));\r\nend","test_suite":"%%\r\nx = [0 1 0];\r\ny = [0 0 1];\r\nx0_correct = 0.29289321881;\r\ny0_correct = 0.29289321881;\r\nr_correct = 0.29289321881;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nth = pi/2:2*pi/3:11*pi/6;\r\nx = cos(th);\r\ny = sin(th);\r\nx0_correct = 0;\r\ny0_correct = 0;\r\nr_correct = 0.5;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [1 4 5];\r\ny = [2 3 6];\r\nx0_correct = 3.47213595500;\r\ny0_correct = 3.52786404500;\r\nr_correct = 0.66770107084;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [1 4 5];\r\ny = [2 3 6];\r\nx0_correct = 3.47213595500;\r\ny0_correct = 3.52786404500;\r\nr_correct = 0.66770107084;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [-1 4 5];\r\ny = [2 -3 6];\r\nx0_correct = 2.36290232380;\r\ny0_correct = 1.66700704764;\r\nr_correct = 2.14246946292;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [12 3 45];\r\ny = [6 78 9];\r\nx0_correct = 23.24160585487;\r\ny0_correct = 19.96162835361;\r\nr_correct = 12.88652365580;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [-1 0 1];\r\ny = [0 19 0];\r\nx0_correct = 0;\r\ny0_correct = 0.94875250476;\r\nr_correct = 0.94875250476;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [10 15 20];\r\ny = [30 45.1 60];\r\nx0_correct = 15.01499995500; \r\ny0_correct = 45.09499981499; \r\nr_correct = 0.01581137249;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nL = 100*rand;\r\nx = [0 L 0];\r\ny = [0 0 L];\r\nd_correct = L/(2+sqrt(2)); \r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-d_correct)\u003c1e-10)\r\nassert(abs(y0-d_correct)\u003c1e-10)\r\nassert(abs(r-d_correct)\u003c1e-10)\r\n\r\n%%\r\nfiletext = fileread('incircle.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-05-20T15:34:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-20T15:33:53.000Z","updated_at":"2023-05-20T15:34:18.000Z","published_at":"2023-05-20T15:34:18.000Z","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 x- and y-coordinates of three points describing the vertices of a triangle and returns the center and radius of a circle inscribed in the triangle (i.e., tangent to each of the three sides).\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":61090,"title":"Covering a 4-pointed star polygon by a circle sector","description":"Given the area, A, of a 4-pointed star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, consider the circle that covers the greater of the two distances between opposite vertices (cf. figure below).\r\nGiven (A,h), find\r\nthe width, L, of the rectangle;\r\nthe angle, α [in Radians], of the sector of the circle such that its area is equal to A;\r\nthe minimum slicing number n, corresponding to the number of congruent circle slices, such that the area of one slice does not exceed the above sector area.\r\ninput: (A, h)\r\noutput: y = [L alpha n]\r\n","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: 751.55px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 375.775px; transform-origin: 408px 375.775px; 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; 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=\"\"\u003eGiven the area, \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; \"\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=\"\"\u003e, of a 4-pointed star polygon formed by the rectangle, with dimensions \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×\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; \"\u003e2L\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, and four triangles, with height \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; \"\u003eh\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 from their bases to the vertices, consider the circle that covers the greater of the two distances between opposite vertices (cf. figure below).\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=\"\"\u003eGiven \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(A,h)\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, find\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.75px; 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 40.875px; transform-origin: 391px 40.875px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; 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=\"\"\u003ethe width, \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL,\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the rectangle;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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=\"\"\u003ethe angle, \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eα\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e [in Radians], of the sector of the circle such that its area is equal to \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; 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 20.4375px; text-align: left; transform-origin: 363px 20.4375px; 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=\"\"\u003ethe minimum slicing number \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, corresponding to the number of congruent circle slices, such that the area of one slice does not exceed the above sector area.\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=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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 \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(A, h)\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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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 \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; \"\u003ey = [L alpha n]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 486.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 243.4px; text-align: left; transform-origin: 384px 243.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"601\" height=\"481\" style=\"vertical-align: baseline;width: 601px;height: 481px\" 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\" alt=\"Covering by sector\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = covering_by_sector(A,h)\r\n y = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nh = 1;\r\ny_correct = [3 3.375 2];\r\nassert(isequal(covering_by_sector(A,h),y_correct))\r\n\r\n%%\r\nA = 36;\r\nh = 2;\r\ny_correct = [3 2.88 3];\r\nassert(isequal(covering_by_sector(A,h),y_correct))\r\n\r\n%%\r\nA = 45;\r\nh = 3;\r\ny_correct = [3 2.5 3];\r\nassert(isequal(covering_by_sector(A,h),y_correct))\r\n\r\n%%\r\nfiletext = fileread('covering_by_sector.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 56;\r\nh = 2; \r\ny_correct = [4 28/9 3];\r\nassert(all(isapprox(covering_by_sector(A,h),y_correct), 'all'))\r\n\r\n%%\r\nA = 50;\r\nh = 5; \r\ny_correct = [2.5 16/9 4];\r\nassert(all(isapprox(covering_by_sector(A,h),y_correct), 'all'))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-12-03T10:39:21.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-30T14:56:09.000Z","updated_at":"2026-03-23T10:36:12.000Z","published_at":"2025-12-03T10:39:21.000Z","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\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a 4-pointed star polygon formed by the rectangle, with dimensions \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×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, consider the circle that covers the greater of the two distances between opposite vertices (cf. figure 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":769,"title":"Calculate the area of a triangle between three points","description":"Calculate the area of a triangle between three points:\r\nP1(X1,Y1)\r\nP2(X2,Y2)\r\nP3(X3,Y3)\r\nthese three points are the vertices of the triangle.","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: 141px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 70.5px; transform-origin: 407px 70.5px; 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: 167.5px 8px; transform-origin: 167.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the area of a triangle between three points:\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=\"\"\u003eP1(X1,Y1)\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=\"\"\u003eP2(X2,Y2)\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=\"\"\u003eP3(X3,Y3)\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: 155.5px 8px; transform-origin: 155.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethese three points are the vertices of the triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"% X=[x1 x2 x3]\r\n% Y=[y1 y2 y3]\r\nfunction y = your_fcn_name(X,Y)\r\n y = X.*Y;\r\nend","test_suite":"%%\r\nX=[1 0 0];\r\nY=[0 0 1];\r\ny_correct = 0.5;\r\nassert(abs(your_fcn_name(X,Y)-y_correct)\u003c1e-3)\r\n\r\n%%\r\nX=[1 1.5 2];\r\nY=[0 1 0];\r\ny_correct = 0.5;\r\nassert(abs(your_fcn_name(X,Y)-y_correct)\u003c1e-3)\r\n\r\n%%\r\nX=[2 3 1];\r\nY=[0 3 4];\r\ny_correct = 3.500;\r\nassert(abs(your_fcn_name(X,Y)-y_correct)\u003c1e-3)\r\n\r\n%%\r\nX=[10 12 -10];\r\nY=[-7 -3 -47];\r\ny_correct = 0;\r\nassert(abs(your_fcn_name(X,Y)-y_correct)\u003c1e-3)\r\n\r\n%%\r\nX=[0 5 0];\r\nY=[6 0 0];\r\ny_correct = 15;\r\nassert(abs(your_fcn_name(X,Y)-y_correct)\u003c1e-3)","published":true,"deleted":false,"likes_count":32,"comments_count":6,"created_by":4320,"edited_by":223089,"edited_at":"2023-02-02T09:07:51.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3428,"test_suite_updated_at":"2023-02-02T09:07:51.000Z","rescore_all_solutions":false,"group_id":17,"created_at":"2012-06-15T14:26:12.000Z","updated_at":"2026-04-06T23:09:50.000Z","published_at":"2012-06-15T14:26:12.000Z","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\u003eCalculate the area of a triangle between three points:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP1(X1,Y1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP2(X2,Y2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP3(X3,Y3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethese three points are the vertices of the triangle.\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\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":50447,"title":"Calculate Triangle Area, A, B and Gamma is given.","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: 359px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 179.5px; transform-origin: 407px 179.5px; 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=\"\"\u003eCalculate Triangle Area:\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; \"\u003e 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; \"\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; \"\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; \"\u003e\u003cspan style=\"\"\u003eand\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; \"\u003e Gamma\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 [degree] is given as 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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-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=\"\"\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=\"\"\u003eRound the answer to four decimal places\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\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaTriangle(A, B, Gamma)\r\n\r\nend","test_suite":"%% \r\nA = 4; B = 6; Gamma = 56.45; % [degree]\r\ny_correct = 10.0008\r\nassert(isequal(AreaTriangle(A, B, Gamma),y_correct))\r\n\r\n%%\r\nA = 5.7; B = 8.9; Gamma = 132; % [degree]\r\n\r\ny_correct = 18.8499\r\nassert(isequal(AreaTriangle(A, B, Gamma),y_correct))\r\n\r\n%%\r\nA = 48.3; B = 643; Gamma = 8; % [degree]\r\n\r\ny_correct = 2161.1425\r\nassert(isequal(AreaTriangle(A, B, Gamma),y_correct))\r\n\r\n%%\r\nA = pi; B = 2*pi; Gamma = 43; % [degree]\r\n\r\ny_correct = 6.7311\r\nassert(isequal(AreaTriangle(A, B, Gamma),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-18T16:05:19.000Z","updated_at":"2026-03-21T09:29:10.000Z","published_at":"2021-02-18T16:05:19.000Z","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\u003eCalculate Triangle Area:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e 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\u003eB \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e Gamma\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [degree] is given as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003e 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of a triangle","description":"A triangle is given with base *'b'* ,vertical hight *'h'* . then find it's area.","description_html":"\u003cp\u003eA triangle is given with base \u003cb\u003e'b'\u003c/b\u003e ,vertical hight \u003cb\u003e'h'\u003c/b\u003e . then find it's area.\u003c/p\u003e","function_template":"function A = trg_area(b,h)\r\n A=f(b,h);\r\nend","test_suite":"%%\r\nb = 1;\r\nh=5\r\ny_correct = 2.5;\r\nassert(isequal(trg_area(b,h),y_correct))\r\n\r\n%%\r\nb = 1;\r\nh=10\r\ny_correct = 5;\r\nassert(isequal(trg_area(b,h),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":22553,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":982,"test_suite_updated_at":"2014-07-07T12:31:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-06-18T17:40:40.000Z","updated_at":"2026-02-13T06:59:31.000Z","published_at":"2014-06-18T17:40:40.000Z","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 triangle is given with base\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'b'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ,vertical hight\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'h'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e . then find it's area.\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":61070,"title":"Square area to triangle area","description":"Given the area, A, of a square with side length, c, if a right angle triangle has the same area A and the hypothenuse length 2c (two times the square side), then find the height, h, of the triangle.\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho","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: 163.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 81.875px; transform-origin: 408px 81.875px; 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=\"\"\u003eGiven the area, \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; \"\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=\"\"\u003e, of a square with side length, \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; \"\u003ec\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, if a right angle triangle has the same area \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; \"\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=\"\"\u003e and the hypothenuse length \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; \"\u003e2c \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(two times the square side), then find the height, \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; \"\u003eh\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 the triangle.\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=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.75px; 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: 392px 40.875px; transform-origin: 392px 40.875px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; 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: 364px 10.2125px; text-align: left; transform-origin: 364px 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=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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: 364px 10.2125px; text-align: left; transform-origin: 364px 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=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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: 364px 10.2125px; text-align: left; transform-origin: 364px 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=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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: 364px 10.2125px; text-align: left; transform-origin: 364px 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=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function h = find_height(A)\r\n h = A;\r\nend","test_suite":"%%\r\nA = 8;\r\nh_correct = 4;\r\nassert(isequal(find_height(A),h_correct))\r\n\r\n%%\r\nfiletext = fileread('find_height.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 9;\r\nh_correct = 3*sqrt(2);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 15;\r\nh_correct = sqrt(30);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 16;\r\nh_correct = 4*sqrt(2);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 18;\r\nh_correct = 6;\r\nassert(isequal(find_height(A),h_correct))\r\n\r\n%%\r\nA = 32;\r\nh_correct = 8;\r\nassert(isequal(find_height(A),h_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":5,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-09T16:09:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-09T13:39:12.000Z","updated_at":"2026-03-23T20:43:13.000Z","published_at":"2025-11-09T16:09:35.000Z","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\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a square with side length, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, if a right angle triangle has the same area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and the hypothenuse length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2c \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(two times the square side), then find the height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\u003eForbidden functions / expressions\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\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":45897,"title":" Volume of Equilateral Triangle Prism","description":"Find volume of equilateral triangle prism\r\nx = side of triangle\r\nl = length of prism","description_html":"\u003cp\u003eFind volume of equilateral triangle prism\r\nx = side of triangle\r\nl = length of prism\u003c/p\u003e","function_template":"function y = volumeofequilateraltriangleprism(x,l)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 2;\r\nl = 5;\r\ny_correct = ((x^2*sqrt(3))/4)*l;\r\nassert(isequal(volumeofequilateraltriangleprism(x,l),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":441903,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":86,"test_suite_updated_at":"2020-06-12T20:14:39.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-12T20:08:02.000Z","updated_at":"2026-02-12T12:18:43.000Z","published_at":"2020-06-12T20:08:53.000Z","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\u003eFind volume of equilateral triangle prism x = side of triangle l = length of prism\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":55895,"title":"Tipos de Triangulos","description":"Dados os tamanhos dos lados de um triangulos A, B e C. Retorne qual o tipo do triangulo: 'equilátero', 'escaleno' ou 'isósceles'.\r\nTipoTriangulo(1, 2, 3) = 'escaleno'","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: 72.4375px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36.2188px; transform-origin: 407px 36.2188px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eDados os tamanhos dos lados de um triangulos A, B e C. Retorne qual o tipo do triangulo: 'equilátero', 'escaleno' ou 'isósceles'.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4375px; 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 10.2188px; transform-origin: 404px 10.2188px; 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; \"\u003eTipoTriangulo(1, 2, 3) = \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); text-emphasis-color: rgb(170, 4, 249); \"\u003e'escaleno'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = TipoTriangulo(A, B, C)\r\n %faça a sua solução\r\nend","test_suite":"%%\r\nA = 1;\r\nB = 2;\r\nC = 3;\r\ny_correct = 'escaleno';\r\nassert(isequal(TipoTriangulo(A, B, C),y_correct))\r\n\r\n\r\n%%\r\nA = 2;\r\nB = 2;\r\nC = 3;\r\ny_correct = 'isósceles';\r\nassert(isequal(TipoTriangulo(A, B, C),y_correct))\r\n\r\n\r\n%%\r\nA = 2;\r\nB = 2;\r\nC = 2;\r\ny_correct = 'equilátero';\r\nassert(isequal(TipoTriangulo(A, B, C),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":2564100,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":32,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-17T17:43:31.000Z","updated_at":"2026-02-09T14:17:00.000Z","published_at":"2022-09-17T17:43:31.000Z","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\u003eDados os tamanhos dos lados de um triangulos A, B e C. Retorne qual o tipo do triangulo: 'equilátero', 'escaleno' ou 'isósceles'.\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[TipoTriangulo(1, 2, 3) = 'escaleno']]\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":45217,"title":"Find a common vertex","description":"First input is T, a triplet list of indices. Second input is i, a single index (positive integer). The goal of this function is to find and return the indices of the rows in the list which contain this particular index. Output format is indifferently a column or a row vector.\r\nFor example if inputs are\r\nT = [1 2 3;...\r\n 1 3 4;...\r\n 1 4 2;...\r\n 2 3 4]\r\nand\r\ni = 2\r\nthe output is the vector\r\nrow_idx = [1 3 4]\r\nsince 2 is contained in rows number 1, 3, and 4 of T. If the index is not in the list, the function must of course return the empty set. Each index is at most contained once per row / triplet.\r\n\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","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: 479.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 239.8px; transform-origin: 408px 239.8px; 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: 385px 31.5px; text-align: left; transform-origin: 385px 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: 375.725px 8px; transform-origin: 375.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFirst input is T, a triplet list of indices. Second input is i, a single index (positive integer). The goal of this function is to find and return the indices of the rows in the list which contain this particular index. Output format is indifferently a column or a row vector.\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: 77.0167px 8px; transform-origin: 77.0167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example if inputs are\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: 405px 40.8667px; transform-origin: 405px 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003eT = [1 2 3;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 1 3 4;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 1 4 2;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 42.35px 8.5px; tab-size: 4; transform-origin: 42.35px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 2 3 4]\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; 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: 405px 10.2167px; transform-origin: 405px 10.2167px; 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; text-wrap-mode: 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: 19.25px 8.5px; tab-size: 4; transform-origin: 19.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ei = 2\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 70.7833px 8px; transform-origin: 70.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe output is the vector\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; 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: 405px 10.2167px; transform-origin: 405px 10.2167px; 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; text-wrap-mode: 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: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003erow_idx = [1 3 4]\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; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; 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: 367.533px 8px; transform-origin: 367.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince 2 is contained in rows number 1, 3, and 4 of T. If the index is not in the list, the function must of course return the empty set. Each index is at most contained once per row / triplet.\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 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: 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function row_idx = find_common_vertex(T,i)\r\n row_idx = i;\r\nend","test_suite":"%% Tetrahedron\r\nT = [1 2 3;...\r\n 1 3 4;...\r\n 1 4 2;...\r\n 2 3 4];\r\n\r\ni = 2;\r\n\r\nrow_idx = [1 3 4];\r\n\r\nassert(isequal(find_common_vertex(T,i),row_idx) || isequal(find_common_vertex(T,i),row_idx'))\r\n\r\n%% Octahedron\r\nT = [1 2 3;...\r\n 1 3 4;...\r\n 1 4 5;...\r\n 1 5 2;...\r\n 6 3 2;...\r\n 6 4 3;...\r\n 6 5 4;...\r\n 6 2 5];\r\n\r\ni = 4;\r\n\r\nrow_idx = [2 3 6 7];\r\n\r\nassert(isequal(find_common_vertex(T,i),row_idx) || isequal(find_common_vertex(T,i),row_idx'))\r\n\r\n%% Triangulated cube\r\nT = [1 2 4;...\r\n 2 3 4;...\r\n 5 6 8;...\r\n 6 7 8;...\r\n 1 2 5;...\r\n 2 5 6;...\r\n 2 3 6;...\r\n 3 6 7;...\r\n 3 4 7;...\r\n 4 7 8;...\r\n 4 1 8;...\r\n 1 8 5];\r\n\r\ni = 6;\r\n\r\nrow_idx = [3 4 6 7 8];\r\n\r\nassert(isequal(find_common_vertex(T,i),row_idx) || isequal(find_common_vertex(T,i),row_idx'))\r\n\r\n%% Empty set test\r\nT = [2 3 5;...\r\n 3 5 7;...\r\n 5 7 11;...\r\n 7 11 13];\r\n\r\ni = 8;\r\n\r\nassert(isempty(find_common_vertex(T,i)))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('find_common_vertex.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:50:48.000Z","deleted_by":null,"deleted_at":null,"solvers_count":43,"test_suite_updated_at":"2025-07-09T05:47:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-12-01T16:22:33.000Z","updated_at":"2026-03-02T14:28:36.000Z","published_at":"2019-12-01T16:58:33.000Z","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\u003eFirst input is T, a triplet list of indices. Second input is i, a single index (positive integer). The goal of this function is to find and return the indices of the rows in the list which contain this particular index. Output format is indifferently a column or a row vector.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 if inputs are\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[T = [1 2 3;...\\n 1 3 4;...\\n 1 4 2;...\\n 2 3 4]]]\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\u003eand\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[i = 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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe output is the vector\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[row_idx = [1 3 4]]]\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 2 is contained in rows number 1, 3, and 4 of T. If the index is not in the list, the function must of course return the empty set. Each index is at most contained once per row / triplet.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\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:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\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":55905,"title":"Triangulo Semelhante","description":"Dados dois vetores A = (a1, a2, a3) e B = (b1, b2, b3) sendo referentes a arestas de triangulos. Verifique se os triangulos são semelhantes, retorne true ou false.\r\nTriangulosSemelhantes([6, 4, 2], [3, 2, 1]) = true;","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: 72.4375px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36.2188px; transform-origin: 407px 36.2188px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eDados dois vetores A = (a1, a2, a3) e B = (b1, b2, b3) sendo referentes a arestas de triangulos. Verifique se os triangulos são semelhantes, retorne true ou false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4375px; 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 10.2188px; transform-origin: 404px 10.2188px; 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; \"\u003eTriangulosSemelhantes([6, 4, 2], [3, 2, 1]) = true;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = TriangulosSemelhantes(A, B)\r\n % faça a sua solução aqui\r\nend","test_suite":"%%\r\nA = [6, 4, 2];\r\nB = [3, 2, 1];\r\ny_correct = true;\r\nassert(isequal(TriangulosSemelhantes(A, B), y_correct))\r\n\r\n%%\r\nA = [7, 6, 2];\r\nB = [3, 2, 1];\r\ny_correct = false;\r\nassert(isequal(TriangulosSemelhantes(A, B), y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":2564100,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":33,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-17T18:36:29.000Z","updated_at":"2026-02-12T12:21:15.000Z","published_at":"2022-09-17T18:36:29.000Z","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\u003eDados dois vetores A = (a1, a2, a3) e B = (b1, b2, b3) sendo referentes a arestas de triangulos. Verifique se os triangulos são semelhantes, retorne true ou false.\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[TriangulosSemelhantes([6, 4, 2], [3, 2, 1]) = true;]]\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":60855,"title":"What kind of triangle?","description":"Write a function named check_triangle that receives three positive integers as input: a, b, and c.\r\nThese three numbers are intended to represent the sides of a triangle.\r\nThe function should return in the variable t one of the following four strings:\r\na. Not a triangle – The numbers cannot represent the sides of a triangle because they do not satisfy the triangle inequality rule: the sum of any two sides must be greater than the third side.\r\n(Example: the triple 2, 3, 20 does not satisfy the rule because 2 + 3 is not greater than 20.)\r\nb. Equilateral – The numbers represent the sides of an equilateral triangle (example: 4, 4, 4).\r\nc. Isosceles – The numbers represent the sides of an isosceles triangle (example: 5, 5, 4).\r\nd. Scalene – The numbers represent the sides of a scalene triangle (a triangle that is neither equilateral nor isosceles) (example: 4, 8, 5).\r\nHint: use the if ... else if ... structure.\r\nAssume that the input always consists of three positive integers (greater than zero).\r\nImportant:\r\nYou must return only the most accurate conclusion regarding the triple a, b, c.\r\nFor example, if the triangle is equilateral, return only the corresponding string \"Equilateral\" and not \"Isosceles\"or \"Scalene\".\r\n\r\nTerms: \r\nEquilateral – all three sides are equal\r\nIsosceles – two sides are equal\r\nScalene – all sides are different\r\nNot a triangle – the numbers cannot form a triangle","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: 624px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 312px; transform-origin: 408px 312px; 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: 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 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; font-weight: 700; \"\u003echeck_triangle\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 receives three positive integers as input: \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; \"\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=\"\"\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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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, 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ec\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; 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=\"\"\u003eThese three numbers are intended to represent the sides of a triangle.\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=\"\"\u003eThe function should return in the variable \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; \"\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 one of the following four strings:\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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-weight: 700; \"\u003eNot a triangle\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 – The numbers cannot represent the sides of a triangle because they do not satisfy the triangle inequality rule: the sum of any two sides must be greater than the third side.\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=\"\"\u003e(Example: the triple \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; \"\u003e2, 3, 20\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 does not satisfy the rule because \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; \"\u003e2 + 3\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 is not greater than \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; \"\u003e20\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; 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=\"\"\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=\"font-weight: 700; \"\u003eEquilateral\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 – The numbers represent the sides of an equilateral triangle (example: \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; \"\u003e4, 4, 4\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; 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=\"\"\u003ec. \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; \"\u003eIsosceles\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 – The numbers represent the sides of an isosceles triangle (example: \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; \"\u003e5, 5, 4\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; 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=\"\"\u003ed. \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; \"\u003eScalene\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 – The numbers represent the sides of a scalene triangle (a triangle that is neither equilateral nor isosceles) (example: \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; \"\u003e4, 8, 5\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; 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=\"\"\u003eHint: use the \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; \"\u003eif ... else if ... \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=\"\"\u003estructure.\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=\"\"\u003eAssume that the input always consists of three positive integers (greater than zero).\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=\"font-weight: 700; \"\u003eImportant:\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=\"\"\u003eYou must return \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; \"\u003eonly the most accurate conclusion\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 regarding the triple \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; \"\u003ea, b, c\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; 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=\"\"\u003eFor example, if the triangle is equilateral, return only the corresponding string \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; \"\u003e\"Equilateral\" \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=\"\"\u003eand not \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; \"\u003e\"Isosceles\"\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=\"\"\u003eor \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; \"\u003e\"Scalene\"\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; 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=\"\"\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=\"font-weight: 700; \"\u003eTerms:\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; 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=\"font-weight: 700; \"\u003eEquilateral\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 – all three sides are equal\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=\"font-weight: 700; \"\u003eIsosceles\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 – two sides are equal\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=\"font-weight: 700; \"\u003eScalene\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 – all sides are different\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=\"font-weight: 700; \"\u003eNot a triangle\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 – the numbers cannot form a triangle\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = check_triangle(a,b,c)\r\n t = 'Not a triangle';\r\nend","test_suite":"%%\r\na=4;\r\nb=6;\r\nc=4;\r\nt_correct = 'Isosceles';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n\r\n\r\n%%\r\na=4;\r\nb=4;\r\nc=4;\r\nt_correct = 'Equilateral';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n\r\n\r\n%%\r\na=3;\r\nb=4;\r\nc=5;\r\nt_correct = 'Scalene';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n\r\n%%\r\na=3;\r\nb=14;\r\nc=15;\r\nt_correct = 'Scalene';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n\r\n%%\r\na=1;\r\nb=1;\r\nc=1;\r\nt_correct = 'Equilateral';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n\r\n\r\n\r\n%%\r\na=4;\r\nb=5;\r\nc=30;\r\nt_correct = 'Not a triangle';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n\r\n%%\r\na=4;\r\nb=2;\r\nc=6;\r\nt_correct = 'Not a triangle';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n\r\n%%\r\na=40;\r\nb=5;\r\nc=3;\r\nt_correct = 'Not a triangle';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n\r\n%%\r\na=4;\r\nb=50;\r\nc=3;\r\nt_correct = 'Not a triangle';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n\r\n%%\r\na=4;\r\nb=4;\r\nc=7;\r\nt_correct = 'Isosceles';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n\r\n%%\r\na=8;\r\nb=8;\r\nc=5;\r\nt_correct = 'Isosceles';\r\nassert(isequal(check_triangle(a,b,c),t_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":2710538,"edited_by":2710538,"edited_at":"2025-04-27T18:25:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":70,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-04-27T17:26:20.000Z","updated_at":"2026-03-04T22:12:48.000Z","published_at":"2025-04-27T17:26:19.000Z","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 named \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\u003echeck_triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that receives three positive integers as input: \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\u003ea\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\u003eb\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\u003ec\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\u003eThese three numbers are intended to represent the sides of a triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 should return in the variable \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\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e one of the following four strings:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNot a triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e – The numbers cannot represent the sides of a triangle because they do not satisfy the triangle inequality rule: the sum of any two sides must be greater than the third side.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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(Example: the triple \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\u003e2, 3, 20\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e does not satisfy the rule because \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\u003e2 + 3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is not greater than \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\u003e20\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\u003eb. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEquilateral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e – The numbers represent the sides of an equilateral triangle (example: \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, 4, 4\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\u003ec. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIsosceles\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e – The numbers represent the sides of an isosceles triangle (example: \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\u003e5, 5, 4\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\u003ed. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScalene\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e – The numbers represent the sides of a scalene triangle (a triangle that is neither equilateral nor isosceles) (example: \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, 8, 5\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\u003eHint: use the \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\u003eif ... else if ... \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003estructure.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssume that the input always consists of three positive integers (greater than 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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eImportant:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 must return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eonly the most accurate conclusion\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e regarding the triple \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\u003ea, b, c\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\u003eFor example, if the triangle is equilateral, return only the corresponding string \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\\\"Equilateral\\\" \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand not \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\\\"Isosceles\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eor \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\\\"Scalene\\\"\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\u003eTerms:\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEquilateral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e – all three sides are equal\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\u003eIsosceles\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e – two sides are equal\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\u003eScalene\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e – all sides are different\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\u003eNot a triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e – the numbers cannot form a triangle\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":50452,"title":"Calculate Triangle Area: A, B and Beta is given","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: 275px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 137.5px; transform-origin: 407px 137.5px; 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=\"\"\u003eCalculate Triangle Area: \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; \"\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; \"\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; \"\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; \"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBeta\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 [degree] is given as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 215px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 107.5px; text-align: left; transform-origin: 384px 107.5px; 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\u003cimg class=\"imageNode\" width=\"269\" height=\"209\" style=\"vertical-align: baseline;width: 269px;height: 209px\" 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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-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=\"\"\u003e Round the answer to four decimal places\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaTriangle(A, B, Beta)\r\n\r\nend","test_suite":"%% \r\nA = 4; B = 4; Beta = 45; % [degree]\r\n\r\ny_correct = 8\r\nassert(isequal(AreaTriangle(A, B, Beta),y_correct))\r\n\r\n%%\r\nA = 6.39; B = 4.9; Beta = 32.9; % [degree]\r\n\r\ny_correct = 15.3134\r\nassert(isequal(AreaTriangle(A, B, Beta),y_correct))\r\n\r\n%%\r\nA = 257; B = 567; Beta = 23.8; % [degree]\r\n\r\ny_correct = 41099.6329\r\nassert(isequal(AreaTriangle(A, B, Beta),y_correct))\r\n\r\n%%\r\nA = 2*pi; B = 3*pi; Beta = 56.3; % [degree]\r\n\r\ny_correct = 29.6088\r\nassert(isequal(AreaTriangle(A, B, Beta),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-18T16:37:21.000Z","updated_at":"2026-03-14T18:27:52.000Z","published_at":"2021-02-18T16:44:29.000Z","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\u003eCalculate Triangle Area: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\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 and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBeta\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [degree] is given as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"209\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"269\\\"/\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\u003c/w:p\u003e\u003cw:p\u003e\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 Round the answer to four decimal 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60982,"title":"Mesh the square with triangles","description":"Problem statement\r\n\r\nAn square is a regular polygon with 4 vertices and 4 edges.\r\nA triangulated mesh T (stands for triangles here) -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh, that is to say give one triangulation T of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\r\n\r\nExample\r\nThe first triangle here can be [1, 2, 3] if counterclockwise oriented.\r\n\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","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: 995.233px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 497.617px; transform-origin: 408px 497.617px; 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: 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: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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: 183.608px 8px; transform-origin: 183.608px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn square is a regular polygon with 4 vertices and 4 edges.\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.1833px 8px; transform-origin: 64.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh \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: 4.275px 8px; transform-origin: 4.275px 8px; 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: 176.983px 8px; transform-origin: 176.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (stands for triangles here) -or a triangulation- is simply 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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 132.633px 8px; transform-origin: 132.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \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 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: 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: 192.275px 8px; transform-origin: 192.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh, that is to say give one triangulation \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: 4.275px 8px; transform-origin: 4.275px 8px; 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: 183.583px 8px; transform-origin: 183.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\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: 92.9583px 8px; transform-origin: 92.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle here can 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: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 3]\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: 89.8583px 8px; transform-origin: 89.8583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented.\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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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 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: 340.5px; 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: 385px 170.25px; text-align: left; transform-origin: 385px 170.25px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"447\" height=\"335\" style=\"vertical-align: baseline;width: 447px;height: 335px\" 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margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\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; 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 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: 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_square()\r\n T = 1;\r\nend","test_suite":"%% Test every possible solutions\r\nT_correct1 = [1 2 3;\r\n 3 4 1];\r\n\r\nT_correct2 = [2 3 4;\r\n 1 2 4];\r\n\r\nassert(isequal(sortrows(sort(mesh_the_square(),2)),sortrows(sort(T_correct1,2)))...\r\n | isequal(sortrows(sort(mesh_the_square(),2)),sortrows(sort(T_correct2,2))))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_square.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:45:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T16:29:27.000Z","updated_at":"2026-02-10T17:10:21.000Z","published_at":"2025-07-23T16:40:49.000Z","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\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\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\u003eAn square is a regular polygon with 4 vertices and 4 edges.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 triangulated mesh \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 (stands for triangles here) -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eYour task here is to mesh, that is to say give one triangulation \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 of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\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\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 first triangle here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"335\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"447\\\"/\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\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\u003eForbidden functions / expressions\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation 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triangles from edge","description":"First input is T, a Triplet list of indices -whom each row actually contains the three indices of a triangle vertices-. size(T) = [nb_triangles, 3]. Second input is e = [e1, e2], a row vector, couple of indices. Output S is the triplet list of indices which Share the edge e. For instance, if\r\ne = [2, 4]\r\nand T a tetrahedron\r\nT = [1, 2, 3;...\r\n 1, 3, 4;...\r\n 1, 2, 4;...\r\n 2, 3, 4]\r\nthen the output of the function is\r\nS = [1, 2, 4;...\r\n 2, 3, 4]\r\nsince both triangles [1, 2, 4] and [2, 3, 4] contain the edge [2, 4].\r\nConditions :\r\nIf the edge is not part of any triangle in the list, the function must of course return the empty set, [].\r\nEdges are symmetric : [e1, e2] is the same edge as [e2, e1]\r\nOrder of rows / edges in the output doesn't matter.\r\nTriangle indices are assumed always to be sorted in ascending order, T = [t1, t2, t3] with t1 \u003c t2 \u003c t3.\r\nEvery indices are positive, distinct integers.\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","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: 572.2px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 286.1px; transform-origin: 408px 286.1px; 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: 385px 31.5px; text-align: left; transform-origin: 385px 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: 374.5px 8px; transform-origin: 374.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFirst input is T, a Triplet list of indices -whom each row actually contains the three indices of a triangle vertices-. size(T) = [nb_triangles, 3]. Second input is e = [e1, e2], a row vector, couple of indices. Output S is the triplet list of indices which Share the edge e. For instance, if\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; 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: 405px 10.2167px; transform-origin: 405px 10.2167px; 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; text-wrap-mode: 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: 38.5px 8.5px; tab-size: 4; transform-origin: 38.5px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ee = [2, 4]\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 61.4583px 8px; transform-origin: 61.4583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand T a tetrahedron\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: 405px 40.8667px; transform-origin: 405px 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003eT = [1, 2, 3;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 1, 3, 4;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 1, 2, 4;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 50.05px 8.5px; tab-size: 4; transform-origin: 50.05px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 2, 3, 4]\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 99.5667px 8px; transform-origin: 99.5667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen the output of the function is\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: 405px 20.4333px; transform-origin: 405px 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003eS = [1, 2, 4;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 50.05px 8.5px; tab-size: 4; transform-origin: 50.05px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 2, 3, 4]\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 197.567px 8px; transform-origin: 197.567px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince both triangles [1, 2, 4] and [2, 3, 4] contain the edge [2, 4].\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: 40.8167px 8px; transform-origin: 40.8167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConditions :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.167px; 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: 392px 51.0833px; transform-origin: 392px 51.0833px; 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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 302.95px 8px; transform-origin: 302.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf the edge is not part of any triangle in the list, the function must of course return the empty set, [].\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 69.6167px 8px; transform-origin: 69.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEdges are symmetric :\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\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: 118.233px 8px; transform-origin: 118.233px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e[e1, e2] is the same edge as [e2, e1]\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 167.692px 8px; transform-origin: 167.692px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOrder of rows / edges in the output doesn't matter.\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 330.342px 8px; transform-origin: 330.342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTriangle indices are assumed always to be sorted in ascending order, T = [t1, t2, t3] with t1 \u0026lt; t2 \u0026lt; t3.\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 17.8917px 8px; transform-origin: 17.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEvery\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\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: 124.817px 8px; transform-origin: 124.817px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eindices are positive, distinct integers.\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; 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function S = find_triangles_from_edge(T,e)\r\n S = [];\r\nend","test_suite":"%% Tetrahedron\r\nT = [1, 2, 3;...\r\n 1, 3, 4;...\r\n 1, 2, 4;...\r\n 2, 3, 4];\r\n\r\ne = [2, 4];\r\n\r\nS = [1, 2, 4;...\r\n 2, 3, 4];\r\n\r\nassert(isequal(sortrows(find_triangles_from_edge(T,e)),S))\r\n\r\n%% Filled octahedron (two pyramids stuck together via their square bases)\r\nT = [1, 2, 3;...\r\n 1, 3, 4;...\r\n 1, 4, 5;...\r\n 1, 2, 5;...\r\n 2, 3, 6;...\r\n 3, 4, 6;...\r\n 4, 5, 6;...\r\n 2, 5, 6;...\r\n 2, 3, 4;...\r\n 2, 4, 5;...\r\n 1, 2, 4;...\r\n 2, 4, 6];\r\n\r\ne = [2, 4];\r\n\r\nS = [1, 2, 4;...\r\n 2, 3, 4;...\r\n 2, 4, 5;...\r\n 2, 4, 6];\r\n\r\nassert(isequal(sortrows(find_triangles_from_edge(T,e)),S))\r\n\r\n%% Triangulated cube\r\nT = [1, 2, 4;...\r\n 2, 3, 4;...\r\n 5, 6, 8;...\r\n 6, 7, 8;...\r\n 1, 2, 5;...\r\n 2, 5, 6;...\r\n 2, 3, 6;...\r\n 3, 6, 7;...\r\n 3, 4, 7;...\r\n 4, 7, 8;...\r\n 1, 4, 8;...\r\n 1, 5, 8];\r\n\r\ne = [3, 7];\r\n\r\nS = [3, 4, 7;...\r\n 3, 6, 7];\r\n\r\nassert(isequal(sortrows(find_triangles_from_edge(T,e)),S))\r\n\r\n%% Empty set test\r\nT = [2, 3, 5;...\r\n 3, 5, 7;...\r\n 5, 7, 11;...\r\n 7, 11, 13];\r\n\r\ne = [6, 8];\r\n\r\nassert(isempty(find_triangles_from_edge(T,e)))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('find_triangles_from_edge.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:51:41.000Z","deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":"2025-07-09T05:48:39.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-12-03T18:46:56.000Z","updated_at":"2025-12-18T17:15:46.000Z","published_at":"2019-12-03T20:30:58.000Z","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\u003eFirst input is T, a Triplet list of indices -whom each row actually contains the three indices of a triangle vertices-. size(T) = [nb_triangles, 3]. Second input is e = [e1, e2], a row vector, couple of indices. Output S is the triplet list of indices which Share the edge e. For instance, 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[e = [2, 4]]]\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\u003eand T a tetrahedron\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[T = [1, 2, 3;...\\n 1, 3, 4;...\\n 1, 2, 4;...\\n 2, 3, 4]]]\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\u003ethen the output of the function 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[S = [1, 2, 4;...\\n 2, 3, 4]]]\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 both triangles [1, 2, 4] and [2, 3, 4] contain the edge [2, 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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConditions :\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 the edge is not part of any triangle in the list, the function must of course return the empty set, [].\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\u003eEdges are symmetric :\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[e1, e2] is the same edge as [e2, e1]\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOrder of rows / edges in the output doesn't matter.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTriangle indices are assumed always to be sorted in ascending order, T = [t1, t2, t3] with t1 \u0026lt; t2 \u0026lt; t3.\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\u003eEvery\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\u003eindices are positive, distinct integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\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:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\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":44085,"title":"Can the given sides form a triangle?","description":"Can the three given sides form a triangle?","description_html":"\u003cp\u003eCan the three given sides form a triangle?\u003c/p\u003e","function_template":"function y = isTriangle(sides)\r\n y = false;\r\nend","test_suite":"%%\r\nx = [3 4 5];\r\ny_correct = true;\r\nassert(isequal(isTriangle(x),y_correct))\r\n\r\n%%\r\nx = [1 3 5];\r\ny_correct = false;\r\nassert(isequal(isTriangle(x),y_correct))\r\n\r\n%%\r\nx = [6 5 3];\r\ny_correct = true;\r\nassert(isequal(isTriangle(x),y_correct))\r\n\r\n%%\r\nx = [3 3 3];\r\ny_correct = true;\r\nassert(isequal(isTriangle(x),y_correct))\r\n\r\n%%\r\nx = [4 7 5];\r\ny_correct = true;\r\nassert(isequal(isTriangle(x),y_correct))\r\n\r\n%%\r\nx = [5 8 3];\r\ny_correct = false;\r\nassert(isequal(isTriangle(x),y_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":63069,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":140,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-03-13T19:09:28.000Z","updated_at":"2026-03-14T18:36:17.000Z","published_at":"2017-03-13T19:15:30.000Z","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\",\"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\u003eCan the three given sides form a triangle?\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":45179,"title":"The length of the equal sides of an isoceles triangle is 'a'.For all the possible (integer) values of the remaining side,find the associated angles between the two equal sides.","description":"the remaining side may have many possible values.only assume integer ones for simplicity.","description_html":"\u003cp\u003ethe remaining side may have many possible values.only assume integer ones for simplicity.\u003c/p\u003e","function_template":"function y = isoceles(a)\r\n y = a;\r\nend","test_suite":"%%\r\na = 2;\r\ny_correct = [ 28.9550 97.1808];\r\nassert(isequal(isoceles(a),y_correct))\r\n%%\r\na = 3;\r\ny_correct = [ 19.1881\t38.9424\t83.6206\t112.8854];\r\nassert(isequal(isoceles(a),y_correct))\r\n%%\r\na = 1;\r\ny_correct = [];\r\nassert(isequal(isoceles(a),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":4,"created_by":363598,"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":1,"created_at":"2019-10-19T16:23:25.000Z","updated_at":"2026-01-18T13:33:34.000Z","published_at":"2019-10-19T17:45:07.000Z","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\u003ethe remaining side may have many possible values.only assume integer ones for simplicity.\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":45218,"title":"Find a common edge","description":"First input is T, a triplet list of indices. Second input is e = [e1 e2], a row vector, couple of indices (positive distinct integers always sorted in ascending order, ie e1 \u003c e2 ). The goal of this function is to find and return the indices of the rows in the list which contain this particular edge. Output format can be either a column or a row vector.\r\nFor example if inputs are\r\nT = [1 2 3 ;\r\n 1 3 4 ;\r\n 1 4 2 ;\r\n 2 3 4]\r\nand\r\ne = [2 3]\r\nthe output is the vector\r\nrow_idx = [1 4]\r\nsince [2 3] is contained in rows number 1 and 4 of T. With the same input T, but with e = [2 4] this time, the output is the vector row_idx = [3 4], since [2 4] is contained in rows number 3 and 4 of T (Note that edge [b a] is the same as edge [a b] so must be the corresponding outputs). If the edge is not in the list, the function must of course return the empty set.\r\n\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","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: 500.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 250.3px; transform-origin: 408px 250.3px; 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: 385px 31.5px; text-align: left; transform-origin: 385px 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: 377.083px 8px; transform-origin: 377.083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFirst input is T, a triplet list of indices. Second input is e = [e1 e2], a row vector, couple of indices (positive distinct integers always sorted in ascending order, ie\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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 23.5417px 8px; transform-origin: 23.5417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ee1 \u0026lt; e2\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: 247.358px 8px; transform-origin: 247.358px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ). The goal of this function is to find and return the indices of the rows in the list which contain this particular edge. Output format can be either a column or a row vector.\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: 77.0167px 8px; transform-origin: 77.0167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example if inputs are\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: 405px 40.8667px; transform-origin: 405px 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 46.2px 8.5px; tab-size: 4; transform-origin: 46.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eT = [1 2 3 ;\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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 46.2px 8.5px; tab-size: 4; transform-origin: 46.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 3 4 ;\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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 46.2px 8.5px; tab-size: 4; transform-origin: 46.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 4 2 ;\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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 42.35px 8.5px; tab-size: 4; transform-origin: 42.35px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 2 3 4]\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; 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: 405px 10.2167px; transform-origin: 405px 10.2167px; 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; text-wrap-mode: 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: 34.65px 8.5px; tab-size: 4; transform-origin: 34.65px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ee = [2 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; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 70.7833px 8px; transform-origin: 70.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe output is the vector\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; 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: 405px 10.2167px; transform-origin: 405px 10.2167px; 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; text-wrap-mode: 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: 57.75px 8.5px; tab-size: 4; transform-origin: 57.75px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003erow_idx = [1 4]\u003c/span\u003e\u003c/span\u003e\u003c/div\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: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; 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: 369.667px 8px; transform-origin: 369.667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince [2 3] is contained in rows number 1 and 4 of T. With the same input T, but with e = [2 4] this time, the output is the vector row_idx = [3 4], since [2 4] is contained in rows number 3 and 4 of T (Note that\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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 117.825px 8px; transform-origin: 117.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eedge [b a] is the same as edge [a b]\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: 1.725px 8px; transform-origin: 1.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e so must be the corresponding outputs). If the edge is not in the list, the function must of course return the empty set.\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 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: 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function row_idx = find_common_edge(T,e)\r\n row_idx = e;\r\nend","test_suite":"%% Tetrahedron 1\r\nT = [1 2 3;...\r\n 1 3 4;...\r\n 1 4 2;...\r\n 2 3 4];\r\n\r\ne = [2 3];\r\nrow_idx = [1 4];\r\n\r\nassert(isequal(find_common_edge(T,e),row_idx) || isequal(find_common_edge(T,e),row_idx'))\r\n\r\n%% Tetrahedron 2\r\nT = [1 2 3;...\r\n 1 3 4;...\r\n 1 4 2;...\r\n 2 3 4];\r\n\r\ne = [2 4];\r\nrow_idx = [3 4];\r\n\r\nassert(isequal(find_common_edge(T,e),row_idx) || isequal(find_common_edge(T,e),row_idx'))\r\n\r\n%% Octahedron\r\nT = [1 2 3;...\r\n 1 3 4;...\r\n 1 4 5;...\r\n 1 5 2;...\r\n 6 3 2;...\r\n 6 4 3;...\r\n 6 5 4;...\r\n 6 2 5];\r\n\r\ne = [1 5];\r\nrow_idx = [3 4];\r\n\r\nassert(isequal(find_common_edge(T,e),row_idx) || isequal(find_common_edge(T,e),row_idx'))\r\n\r\n%% Triangulated cube\r\nT = [1 2 4;...\r\n 2 3 4;...\r\n 5 6 8;...\r\n 6 7 8;...\r\n 1 2 5;...\r\n 2 5 6;...\r\n 2 3 6;...\r\n 3 6 7;...\r\n 3 4 7;...\r\n 4 7 8;...\r\n 4 1 8;...\r\n 1 8 5];\r\n\r\ne = [6 7];\r\nrow_idx = [4 8];\r\n\r\nassert(isequal(find_common_edge(T,e),row_idx) || isequal(find_common_edge(T,e),row_idx'))\r\n\r\n%% Empty set test\r\nT = [2 3 5;...\r\n 3 5 7;...\r\n 5 7 11;...\r\n 7 11 13];\r\n\r\ne = [6 28];\r\n\r\nassert(isempty(find_common_edge(T,e)))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('find_common_edge.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:50:32.000Z","deleted_by":null,"deleted_at":null,"solvers_count":42,"test_suite_updated_at":"2025-07-09T05:45:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-12-01T17:21:36.000Z","updated_at":"2026-03-14T18:58:02.000Z","published_at":"2019-12-01T18:01:01.000Z","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\u003eFirst input is T, a triplet list of indices. Second input is e = [e1 e2], a row vector, couple of indices (positive distinct integers always sorted in ascending order, ie\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\u003ee1 \u0026lt; e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ). The goal of this function is to find and return the indices of the rows in the list which contain this particular edge. Output format can be either a column or a row vector.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 if inputs are\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[T = [1 2 3 ;\\n 1 3 4 ;\\n 1 4 2 ;\\n 2 3 4]]]\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\u003eand\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[e = [2 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\u003ethe output is the vector\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[row_idx = [1 4]]]\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 [2 3] is contained in rows number 1 and 4 of T. With the same input T, but with e = [2 4] this time, the output is the vector row_idx = [3 4], since [2 4] is contained in rows number 3 and 4 of T (Note that\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\u003eedge [b a] is the same as edge [a b]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e so must be the corresponding outputs). If the edge is not in the list, the function must of course return the empty set.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\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:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\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":60166,"title":"Recursive triangle area","description":"Given triangle 1 with sides of length a, b, and c. Triangle 2 is constructed within triangle 1 by bisecting each side. Triangle 3 is constructed within triangle 2 by bisecting each of triangle 2's sides. And so on. \r\nFind the area of triangle n.","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: 71.9661px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 359.492px 35.9766px; transform-origin: 359.499px 35.9831px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 41.9792px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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: 336.497px 20.9896px; text-align: left; transform-origin: 336.497px 20.9896px; 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=\"\"\u003eGiven triangle 1 with sides of length a, b, and c. Triangle 2 is constructed within triangle 1 by bisecting each side. Triangle 3 is constructed within triangle 2 by bisecting each of triangle 2's sides. And so on. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9896px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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: 336.497px 10.4948px; text-align: left; transform-origin: 336.497px 10.4948px; 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=\"\"\u003eFind the area of triangle n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = your_fcn_name(a,b,c,n)\r\n area = a+b+c+n;\r\nend","test_suite":"%%\r\na=1;b=1;c=sqrt(2);n=1;\r\ny_correct = 0.50;\r\nassert(your_fcn_name(a,b,c,n) - y_correct \u003c y_correct/1000)\r\n\r\n\r\n%%\r\na=100;b=100;c=100;n=2;\r\ny_correct = 1082.53;\r\nassert(your_fcn_name(a,b,c,n) - y_correct \u003c y_correct/1000)\r\n\r\n\r\n%%\r\na=13;b=33;c=44;n=4;\r\ny_correct = 2.0540;\r\nassert(your_fcn_name(a,b,c,n) - y_correct \u003c y_correct/1000)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":3293343,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-30T18:08:43.000Z","updated_at":"2026-03-11T15:33:11.000Z","published_at":"2024-04-30T18:08:43.000Z","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:t\u003eGiven triangle 1 with sides of length a, b, and c. Triangle 2 is constructed within triangle 1 by bisecting each side. Triangle 3 is constructed within triangle 2 by bisecting each of triangle 2's sides. 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\u003eFind the area of triangle n.\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":60980,"title":"Mesh the tetrahedron","description":"Problem statement\r\n\r\nAn tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five well known platonic solids.\r\nA triangulated mesh -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh this tetrahedron. To do so, you will list the triangles/rows in a matrix of triangles, T. You will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles [1, 2, 3] and [3, 2, 1] are distinct).\r\nOn the other hand [1, 2, 3], [2, 3, 1] and [3, 1, 2] are one same unique triangle.\r\nThe row order of the triangles in the list doesn't matter.\r\n \r\nEdit / update\r\nTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\r\n\r\nExample\r\nThe first triangle (X \u003e 0 and Y \u003e 0) here can be [1, 2, 4] if counterclockwise oriented (normals outward).\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","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: 1194.73px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 597.367px; transform-origin: 408px 597.367px; 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: 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: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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; 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: 374.592px 8px; transform-origin: 374.592px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five well known platonic solids.\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.542px 8px; transform-origin: 157.542px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh -or a triangulation- is simply 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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 206.533px 8px; transform-origin: 206.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \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 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: 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: 385px 31.5px; text-align: left; transform-origin: 385px 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: 328.017px 8px; transform-origin: 328.017px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh this tetrahedron. To do so, you will list the triangles/rows in a matrix of triangles, \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: 7.51667px 8px; transform-origin: 7.51667px 8px; 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: 49.4667px 8px; transform-origin: 49.4667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles \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: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3]\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 8px; transform-origin: 15.5583px 8px; 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: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[3, 2, 1]\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: 40.0583px 8px; transform-origin: 40.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are distinct).\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: 58.3417px 8px; transform-origin: 58.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the other hand \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: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3]\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 8px; transform-origin: 3.88333px 8px; 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: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[2, 3, 1]\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 8px; transform-origin: 15.5583px 8px; 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: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[3, 1, 2]\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: 94.5333px 8px; transform-origin: 94.5333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are one same unique triangle.\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: 168.575px 8px; transform-origin: 168.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe row order of the triangles in the list doesn't matter.\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: 13.5917px 8px; transform-origin: 13.5917px 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: 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: 41.9833px 8px; transform-origin: 41.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEdit / update\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: 351.75px 8px; transform-origin: 351.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\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 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: 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: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\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: 52.1167px 8px; transform-origin: 52.1167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle \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: 53.2917px 8px; transform-origin: 53.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(X \u0026gt; 0 and Y \u0026gt; 0)\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: 42.7833px 8px; transform-origin: 42.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e here can 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: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 4]\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: 148.208px 8px; transform-origin: 148.208px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented (normals outward).\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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan 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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: 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 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: 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: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; 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: 392px 40.8667px; transform-origin: 392px 40.8667px; 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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\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; 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 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: 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_tetrahedron()\r\n T = 1;\r\nend","test_suite":"%%\r\nT_correct = [1 2 4;\r\n 2 3 4;\r\n 3 1 4;\r\n 1 3 2];\r\n\r\n% Check every possible solutions\r\nassert(isequal(sortrows(sort(mesh_the_tetrahedron(),2)),sortrows(sort(T_correct,2))))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_tetrahedron.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:43:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":39,"test_suite_updated_at":"2025-07-23T16:17:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T11:03:01.000Z","updated_at":"2026-03-31T18:44:34.000Z","published_at":"2025-07-23T11:11:01.000Z","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\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\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\u003eAn tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five well known platonic solids.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 triangulated mesh -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eYour task here is to mesh this tetrahedron. To do so, you will list the triangles/rows in a matrix of triangles, \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\u003eYou will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 3]\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3, 2, 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are distinct).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the other hand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 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[2, 3, 1]\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3, 1, 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are one same unique triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eEdit / update\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 first triangle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(X \u0026gt; 0 and Y \u0026gt; 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented (normals outward).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"378\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"504\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\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\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\u003eForbidden functions / expressions\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 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Numbers Below N","description":"This is an offshoot of \u003chttp://www.mathworks.com/matlabcentral/cody/problems/5-triangle-numbers Cody Problem 5: Triangle Numbers\u003e.\r\n\r\nTriangle numbers are the sums of successive integers. So 6 is a triangle number because\r\n\r\n 6 = 1 + 2 + 3\r\n\r\nwhich can be displayed in a triangular shape like so\r\n\r\n *\r\n * *\r\n * * * \r\n\r\nReturn all triangle numbers below _N_.","description_html":"\u003cp\u003eThis is an offshoot of \u003ca href=\"http://www.mathworks.com/matlabcentral/cody/problems/5-triangle-numbers\"\u003eCody Problem 5: Triangle Numbers\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eTriangle numbers are the sums of successive integers. So 6 is a triangle number because\u003c/p\u003e\u003cpre\u003e 6 = 1 + 2 + 3\u003c/pre\u003e\u003cp\u003ewhich can be displayed in a triangular shape like so\u003c/p\u003e\u003cpre\u003e *\r\n * *\r\n * * * \u003c/pre\u003e\u003cp\u003eReturn all triangle numbers below \u003ci\u003eN\u003c/i\u003e.\u003c/p\u003e","function_template":"function y = TriBeNum(num)\r\n y = 1:num;\r\nend","test_suite":"%%\r\nx = 100;\r\ny_correct = cumsum(1:13);\r\nassert(isequal(TriBeNum(x),y_correct))\r\n\r\n%%\r\nx = 1000;\r\ny_correct = cumsum(1:44);\r\nassert(isequal(TriBeNum(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":134,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":237,"test_suite_updated_at":"2012-02-08T23:52:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-08T23:52:34.000Z","updated_at":"2026-03-14T18:52:07.000Z","published_at":"2012-02-08T23:54:52.000Z","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 is an offshoot 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.mathworks.com/matlabcentral/cody/problems/5-triangle-numbers\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 5: Triangle Numbers\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\u003eTriangle numbers are the sums of successive integers. So 6 is a triangle number because\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[ 6 = 1 + 2 + 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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhich can be displayed in a triangular shape like so\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[ *\\n * *\\n * * *]]\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\u003eReturn all triangle numbers below\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\u003eN\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\"},{\"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":45259,"title":"Build edges list","description":"Input T is a triangulation connectivity indices list (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\r\nThe purpose of this function is to query the list E of all the edges.\r\nFor instance if T = [1, 2, 3; 4, 5, 6; 7, 8, 9], then the output of the function must be E = [1, 2; 1, 3; 2, 3; 4, 5; 4, 6; 5, 6; 7, 8; 7, 9; 8, 9] (all the 3 possible combination of the 3 vertices of a triangle / row, for every triangle / row of the list).\r\nHypothesis on output E :\r\nsize(E) = [N, 2], with N the number of edges\r\nE doesn't need to be ordered neither following dimension 1 (rows) nor dimension 2 (columns), but must not contain duplicated edges\r\nEdges are symmetric : [e1, e2] is the same edge as [e2, e1]\r\nEvery indices are positive, distinct integers.\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","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: 366.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 183.083px; transform-origin: 408px 183.083px; 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: 367.967px 8px; transform-origin: 367.967px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInput T is a triangulation connectivity indices list (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\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: 200.692px 8px; transform-origin: 200.692px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe purpose of this function is to query the list E of all the edges.\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384.55px 8px; transform-origin: 384.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor instance if T = [1, 2, 3; 4, 5, 6; 7, 8, 9], then the output of the function must be E = [1, 2; 1, 3; 2, 3; 4, 5; 4, 6; 5, 6; 7, 8; 7, 9; 8, 9] (all the 3 possible combination of the 3 vertices of a triangle / row, for every triangle / row of the list).\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: 82.8083px 8px; transform-origin: 82.8083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHypothesis on output E :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.167px; 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: 392px 51.0833px; transform-origin: 392px 51.0833px; 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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 135.933px 8px; transform-origin: 135.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esize(E) = [N, 2], with N the number of edges\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; 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: 364px 20.4333px; text-align: left; transform-origin: 364px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 318.758px 8px; transform-origin: 318.758px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eE doesn't need to be ordered neither following dimension 1 (rows) nor dimension 2 (columns), but must\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\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: 39.65px 8px; transform-origin: 39.65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003enot contain duplicated edges\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 194.858px 8px; transform-origin: 194.858px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEdges are symmetric : [e1, e2] is the same edge as [e2, e1]\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 133.808px 8px; transform-origin: 133.808px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEvery indices are positive, distinct integers.\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; 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function E = query_edges_list(T)\r\n E = T;\r\nend","test_suite":"%% Description example\r\nT = [1, 2, 3;...\r\n 4, 5, 6;...\r\n 7, 8, 9];\r\n \r\nE = [1, 2;...\r\n 1, 3;...\r\n 2, 3;...\r\n 4, 5;...\r\n 4, 6;...\r\n 5, 6;...\r\n 7, 8;...\r\n 7, 9;...\r\n 8, 9];\r\n\r\nassert(isequal(sortrows(sort(query_edges_list(T),2)),E))\r\n\r\n%% Another test\r\nT = [2, 3, 5;...\r\n 7, 11, 13;...\r\n 17, 19, 23];\r\n \r\nE = [2, 3;...\r\n 2, 5;...\r\n 3, 5;...\r\n 7, 11;...\r\n 7, 13;...\r\n 11, 13;...\r\n 17, 19;...\r\n 17, 23;...\r\n 19, 23];\r\n\r\nassert(isequal(sortrows(sort(query_edges_list(T),2)),E))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('query_edges_list.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:49:28.000Z","deleted_by":null,"deleted_at":null,"solvers_count":40,"test_suite_updated_at":"2025-07-09T05:51:51.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-08T15:52:04.000Z","updated_at":"2025-12-07T21:53:51.000Z","published_at":"2020-01-08T17:13:08.000Z","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\u003eInput T is a triangulation connectivity indices list (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 purpose of this function is to query the list E of all the edges.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 instance if T = [1, 2, 3; 4, 5, 6; 7, 8, 9], then the output of the function must be E = [1, 2; 1, 3; 2, 3; 4, 5; 4, 6; 5, 6; 7, 8; 7, 9; 8, 9] (all the 3 possible combination of the 3 vertices of a triangle / row, for every triangle / row of the list).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\u003eHypothesis on output E :\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\u003esize(E) = [N, 2], with N the number of edges\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\u003eE doesn't need to be ordered neither following dimension 1 (rows) nor dimension 2 (columns), but must\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\u003enot contain duplicated edges\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEdges are symmetric : [e1, e2] is the same edge as [e2, e1]\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\u003eEvery indices are positive, distinct integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\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:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\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":60984,"title":"Mesh the icosahedron","description":"Problem statement\r\n\r\nAn icosahedron is a regular polyhedron with 12 vertices and 20 triangular faces. It is also one of the five well known platonic solids. \r\nA triangulation, or triangulated mesh, is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh this icosahedron. To do so, you will list the triangles/rows in a matrix of triangles, T.\r\nThe row order of the triangles in the list doesn't matter.\r\n\r\nTip\r\nVertex indices are written on the figure below; use it to help you visualize;\r\nYou can start with the triangles of the top cap and bottom cap, they are the easiest ones to identify here.\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","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: 996.1px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 498.05px; transform-origin: 408px 498.05px; 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: 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: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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; 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: 384.717px 8px; transform-origin: 384.717px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn icosahedron is a regular polyhedron with 12 vertices and 20 triangular faces. It is also one of the five well known platonic solids. \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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 150.925px 8px; transform-origin: 150.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulation, or triangulated mesh, is simply 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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 229.017px 8px; transform-origin: 229.017px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \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 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: 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: 334.633px 8px; transform-origin: 334.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh this icosahedron. To do so, you will list the triangles/rows in a matrix of triangles, T\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: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 168.575px 8px; transform-origin: 168.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe row order of the triangles in the list doesn't matter.\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 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: 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: 10.3667px 8px; transform-origin: 10.3667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTip\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; 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: 392px 20.4333px; transform-origin: 392px 20.4333px; 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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 226.783px 8px; transform-origin: 226.783px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eVertex indices are written on the figure below; use it to help you visualize;\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 321.4px 8px; transform-origin: 321.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou can start with the triangles of the top cap and bottom cap, they are the easiest ones to identify here.\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; 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 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: 339.5px; font-family: Helvetica, Arial, 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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: 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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; 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: 392px 40.8667px; transform-origin: 392px 40.8667px; 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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\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; 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_icosahedron()\r\n T = 1;\r\nend","test_suite":"%%\r\nT_correct = [1 2 3;\r\n 1 3 4;\r\n 1 4 5;\r\n 1 5 6;\r\n 1 6 2; \r\n 8 7 9;\r\n 7 10 9;\r\n 7 11 10;\r\n 7 12 11;\r\n 7 8 12; \r\n 2 11 3;\r\n 3 11 12\r\n 3 12 4;\r\n 4 12 8;\r\n 4 8 5;\r\n 5 8 9;\r\n 5 9 6;\r\n 6 9 10;\r\n 2 6 10;\r\n 2 10 11];\r\n\r\n% Check every possible solutions\r\nassert(isequal(sortrows(sort(mesh_the_icosahedron(),2)),sortrows(sort(T_correct,2))))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_icosahedron.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:46:02.000Z","deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T20:09:09.000Z","updated_at":"2026-02-13T17:44:47.000Z","published_at":"2025-07-24T14:11:48.000Z","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\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\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\u003eAn icosahedron is a regular polyhedron with 12 vertices and 20 triangular faces. It is also one of the five well known platonic solids. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 triangulation, or triangulated mesh, is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eYour task here is to mesh this icosahedron. To do so, you will list the triangles/rows in a matrix of triangles, T\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\u003c/w:p\u003e\u003cw:p\u003e\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 row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eTip\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\u003eVertex indices are written on the figure below; use it to help you visualize;\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\u003eYou can start with the triangles of the top cap and bottom cap, they are the easiest ones to identify here.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"334\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"446\\\"/\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\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\u003eForbidden functions / expressions\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\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 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and wrong","description":"Given a vector of lengths [a b c], determines whether a triangle with those sides lengths is a right triangle: \u003chttp://en.wikipedia.org/wiki/Right_triangle\u003e.\r\n\r\nExamples:\r\n\r\n[3 4 5] ---\u003e true\r\n\r\n[5 12 13] ---\u003e true\r\n\r\n[5 5 5] ---\u003e false","description_html":"\u003cp\u003eGiven a vector of lengths [a b c], determines whether a triangle with those sides lengths is a right triangle: \u003ca href=\"http://en.wikipedia.org/wiki/Right_triangle\"\u003ehttp://en.wikipedia.org/wiki/Right_triangle\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cp\u003e[3 4 5] ---\u003e true\u003c/p\u003e\u003cp\u003e[5 12 13] ---\u003e true\u003c/p\u003e\u003cp\u003e[5 5 5] ---\u003e false\u003c/p\u003e","function_template":"function y = right(sides)\r\n y = sides;\r\nend","test_suite":"%%\r\nsides = [3 4 5];\r\ntf_correct = true;\r\nassert(isequal(right(sides),tf_correct))\r\n%%\r\nsides = [3 5 4];\r\ntf_correct = true;\r\nassert(isequal(right(sides),tf_correct))\r\n%%\r\nsides = [5 12 13];\r\ntf_correct = true;\r\nassert(isequal(right(sides),tf_correct))\r\n%%\r\nsides = [5 5 5];\r\ntf_correct = false;\r\nassert(isequal(right(sides),tf_correct))\r\n%%\r\nsides = [113 112 15];\r\ntf_correct = true;\r\nassert(isequal(right(sides),tf_correct))\r\n%%\r\nsides = [113 110 15];\r\ntf_correct = false;\r\nassert(isequal(right(sides),tf_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":11,"comments_count":3,"created_by":39,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1440,"test_suite_updated_at":"2013-05-25T12:43:14.000Z","rescore_all_solutions":false,"group_id":17,"created_at":"2012-01-29T15:17:31.000Z","updated_at":"2026-02-27T10:50:39.000Z","published_at":"2012-02-17T20:59:33.000Z","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 vector of lengths [a b c], determines whether a triangle with those sides lengths is a right triangle:\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/Right_triangle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://en.wikipedia.org/wiki/Right_triangle\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\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[3 4 5] ---\u0026gt; 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\u003e[5 12 13] ---\u0026gt; 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\u003e[5 5 5] ---\u0026gt; false\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":45230,"title":"Remove duplicated triangles","description":"Input T is a triangulation (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\r\nIt sometimes happens a triangle may be duplicated several times. The goal of this problem is to remove all the duplicated triangles of T, and to keep only one.\r\nFor instance if :\r\nT_in = [1 2 3;...\r\n 4 5 6;...\r\n 1 2 3;...\r\n 7 8 9;...\r\n 6 4 5;...\r\n 10 11 12;...\r\n 2 1 3;...\r\n 8 7 9;...\r\n 10 11 12]\r\nthen the output must be :\r\nT_out = [1 2 3;...\r\n 4 5 6;...\r\n 7 8 9;...\r\n 10 11 12]\r\nsince rows [1 2 3], [6 4 5], [2 1 3], [8 7 9], and [10 11 12] are just duplicata. Indeed triangle [i2 i1 i3] is the same as triangle [i1 i2 i3] for example.\r\nHypothesis :\r\nT is always a N x 3 integer matrix with N \u003e 0 (non empty matrix)\r\nEach row / triangle of T always contains three distinct integers\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","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: 673.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 336.75px; transform-origin: 408px 336.75px; 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: 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: 380.425px 8px; transform-origin: 380.425px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInput T is a triangulation (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.533px 8px; transform-origin: 376.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIt sometimes happens a triangle may be duplicated several times. The goal of this problem is to remove all the duplicated triangles of T, and to keep only one.\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: 47.8333px 8px; transform-origin: 47.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor instance if :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 183.9px; 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: 405px 91.95px; transform-origin: 405px 91.95px; 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 53.9px 8.5px; transform-origin: 53.9px 8.5px; \"\u003eT_in = [1 2 3;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 53.9px 8.5px; transform-origin: 53.9px 8.5px; \"\u003e 4 5 6;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 53.9px 8.5px; transform-origin: 53.9px 8.5px; \"\u003e 1 2 3;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 53.9px 8.5px; transform-origin: 53.9px 8.5px; \"\u003e 7 8 9;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 53.9px 8.5px; transform-origin: 53.9px 8.5px; \"\u003e 6 4 5;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 77px 8.5px; tab-size: 4; transform-origin: 77px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 65.45px 8.5px; transform-origin: 65.45px 8.5px; \"\u003e 10 11 12;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 53.9px 8.5px; transform-origin: 53.9px 8.5px; \"\u003e 2 1 3;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 53.9px 8.5px; transform-origin: 53.9px 8.5px; \"\u003e 8 7 9;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 10 11 12]\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 77.3917px 8px; transform-origin: 77.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen the output must be :\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: 405px 40.8667px; transform-origin: 405px 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 69.3px 8.5px; tab-size: 4; transform-origin: 69.3px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 57.75px 8.5px; transform-origin: 57.75px 8.5px; \"\u003eT_out = [1 2 3;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 69.3px 8.5px; tab-size: 4; transform-origin: 69.3px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 57.75px 8.5px; transform-origin: 57.75px 8.5px; \"\u003e 4 5 6;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 69.3px 8.5px; tab-size: 4; transform-origin: 69.3px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 57.75px 8.5px; transform-origin: 57.75px 8.5px; \"\u003e 7 8 9;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 69.3px 8.5px; tab-size: 4; transform-origin: 69.3px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 10 11 12]\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; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; 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: 385px 8px; transform-origin: 385px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince rows [1 2 3], [6 4 5], [2 1 3], [8 7 9], and [10 11 12] are just duplicata. Indeed triangle [i2 i1 i3] is the same as triangle [i1 i2 i3] for example.\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: 38.5083px 8px; transform-origin: 38.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHypothesis :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; 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: 392px 20.4333px; transform-origin: 392px 20.4333px; 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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 209.408px 8px; transform-origin: 209.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eT is always a N x 3 integer matrix with N \u0026gt; 0 (non empty matrix)\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 191.758px 8px; transform-origin: 191.758px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach row / triangle of T always contains three distinct integers\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; 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T_out = remove_duplicated_triangles(T_in)\r\n T_out = T_in;\r\nend","test_suite":"%% Intro example\r\nT_in = [1 2 3;...\r\n 4 5 6;...\r\n 1 2 3;...\r\n 7 8 9;...\r\n 6 4 5;...\r\n 10 11 12;...\r\n 2 1 3;...\r\n 8 7 9;...\r\n 10 11 12];\r\n \r\nT_out = [1 2 3;...\r\n 4 5 6;...\r\n 7 8 9;...\r\n 10 11 12];\r\n\r\nassert(isequal(remove_duplicated_triangles(T_in),T_out))\r\n\r\n%% Single triangle\r\nT_in = [3 5 7];\r\nT_out = T_in;\r\nassert(isequal(remove_duplicated_triangles(T_in),T_out))\r\n\r\n%% One duplicated triangle\r\nT_in = [2 11 13;...\r\n 2 13 11;...\r\n 11 2 13;...\r\n 11 13 2;...\r\n 13 2 11;...\r\n 13 11 2];\r\n\r\nT_out = [2 11 13];\r\nassert(isequal(remove_duplicated_triangles(T_in),T_out))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('remove_duplicated_triangles.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:50:13.000Z","deleted_by":null,"deleted_at":null,"solvers_count":50,"test_suite_updated_at":"2025-07-09T05:52:22.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-12-11T10:22:14.000Z","updated_at":"2025-11-16T17:58:55.000Z","published_at":"2019-12-11T10:37:52.000Z","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\u003eInput T is a triangulation (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 sometimes happens a triangle may be duplicated several times. The goal of this problem is to remove all the duplicated triangles of T, and to keep only one.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 instance 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[T_in = [1 2 3;...\\n 4 5 6;...\\n 1 2 3;...\\n 7 8 9;...\\n 6 4 5;...\\n 10 11 12;...\\n 2 1 3;...\\n 8 7 9;...\\n 10 11 12]]]\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\u003ethen the output must be :\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[T_out = [1 2 3;...\\n 4 5 6;...\\n 7 8 9;...\\n 10 11 12]]]\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 rows [1 2 3], [6 4 5], [2 1 3], [8 7 9], and [10 11 12] are just duplicata. Indeed triangle [i2 i1 i3] is the same as triangle [i1 i2 i3] for 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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHypothesis :\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT is always a N x 3 integer matrix with N \u0026gt; 0 (non empty matrix)\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\u003eEach row / triangle of T always contains three distinct integers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\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:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\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":61076,"title":"Covering rectangle area of a four-pointed star polygon","description":"Given the four-pointed star polygon formed by the rectangle, with dimensions l1xl2, and four triangles, with height, h, from their bases to the apices, find the rectangle, with dimensions y1xy2, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). Given x=[l1 l2 h], return y=[y1 y2].\r\n\r\n","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: 520.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 260.4px; transform-origin: 408px 260.4px; 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: 385px 31.5px; text-align: left; transform-origin: 385px 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=\"\"\u003eGiven the four-pointed star polygon formed by the rectangle, with dimensions \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; \"\u003el1xl2\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, and four triangles, with height, \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; \"\u003eh,\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 from their bases to the apices, find the rectangle, with dimensions \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; \"\u003ey1xy2\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, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). Given \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; \"\u003ex=[l1 l2 h]\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, return \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; \"\u003ey=[y1 y2]\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: 418.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 209.4px; text-align: left; transform-origin: 385px 209.4px; white-space-collapse: preserve; 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: 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=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = covering(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = [2 7 4];\r\ny_correct = [5 10];\r\nassert(isequal(covering(x),y_correct))\r\n\r\n%%\r\nx = [7 2 1];\r\ny_correct = [2.5 -2.5] + 1.5*sqrt(13);\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nx = [5 2 1];\r\ny_correct = [3 -3]/2 + sqrt(77)/2;\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nfiletext = fileread('covering.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = [7 9 5];\r\ny_correct = [11 13];\r\nassert(isequal(covering(x),y_correct))\r\n\r\n%%\r\nx = [7 9 1];\r\ny_correct = [-1 1] + 4*sqrt(5);\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-16T14:03:25.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-15T16:57:30.000Z","updated_at":"2026-03-27T12:50:09.000Z","published_at":"2025-11-16T14:03:25.000Z","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\u003eGiven the four-pointed star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1xl2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the apices, find the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey1xy2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). Given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex=[l1 l2 h]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey=[y1 y2]\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"413\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"508\\\"/\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 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the hypotenuse of a right triangle without using ^ and sqrt ()","description":"Find out the hypotenuse of right triangle.\r\n\r\n\r\nSay a = 4, b = 3 then c = 5 \r\n\r\n\r\nPlease don't use ^ and sqrt() function. ","description_html":"\u003cp\u003eFind out the hypotenuse of right triangle.\u003c/p\u003e\u003cp\u003eSay a = 4, b = 3 then c = 5\u003c/p\u003e\u003cp\u003ePlease don't use ^ and sqrt() function.\u003c/p\u003e","function_template":"function y = hypotenuse(a,b)\r\n y = sqrt(a^2+b^2)\r\nend","test_suite":"%%\r\na = 3;\r\nb= 4;\r\ny_correct = 5;\r\nassert(abs(hypotenuse(a,b)-y_correct)\u003c0.0001)\r\n\r\n%%\r\na = 2;\r\nb = pi * 2;\r\ny_correct = sqrt(a^2+b^2);\r\nassert(abs(hypotenuse(a,b)-y_correct)\u003c0.0001)\r\n\r\n%%\r\na = randi(10);\r\nb = randi(13);\r\ny_correct = sqrt(a^2+b^2);\r\nassert(abs(hypotenuse(a,b)-y_correct)\u003c0.0001)\r\n\r\n%%\r\nuser_solution = fileread('hypotenuse.m');\r\nassert(isempty(strfind(user_solution,'^')));\r\n\r\n%%\r\nassessFunctionAbsence({'sqrt'}, 'FileName', 'hypotenuse.m');\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":14644,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":104,"test_suite_updated_at":"2016-11-30T19:36:02.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-16T08:20:00.000Z","updated_at":"2026-04-03T02:50:47.000Z","published_at":"2016-10-16T08:20:07.000Z","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\u003eFind out the hypotenuse of right triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSay a = 4, b = 3 then c = 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\u003ePlease don't use ^ and sqrt() function.\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":43601,"title":"Find the sines of an isosceles triangle when given its area and height","description":"Find the sines of an isosceles triangle when given its area and height.\r\nFor example, when A=12 and h=4, the result is [0.8 0.8 0.96].","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: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; 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: 219.5px 8px; transform-origin: 219.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the sines of an isosceles triangle when given its area and height.\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: 192.5px 8px; transform-origin: 192.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, when A=12 and h=4, the result is [0.8 0.8 0.96].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = theSineOfAnglesOfATriangle(A,h)\r\n y = x;\r\nend","test_suite":"%%\r\nA = 12;\r\nh = 4;\r\ny_correct = [0.8, 0.8, 0.96];\r\ny = theSineOfAnglesOfATriangle(A,h);\r\ntolerance = 1e-4;\r\nassert(abs(y(1)-y_correct(1))\u003ctolerance)\r\nassert(abs(y(2)-y_correct(2))\u003ctolerance)\r\nassert(abs(y(3)-y_correct(3))\u003ctolerance)\r\n\r\n%%\r\nA = 48;\r\nh = 8;\r\ny_correct = [0.8, 0.8, 0.96];\r\ny = theSineOfAnglesOfATriangle(A,h);\r\ntolerance = 1e-4;\r\nassert(abs(y(1)-y_correct(1))\u003ctolerance)\r\nassert(abs(y(2)-y_correct(2))\u003ctolerance)\r\nassert(abs(y(3)-y_correct(3))\u003ctolerance)\r\n\r\n%%\r\nA = 40;\r\nh = 10;\r\ny_correct = [0.9285, 0.9285, 0.6897];\r\ny = theSineOfAnglesOfATriangle(A,h);\r\ntolerance = 1e-4;\r\nassert(abs(y(1)-y_correct(1))\u003ctolerance)\r\nassert(abs(y(2)-y_correct(2))\u003ctolerance)\r\nassert(abs(y(3)-y_correct(3))\u003ctolerance)\r\n\r\n%%\r\nA = 11;\r\nh = 7;\r\ny_correct = [0.9757, 0.9757, 0.4274];\r\ny = theSineOfAnglesOfATriangle(A,h);\r\ntolerance = 1e-4;\r\nassert(abs(y(1)-y_correct(1))\u003ctolerance)\r\nassert(abs(y(2)-y_correct(2))\u003ctolerance)\r\nassert(abs(y(3)-y_correct(3))\u003ctolerance)\r\n\r\n%%\r\nA = 10;\r\nh = 7;\r\ny_correct = [0.9798, 0.9798, 0.3918];\r\ny = theSineOfAnglesOfATriangle(A,h);\r\ntolerance = 1e-4;\r\nassert(abs(y(1)-y_correct(1))\u003ctolerance)\r\nassert(abs(y(2)-y_correct(2))\u003ctolerance)\r\nassert(abs(y(3)-y_correct(3))\u003ctolerance)\r\n\r\n%%\r\nA = 100;\r\nh = 90;\r\ny_correct = [0.9999, 0.9999, 0.0247];\r\ny = theSineOfAnglesOfATriangle(A,h);\r\ntolerance = 1e-4;\r\nassert(abs(y(1)-y_correct(1))\u003ctolerance)\r\nassert(abs(y(2)-y_correct(2))\u003ctolerance)\r\nassert(abs(y(3)-y_correct(3))\u003ctolerance)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":15,"created_by":90467,"edited_by":223089,"edited_at":"2023-02-04T06:18:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":57,"test_suite_updated_at":"2023-02-04T06:18:22.000Z","rescore_all_solutions":false,"group_id":37,"created_at":"2016-10-23T10:38:22.000Z","updated_at":"2026-02-08T11:35:41.000Z","published_at":"2016-10-23T10:38:22.000Z","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\u003eFind the sines of an isosceles triangle when given its area and height.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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, when A=12 and h=4, the result is [0.8 0.8 0.96].\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":60978,"title":"Mesh the octahedron","description":"Problem statement\r\n\r\nAn octahedron is a regular polyhedron with 6 vertices and 8 triangular faces. It is also one of the five well known platonic solids.\r\nA triangulated mesh -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh this octahedron. To do so, you will list the triangles/rows in a matrix of triangles, T. You will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles [1, 2, 3] and [3, 2, 1] are distinct).\r\nOn the other hand [1, 2, 3], [2, 3, 1] and [3, 1, 2] are one same unique triangle.\r\nThe row order of the triangles in the list doesn't matter.\r\n\r\nEdit / update\r\nTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\r\n\r\nExample\r\nThe first triangle (X \u003e 0, Y \u003e 0, and Z \u003e 0) here can be [1, 2, 5] if counterclockwise oriented (normals are outward oriented).\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","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: 1200.23px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 600.117px; transform-origin: 408px 600.117px; 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: 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: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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; 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: 373.817px 8px; transform-origin: 373.817px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn octahedron is a regular polyhedron with 6 vertices and 8 triangular faces. It is also one of the five well known platonic solids.\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.542px 8px; transform-origin: 157.542px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh -or a triangulation- is simply 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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 206.533px 8px; transform-origin: 206.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \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 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: 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: 385px 31.5px; text-align: left; transform-origin: 385px 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: 327.242px 8px; transform-origin: 327.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh this octahedron. To do so, you will list the triangles/rows in a matrix of triangles, \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: 7.51667px 8px; transform-origin: 7.51667px 8px; 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: 49.9333px 8px; transform-origin: 49.9333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles \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: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3]\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 8px; transform-origin: 15.5583px 8px; 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: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[3, 2, 1]\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: 40.0583px 8px; transform-origin: 40.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are distinct).\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: 58.3417px 8px; transform-origin: 58.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the other hand \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: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3]\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 8px; transform-origin: 3.88333px 8px; 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: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[2, 3, 1]\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 8px; transform-origin: 15.5583px 8px; 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: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[3, 1, 2]\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: 94.5333px 8px; transform-origin: 94.5333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are one same unique triangle.\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: 168.575px 8px; transform-origin: 168.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe row order of the triangles in the list doesn't matter.\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 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: 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: 41.9833px 8px; transform-origin: 41.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEdit / update\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: 351.75px 8px; transform-origin: 351.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\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 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: 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: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\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: 52.1167px 8px; transform-origin: 52.1167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle \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: 75.2583px 8px; transform-origin: 75.2583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(X \u0026gt; 0, Y \u0026gt; 0, and Z \u0026gt; 0)\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: 42.7833px 8px; transform-origin: 42.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e here can 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: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 5]\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: 187.5px 8px; transform-origin: 187.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented (normals are outward oriented).\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 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: 383.5px; 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: 385px 191.75px; text-align: left; transform-origin: 385px 191.75px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"504\" height=\"378\" style=\"vertical-align: baseline;width: 504px;height: 378px\" 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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: 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 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: 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: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; 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: 392px 40.8667px; transform-origin: 392px 40.8667px; 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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\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; 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 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: 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_octahedron()\r\n T = 1;\r\nend","test_suite":"%%\r\nT_correct = [1 2 5;\r\n 2 3 5;\r\n 3 4 5;\r\n 4 1 5;\r\n 2 1 6;\r\n 3 2 6;\r\n 4 3 6;\r\n 1 4 6];\r\n\r\n% Check every possible solutions\r\nassert(isequal(sortrows(sort(mesh_the_octahedron(),2)),sortrows(sort(T_correct,2))))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_octahedron.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:44:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":50,"test_suite_updated_at":"2025-07-23T16:11:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T08:24:47.000Z","updated_at":"2026-03-31T18:40:36.000Z","published_at":"2025-07-23T09:23:40.000Z","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\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\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\u003eAn octahedron is a regular polyhedron with 6 vertices and 8 triangular faces. It is also one of the five well known platonic solids.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 triangulated mesh -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eYour task here is to mesh this octahedron. To do so, you will list the triangles/rows in a matrix of triangles, \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\u003eYou will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 3]\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3, 2, 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are distinct).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the other hand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 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[2, 3, 1]\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3, 1, 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are one same unique triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eEdit / update\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 first triangle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(X \u0026gt; 0, Y \u0026gt; 0, and Z \u0026gt; 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented (normals are outward oriented).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"378\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"504\\\"/\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\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 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neighbor triangle indices","description":"First input T is a triangulation (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\r\nGiven a second input t (a certain triangle row index), one would like to query the list L of all its triangle neighbor indices. A triangle is neighbor to another triangle if they share exactly one edge.\r\nFor instance if\r\nT = [1 2 4;...\r\n 2 3 4;...\r\n 5 6 8;...\r\n 6 7 8;...\r\n 1 2 5;...\r\n 2 5 6;...\r\n 2 3 6;...\r\n 3 6 7;...\r\n 3 4 7;...\r\n 4 7 8;...\r\n 4 1 8;...\r\n 1 8 5]\r\nand t = 3, then the function should return\r\nL = [4, 6, 12]'\r\nsince rows / (triangles of T) 4, 6, and 12 contain an edge in common with triangle / row 3.edge [6 8] for the first, edge [5 6] for the second, and edge [8 5] for the third.\r\nHypothesis :\r\n- Since a triangle is not considered neighbor of itself, t should not be part of L.\r\n- Order doesn't matter, but T must be a column vector containing all the neighbor triangle -row- indices (except itself then) once only. No duplicata is admitted.\r\n- Edges are symmetric : [e1, e2] is the same edge as [e2, e1]\r\n- Every indices are positive, distinct integers.\r\n\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","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: 782.633px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 391.317px; transform-origin: 408px 391.317px; 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: 349.292px 8px; transform-origin: 349.292px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFirst input T is a triangulation (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.767px 8px; transform-origin: 368.767px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a second input t (a certain triangle row index), one would like to query the list L of all its triangle neighbor indices.\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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 7px 8px; transform-origin: 7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eA triangle is neighbor to another triangle if they share exactly one edge.\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: 43.95px 8px; transform-origin: 43.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor instance if\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 245.2px; 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: 405px 122.6px; transform-origin: 405px 122.6px; 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003eT = [1 2 4;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 2 3 4;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 5 6 8;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 6 7 8;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 1 2 5;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 2 5 6;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 2 3 6;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 3 6 7;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 3 4 7;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 4 7 8;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 4 1 8;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 42.35px 8.5px; tab-size: 4; transform-origin: 42.35px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 8 5]\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 125.833px 8px; transform-origin: 125.833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand t = 3, then the function should return\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; 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: 405px 10.2167px; transform-origin: 405px 10.2167px; 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; text-wrap-mode: 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: 57.75px 8.5px; tab-size: 4; transform-origin: 57.75px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eL = [4, 6, 12]'\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; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; 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: 378.042px 8px; transform-origin: 378.042px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince rows / (triangles of T) 4, 6, and 12 contain an edge in common with triangle / row 3.edge [6 8] for the first, edge [5 6] for the second, and edge [8 5] for the third.\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: 38.5083px 8px; transform-origin: 38.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHypothesis :\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: 162.6px 8px; transform-origin: 162.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e- Since a triangle is not considered neighbor of itself,\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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 82.0167px 8px; transform-origin: 82.0167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003et should not be part of L.\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.4417px 8px; transform-origin: 81.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e- Order doesn't matter, but\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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 180.008px 8px; transform-origin: 180.008px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eT must be a column vector containing all the neighbor\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: 109.692px 8px; transform-origin: 109.692px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e triangle -row- indices (except itself then) once only.\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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 82.8167px 8px; transform-origin: 82.8167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNo duplicata is admitted.\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: 2.33333px 8px; transform-origin: 2.33333px 8px; 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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 194.858px 8px; transform-origin: 194.858px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEdges are symmetric : [e1, e2] is the same edge as [e2, e1]\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: 138.083px 8px; transform-origin: 138.083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e- Every indices are positive, distinct integers.\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 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: 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function L = find_neighbor_triangles_indices(T,t);\r\n L = t;\r\nend","test_suite":"%% Tetrahedron, all triangles have all the other 3 neighbor triangles \r\nT = [1, 2, 3;...\r\n 1, 3, 4;...\r\n 1, 2, 4;...\r\n 2, 3, 4];\r\n \r\nt = 2;\r\n\r\nL = [1, 3, 4]';\r\nassert(isequal(sort(find_neighbor_triangles_indices(T,t)),L))\r\n\r\n%% Triangulated cube (same as problem description)\r\nT = [1, 2, 4;...\r\n 2, 3, 4;...\r\n 5, 6, 8;...\r\n 6, 7, 8;...\r\n 1, 2, 5;...\r\n 2, 5, 6;...\r\n 2, 3, 6;...\r\n 3, 6, 7;...\r\n 3, 4, 7;...\r\n 4, 7, 8;...\r\n 1, 4, 8;...\r\n 1, 5, 8];\r\n \r\nt = 3;\r\n\r\nL = [4, 6, 12]';\r\nassert(isequal(sort(find_neighbor_triangles_indices(T,t)),L))\r\n\r\n%% Filled octahedron (two pyramids stuck together via their square bases)\r\nT = [1, 2, 3;...\r\n 1, 3, 4;...\r\n 1, 4, 5;...\r\n 1, 2, 5;...\r\n 2, 3, 6;...\r\n 3, 4, 6;...\r\n 4, 5, 6;...\r\n 2, 5, 6;...\r\n 2, 3, 4;...\r\n 2, 4, 5;...\r\n 1, 2, 4;...\r\n 2, 4, 6];\r\n\r\nt = 6;\r\n\r\nL = [2, 5, 7, 9, 12]';\r\nassert(isequal(sort(find_neighbor_triangles_indices(T,t)),L))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('find_neighbor_triangles_indices.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:49:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":"2025-07-09T05:52:10.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-07T12:33:20.000Z","updated_at":"2025-11-16T17:50:56.000Z","published_at":"2020-01-07T13:06:47.000Z","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\u003eFirst input T is a triangulation (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 second input t (a certain triangle row index), one would like to query the list L of all its triangle neighbor indices.\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\u003eA triangle is neighbor to another triangle if they share exactly one edge.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 instance 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[T = [1 2 4;...\\n 2 3 4;...\\n 5 6 8;...\\n 6 7 8;...\\n 1 2 5;...\\n 2 5 6;...\\n 2 3 6;...\\n 3 6 7;...\\n 3 4 7;...\\n 4 7 8;...\\n 4 1 8;...\\n 1 8 5]]]\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\u003eand t = 3, then the function should return\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[L = [4, 6, 12]']]\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 rows / (triangles of T) 4, 6, and 12 contain an edge in common with triangle / row 3.edge [6 8] for the first, edge [5 6] for the second, and edge [8 5] for the third.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHypothesis :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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- Since a triangle is not considered neighbor of itself,\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\u003et should not be part of L.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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- Order doesn't matter, but\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\u003eT must be a column vector containing all the neighbor\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e triangle -row- indices (except itself then) once 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\u003eNo duplicata is admitted.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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: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\u003eEdges are symmetric : [e1, e2] is the same edge as [e2, e1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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- Every indices are positive, distinct integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\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:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\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":60986,"title":"Mesh the convex hull of a random 3D point cloud","description":"Problem statement\r\n\r\nThe convex hull of a 3D point set is actually a first -though rough- triangulation of it.\r\nA triangulation, or triangulated mesh, is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\nUse Matlab functions to compute the convex hull of the random point clouds given in the tests here below.\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","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: 795.233px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 397.617px; transform-origin: 408px 397.617px; 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: 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: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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: 256.717px 8px; transform-origin: 256.717px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe convex hull of a 3D point set is actually a first -though rough- triangulation of 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; 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: 150.925px 8px; transform-origin: 150.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulation, or triangulated mesh, is simply 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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 229.017px 8px; transform-origin: 229.017px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \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: 327.125px 8px; transform-origin: 327.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUse Matlab functions to compute the convex hull of the random point clouds given in the tests here below.\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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 341.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; 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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: 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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; 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: 392px 40.8667px; transform-origin: 392px 40.8667px; 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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\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; 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_convex_hull(V)\r\n T = V;\r\nend","test_suite":"%% Point set #1\r\nV = [0.7253 -0.3789 0.5520\r\n 0.4471 -0.3044 0.8245\r\n 0.8241 0.6916 0.2092\r\n -0.7553 -0.5126 0.2692\r\n -0.2179 -0.8765 -0.3024\r\n -0.0984 0.3260 0.8808\r\n -0.9354 -0.0462 0.2274\r\n 0.2122 -0.6391 0.6226\r\n -0.0248 -0.1993 -0.8833\r\n 0.0772 0.9644 -0.2436\r\n -0.1098 -0.0333 -0.9851\r\n -0.6662 0.0466 0.7499\r\n -0.6866 0.5290 -0.5468\r\n 0.0357 0.0086 -0.9728\r\n 0.0829 -0.2777 -1.0373\r\n -0.3445 0.5795 0.6257];\r\n\r\nT_correct = [1 2 8;\r\n 1 3 2;\r\n 1 5 15;\r\n 1 8 5;\r\n 1 15 3;\r\n 2 3 6;\r\n 2 6 12;\r\n 2 12 8;\r\n 3 10 16;\r\n 3 14 10;\r\n 3 15 14;\r\n 3 16 6;\r\n 4 5 8;\r\n 4 7 13;\r\n 4 8 12;\r\n 4 12 7;\r\n 4 13 5;\r\n 5 11 15;\r\n 5 13 11;\r\n 6 16 12;\r\n 7 12 16;\r\n 7 16 13;\r\n 10 13 16;\r\n 10 14 13;\r\n 11 13 14;\r\n 11 14 15];\r\n\r\nassert(isequal(mesh_the_convex_hull(V),T_correct))\r\n\r\n\r\n%% Point set #2\r\nV = [-0.0775 -0.4239 0.9421;\r\n -0.8154 0.0299 -0.4279;\r\n 0.6777 -0.4686 -0.6602;\r\n -0.2960 -0.8871 0.5367;\r\n -0.0034 -0.0899 0.9352;\r\n 0.8245 -0.5624 0.0630;\r\n 0.6048 -0.7364 -0.3692;\r\n 0.4215 0.9403 -0.2533;\r\n 0.3255 0.0593 -0.8884;\r\n 0.4979 -0.0671 0.8623;\r\n -1.0254 0.1883 -0.0015;\r\n 0.7398 0.2020 -0.4934;\r\n 0.7488 0.5209 -0.0621;\r\n -0.0994 -0.5682 -0.8936;\r\n -0.8099 -0.0951 -0.4470;\r\n 0.3038 -0.9284 -0.4938];\r\n\r\nT_correct = [1 4 6;\r\n 1 5 11;\r\n 1 6 10;\r\n 1 10 5;\r\n 1 11 4;\r\n 2 8 9;\r\n 2 9 14;\r\n 2 11 8;\r\n 2 14 15;\r\n 2 15 11;\r\n 3 6 7;\r\n 3 7 16;\r\n 3 9 12;\r\n 3 12 6;\r\n 3 14 9;\r\n 3 16 14;\r\n 4 11 15;\r\n 4 14 16;\r\n 4 15 14;\r\n 4 16 6;\r\n 5 8 11;\r\n 5 10 8;\r\n 6 12 13;\r\n 6 13 10;\r\n 6 16 7;\r\n 8 10 13;\r\n 8 12 9;\r\n 8 13 12];\r\n\r\nassert(isequal(mesh_the_convex_hull(V),T_correct))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_convex_hull.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:46:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T20:10:16.000Z","updated_at":"2026-02-13T17:40:03.000Z","published_at":"2025-07-24T18:00:49.000Z","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\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\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 convex hull of a 3D point set is actually a first -though rough- triangulation of 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\u003eA triangulation, or triangulated mesh, is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUse Matlab functions to compute the convex hull of the random point clouds given in the tests here below.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"336\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"448\\\"/\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\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\u003eForbidden functions / expressions\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\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 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for everyone!","description":"Accordingly to the \u003chttp://nl.mathworks.com/matlabcentral/cody/problems/42460-the-cake-is-a-lie problem 42460\u003e. All the children have eaten the cake and they were playing in the garden. You was trying to make barbecue, but someone spoken \"maybe pancakes?\" and all the children want pancakes. They want it now! Grab a frying pan and make a big pancake, then use minimum number of cuts to serve pancake to all the children at the same time.","description_html":"\u003cp\u003eAccordingly to the \u003ca href = \"http://nl.mathworks.com/matlabcentral/cody/problems/42460-the-cake-is-a-lie\"\u003eproblem 42460\u003c/a\u003e. All the children have eaten the cake and they were playing in the garden. You was trying to make barbecue, but someone spoken \"maybe pancakes?\" and all the children want pancakes. They want it now! Grab a frying pan and make a big pancake, then use minimum number of cuts to serve pancake to all the children at the same time.\u003c/p\u003e","function_template":"function y = pancake(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 1;y_correct = 0;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 2;y_correct = 1;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 4;y_correct = 2;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 7;y_correct = 3;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 12;y_correct = 5;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 27;y_correct = 7;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 127;y_correct = 16;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 2015;y_correct = 63;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 4060225;y_correct = 2850;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 1234567890;y_correct = 49690;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 1362067890;y_correct = 52193;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 2030000;y_correct = 2015;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 11581428900;y_correct = 152193;\r\nassert(isequal(pancake(x),y_correct))\r\n%%\r\nx = 9007199187632129; y_correct = 134217727;\r\nassert(isequal(pancake(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":"2015-08-07T07:58:07.000Z","rescore_all_solutions":false,"group_id":37,"created_at":"2015-08-06T09:41:35.000Z","updated_at":"2026-03-14T18:55:26.000Z","published_at":"2015-08-06T09:44:29.000Z","restored_at":"2018-02-06T15:11:34.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"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\u003eAccordingly to 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=\\\"http://nl.mathworks.com/matlabcentral/cody/problems/42460-the-cake-is-a-lie\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eproblem 42460\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. All the children have eaten the cake and they were playing in the garden. You was trying to make barbecue, but someone spoken \\\"maybe pancakes?\\\" and all the children want pancakes. They want it now! Grab a frying pan and make a big pancake, then use minimum number of cuts to serve pancake to all the children at the same 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":163,"title":"Love triangles","description":"Given a vector of lengths [a b c], determines whether a triangle with non-zero area (in two-dimensional Euclidean space, smarty!) could have sides of those lengths.\r\n\r\nExamples:\r\n\r\n[1 2 1000] ---\u003e false\r\n\r\n[3 4 5] ---\u003e true\r\n\r\n[5 5 5] ---\u003e true","description_html":"\u003cp\u003eGiven a vector of lengths [a b c], determines whether a triangle with non-zero area (in two-dimensional Euclidean space, smarty!) could have sides of those lengths.\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cp\u003e[1 2 1000] ---\u003e false\u003c/p\u003e\u003cp\u003e[3 4 5] ---\u003e true\u003c/p\u003e\u003cp\u003e[5 5 5] ---\u003e true\u003c/p\u003e","function_template":"function tf = triangle(sides)\r\n tf = true;\r\nend","test_suite":"%%\r\nsides = [1 2 1000];\r\ny_correct = false;\r\nassert(isequal(triangle(sides),y_correct))\r\n\r\n%%\r\nsides = [3 4 5];\r\ny_correct = true;\r\nassert(isequal(triangle(sides),y_correct))\r\n\r\n%%\r\nsides = [5 5 5];\r\ny_correct = true;\r\nassert(isequal(triangle(sides),y_correct))\r\n\r\n%%\r\nsides = [6 6 6];\r\ny_correct = true;\r\nassert(isequal(triangle(sides),y_correct))\r\n\r\n%%\r\nsides = [1 1 1];\r\ny_correct = true;\r\nassert(isequal(triangle(sides),y_correct))\r\n\r\n%%\r\nsides = [1 2 2];\r\ny_correct = true;\r\nassert(isequal(triangle(sides),y_correct))\r\n\r\n%%\r\nsides = [2 2 5];\r\ny_correct = false;\r\nassert(isequal(triangle(sides),y_correct))\r\n\r\n%%\r\nsides = [5 2 2];\r\ny_correct = false;\r\nassert(isequal(triangle(sides),y_correct))\r\n\r\n\r\n%%\r\nsides = [1 3 1];\r\ny_correct = false;\r\nassert(isequal(triangle(sides),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":39,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":591,"test_suite_updated_at":"2013-03-09T04:38:31.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-29T15:07:57.000Z","updated_at":"2026-03-29T20:34:50.000Z","published_at":"2012-01-29T15:07:57.000Z","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 vector of lengths [a b c], determines whether a triangle with non-zero area (in two-dimensional Euclidean space, smarty!) could have sides of those lengths.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003e[1 2 1000] ---\u003e 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\u003e[3 4 5] ---\u003e 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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[5 5 5] ---\u003e true\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":45256,"title":"List one vertex neighbors","description":"First input T is a triangulation connectivity indices list (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\r\nSecond input i is a vertex index (positive integer).\r\nThe purpose of this function is to query the list L of all i neighbor indices.\r\nFor instance if\r\nT = [1 2 4;...\r\n 2 3 4;...\r\n 5 6 8;...\r\n 6 7 8;...\r\n 1 2 5;...\r\n 2 5 6;...\r\n 2 3 6;...\r\n 3 6 7;...\r\n 3 4 7;...\r\n 4 7 8;...\r\n 4 1 8;...\r\n 1 8 5]\r\nand i = 3, then the function should return\r\nL = [2, 4, 6, 7]\r\nsince 2, 4, 6, and 7 are all part of triangles / rows in which 3 is also a vertex member.\r\nHypothesis :\r\n- Output L doesn't need to be ordered, but must not contain duplicated index.\r\n- Output L is a row vector , and if the vertex index is not in the list , the function must of course return the empty set, [].\r\n\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","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: 710.633px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 355.317px; transform-origin: 408px 355.317px; 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: 383.133px 8px; transform-origin: 383.133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFirst input T is a triangulation connectivity indices list (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\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: 152.483px 8px; transform-origin: 152.483px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSecond input i is a vertex index (positive integer).\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: 223.658px 8px; transform-origin: 223.658px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe purpose of this function is to query the list L of all i neighbor indices.\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; 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\"\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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003eT = [1 2 4;\u003c/span\u003e\u003cspan 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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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 5 6 8;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 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min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 6 7 8;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 1 2 5;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 2 5 6;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 2 3 6;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 3 6 7;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 3 4 7;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 4 7 8;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e 4 1 8;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 42.35px 8.5px; tab-size: 4; transform-origin: 42.35px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 8 5]\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 125.45px 8px; transform-origin: 125.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand i = 3, then the function should return\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; 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: 405px 10.2167px; transform-origin: 405px 10.2167px; 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; text-wrap-mode: 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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eL = [2, 4, 6, 7]\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 261.758px 8px; transform-origin: 261.758px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince 2, 4, 6, and 7 are all part of triangles / rows in which 3 is also a vertex member.\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: 38.5083px 8px; transform-origin: 38.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHypothesis :\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: 2.33333px 8px; transform-origin: 2.33333px 8px; 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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 29.15px 8px; transform-origin: 29.15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput L\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: 116.075px 8px; transform-origin: 116.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e doesn't need to be ordered, but must\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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 96.8px 8px; transform-origin: 96.8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003enot contain duplicated index.\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.33333px 8px; transform-origin: 2.33333px 8px; 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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 80.0917px 8px; transform-origin: 80.0917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput L is a row 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: 17.5px 8px; transform-origin: 17.5px 8px; 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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 112.75px 8px; transform-origin: 112.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eif the vertex index is not in the list\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: 42px 8px; transform-origin: 42px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e , 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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 119.392px 8px; transform-origin: 119.392px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003emust of course return the empty set\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 8px; transform-origin: 3.88333px 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: 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 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: 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function L = query_vertex_neighbors(T,i)\r\n L = i;\r\nend","test_suite":"%% triangulated cube\r\nT = [1 2 4;...\r\n 2 3 4;...\r\n 5 6 8;...\r\n 6 7 8;...\r\n 1 2 5;...\r\n 2 5 6;...\r\n 2 3 6;...\r\n 3 6 7;...\r\n 3 4 7;...\r\n 4 7 8;...\r\n 4 1 8;...\r\n 1 8 5];\r\n \r\ni = 3;\r\nL = [2 4 6 7];\r\nassert(isequal(sort(query_vertex_neighbors(T,i),2),L))\r\n\r\n%% Octahedron\r\nT = [1 2 3;...\r\n 1 3 4;...\r\n 1 4 5;...\r\n 1 5 2;...\r\n 6 3 2;...\r\n 6 4 3;...\r\n 6 5 4;...\r\n 6 2 5];\r\n \r\ni = 5;\r\nL = [1 2 4 6];\r\nassert(isequal(sort(query_vertex_neighbors(T,i),2),L))\r\n\r\n%% Empty set test\r\nT = [2 3 5;...\r\n 3 5 7;...\r\n 5 7 11;...\r\n 7 11 13];\r\n\r\ni = 6;\r\n\r\nassert(isempty(query_vertex_neighbors(T,i)))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('query_vertex_neighbors.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:51:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":27,"test_suite_updated_at":"2025-07-09T05:47:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-07T09:24:11.000Z","updated_at":"2025-11-18T16:44:59.000Z","published_at":"2020-01-07T09:56:23.000Z","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\u003eFirst input T is a triangulation connectivity indices list (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 input i is a vertex index (positive integer).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 purpose of this function is to query the list L of all i neighbor indices.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 instance 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[T = [1 2 4;...\\n 2 3 4;...\\n 5 6 8;...\\n 6 7 8;...\\n 1 2 5;...\\n 2 5 6;...\\n 2 3 6;...\\n 3 6 7;...\\n 3 4 7;...\\n 4 7 8;...\\n 4 1 8;...\\n 1 8 5]]]\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\u003eand i = 3, then the function should return\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[L = [2, 4, 6, 7]]]\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 2, 4, 6, and 7 are all part of triangles / rows in which 3 is also a vertex member.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHypothesis :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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: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\u003eOutput L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e doesn't need to be ordered, but must\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\u003enot contain duplicated index.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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: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\u003eOutput L is a row vector\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\u003eif the vertex index is not in the list\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e , 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:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emust of course return the empty set\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\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\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:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\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":2021,"title":"Is this triangle right-angled?","description":"Given three positive numbers a, b, c, where c is the largest number, return true if the triangle with sides a, b and c is right-angled. Otherwise, return false.","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: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; 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 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: 233.5px 8px; transform-origin: 233.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven three positive numbers a, b, c, where c is the largest number, return\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-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=\"font-weight: 700; \"\u003etrue\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: 118px 8px; transform-origin: 118px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if the triangle with sides a, b and c is right-angled. Otherwise, return\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003efalse\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\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function flag = isRightAngled(a, b, c)\r\n flag = false;\r\nend","test_suite":"%%\r\na = 3;\r\nb = 4;\r\nc = 5;\r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 2;\r\nb = 3;\r\nc = 4;\r\nflag_correct = false; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5;\r\nb = 12;\r\nc = 13;\r\nflag_correct = true; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n\r\n%%\r\na = 17;\r\nb = 19;\r\nc = 23;\r\nflag_correct = false; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n\r\n%%\r\na = 12;\r\nb = 35;\r\nc = 37;\r\nflag_correct = true; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n\r\n%%\r\na = 10*rand;\r\nb = a;\r\nc = a;\r\nflag_correct = false; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))","published":true,"deleted":false,"likes_count":38,"comments_count":7,"created_by":974,"edited_by":223089,"edited_at":"2023-05-04T07:40:55.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6418,"test_suite_updated_at":"2023-05-04T07:40:55.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:28:55.000Z","updated_at":"2026-04-06T22:39:36.000Z","published_at":"2013-11-28T17:12:28.000Z","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\u003eGiven three positive numbers a, b, c, where c is the largest number, return\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\u003etrue\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if the triangle with sides a, b and c is right-angled. Otherwise, return\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\u003efalse\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":61088,"title":"Covering a four-pointed star polygon by circles","description":"Given the area, A, of a star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).\r\nGiven (A,h), return the 2x2 matrix M = [A1/π a1; A2/π a2], where\r\nin the first row (i=1), A1 stands for the area of the circle that covers the minimum distance (cf. left figure), and a1 stands for the logical 1 if A1 is smaller than or reaches the area A or a1 stands for the logical 0 if A1 surpasses A;\r\nin the second row (i=2), A2 stands for the area of the circle that covers the maximum distance (cf. right figure), and a2 has the same previous false-true meaning relative to the areas A2 and A. Obviously, that A2 \u003e A holds true, then a2 = 0.\r\ninput: (A, h)\r\noutput: M = [A1/π a1; A2/π 0]\r\n","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: 748.987px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 374.487px; transform-origin: 408px 374.494px; 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=\"\"\u003eGiven the area, \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; \"\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=\"\"\u003e, of a star polygon formed by the rectangle, with dimensions \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×\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; \"\u003e2L\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, and four triangles, with height \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; \"\u003eh\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 from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).\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=\"\"\u003eGiven \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(A,h)\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, return the \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; \"\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=\"\"\u003ex\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; \"\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=\"\"\u003e 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=\"font-style: italic; \"\u003eM = [A1/π a1; A2/π a2]\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, where\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.188px; 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 51.0875px; transform-origin: 391px 51.0938px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.875px; 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 20.4375px; text-align: left; transform-origin: 363px 20.4375px; 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=\"\"\u003ein the first row \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=1)\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; unicode-bidi: normal; \"\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of the circle that covers the minimum distance (cf. left figure), 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is smaller than or reaches the area \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e0\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e surpasses \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 61.3125px; 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 30.65px; text-align: left; transform-origin: 363px 30.6562px; 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=\"\"\u003ein the second row \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=2)\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; unicode-bidi: normal; \"\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of the circle that covers the maximum distance (cf. right figure), 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea2\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has the same previous false-true meaning relative to the areas \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\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; unicode-bidi: normal; \"\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Obviously, that A2 \u0026gt; A holds true, then \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea2 = 0\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\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=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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 \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(A, h)\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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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 \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 = [A1/π a1; A2/π 0]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 484.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 242.4px; text-align: left; transform-origin: 384px 242.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"601\" height=\"479\" style=\"vertical-align: baseline;width: 601px;height: 479px\" 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\" alt=\"Covering by circles\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = covering_by_circles(A,h)\r\n M = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nh = 1;\r\nM_correct = [6.25 1; 16 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nA = 36;\r\nh = 2;\r\nM_correct = [12.25 0; 25 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nA = 56;\r\nh = 2;\r\nM_correct = [16 1; 36 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nfiletext = fileread('covering_by_circles.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 68;\r\nh = 1.2;\r\nM_correct = [13.69 1; 38.44 0];\r\nassert(all(isapprox(covering_by_circles(A,h),M_correct), 'all'))\r\n\r\n%%\r\nA = 89;\r\nh = 2.6;\r\nM_correct = [26.01 1; 57.76 0];\r\nassert(all(isapprox(covering_by_circles(A,h),M_correct), 'all'))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-30T13:14:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-29T14:26:03.000Z","updated_at":"2026-03-22T14:02:11.000Z","published_at":"2025-11-30T13:14:56.000Z","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:t\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a star polygon formed by the rectangle, with dimensions \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×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A,h)\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1/π a1; A2/π a2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\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\u003ein the first row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=1)\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\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of the circle that covers the minimum distance (cf. left figure), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is smaller than or reaches the area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e surpasses \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\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=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the second row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of the circle that covers the maximum distance (cf. right figure), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has the same previous false-true meaning relative to the areas \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Obviously, that A2 \u0026gt; A holds true, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2 = 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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\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(A, h)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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:rFonts 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":5,"title":"Triangle Numbers","description":"Triangle numbers are the sums of successive integers. So 6 is a triangle number because\r\n 6 = 1 + 2 + 3\r\nwhich can be displayed in a triangular shape like so\r\n *\r\n * *\r\n * * *\r\nThus 6 = triangle(3). Given n, return t, the triangular number for n.\r\nExample:\r\n Input n = 4\r\n Output t is 10","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: 265.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 132.8px; transform-origin: 407px 132.8px; 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: 282px 8px; transform-origin: 282px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTriangle numbers are the sums of successive integers. So 6 is a triangle number because\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; 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 10.2167px; transform-origin: 404px 10.2167px; 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: 56px 8.5px; tab-size: 4; transform-origin: 56px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 6 = 1 + 2 + 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; 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: 162px 8px; transform-origin: 162px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhich can be displayed in a triangular shape like so\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: 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 *\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: 32px 8.5px; tab-size: 4; transform-origin: 32px 8.5px; 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: 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: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; 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\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: 208.5px 8px; transform-origin: 208.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThus 6 = triangle(3). Given n, return t, the triangular number for 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: 28.5px 8px; transform-origin: 28.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample:\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: 52px 8.5px; tab-size: 4; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003e Input \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: 20px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 20px 8.5px; \"\u003en = 4\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: 60px 8.5px; tab-size: 4; transform-origin: 60px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003e Output \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: 28px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 28px 8.5px; \"\u003et is 10\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = triangle(n)\r\n t = n;\r\nend","test_suite":"%%\r\nfiletext = fileread('triangle.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'if') || contains(filetext, 'switch'); \r\nassert(~illegal)\r\n\r\n%%\r\nn = 1;\r\nt = 1;\r\nassert(isequal(triangle(n),t))\r\n\r\n%%\r\nn = 3;\r\nt = 6;\r\nassert(isequal(triangle(n),t))\r\n\r\n%%\r\nn = 5;\r\nt = 15;\r\nassert(isequal(triangle(n),t))\r\n\r\n%%\r\nn = 30;\r\nt = 465;\r\nassert(isequal(triangle(n),t))\r\n\r\n%%\r\nn = 30;\r\nt = 465;\r\nassert(isequal(triangle(n),t))","published":true,"deleted":false,"likes_count":143,"comments_count":27,"created_by":1,"edited_by":223089,"edited_at":"2022-12-21T10:26:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":30174,"test_suite_updated_at":"2022-12-21T10:26:58.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:17.000Z","updated_at":"2026-04-06T14:52:51.000Z","published_at":"2012-01-18T01:00:17.000Z","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\u003eTriangle numbers are the sums of successive integers. So 6 is a triangle number because\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[ 6 = 1 + 2 + 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\u003ewhich can be displayed in a triangular shape like so\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[ *\\n * *\\n * * *]]\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\u003eThus 6 = triangle(3). Given n, return t, the triangular number for 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\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 n = 4\\n Output t is 10]]\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":45261,"title":"List every vertices neighbor indices","description":"Input T is a triangulation.\r\nThe purpose of this function is to query at once the cell array N of all vertex neighbor indices... of every vertices, nothing less (!)\r\nOutput N must be a cell array since of course each vertex may have a different number of neighbors.\r\nFor example, for an input filled octahedron whom triangulation is\r\nT = [1, 2, 3;...\r\n 1, 3, 4;...\r\n 1, 4, 5;...\r\n 1, 2, 5;...\r\n 2, 3, 6;...\r\n 3, 4, 6;...\r\n 4, 5, 6;...\r\n 2, 5, 6;...\r\n 2, 3, 4;...\r\n 2, 4, 5;...\r\n 1, 2, 4;...\r\n 2, 4, 6],\r\nthen the output N is a 6x1 cell array of integers row vectors, such that :\r\nN(1,1) = {[2, 3, 4, 5]};\r\nN(2,1) = {[1, 3, 4, 5, 6]};\r\nN(3,1) = {[1, 2, 4, 6]};\r\nN(4,1) = {[1, 2, 3, 5, 6]};\r\nN(5,1) = {[1, 2, 4, 6]};\r\nN(6,1) = {[2, 3, 4, 5]};\r\nIndeed vertex #2 is part of triangles [1, 2, 3], [1, 2, 5], [2, 3, 6], [2, 5, 6], [2, 3, 4], [2, 4, 5], [1, 2, 4], and [2, 4, 6], it then admit all the other vertices as neighbors ([1, 3, 4, 5, 6]).\r\nHypothesis / conditions :\r\na vertex is the neighbor of another if they are linked with an edge in at least one same triangle. A vertex is not neighbor of itself.\r\nOutput N row order is crucial since row number actually corresponds to the vertex id / index.\r\nOutput N cells content order doesn't matter, but it doesn't admit any duplicated index / value.\r\nTip : solving my previous problems, and especially query_vertex_neighbors will help you to fully understand and solve this one.\r\nNB : the question of unreferenced vertices is not tacled here. We just supposed there are not.\r\n\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","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: 936.533px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 468.267px; transform-origin: 408px 468.267px; 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: 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: 34.6083px 8px; transform-origin: 34.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInput T is 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: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/help/matlab/ref/triangulation.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003etriangulation\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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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; 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: 372.617px 8px; transform-origin: 372.617px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe purpose of this function is to query at once the cell array N of all vertex neighbor indices... of every vertices, nothing less (!)\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: 311.425px 8px; transform-origin: 311.425px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOutput N must be a cell array since of course each vertex may have a different number of neighbors.\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: 198.783px 8px; transform-origin: 198.783px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, for an input filled octahedron whom triangulation is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 245.2px; 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: 405px 122.6px; transform-origin: 405px 122.6px; 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003eT = [1, 2, 3;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 1, 3, 4;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 1, 4, 5;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 1, 2, 5;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 2, 3, 6;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 3, 4, 6;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 4, 5, 6;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 2, 5, 6;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 2, 3, 4;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 2, 4, 5;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e 1, 2, 4;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 2, 4, 6],\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 218.575px 8px; transform-origin: 218.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen the output N is a 6x1 cell array of integers row vectors, such that :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 122.6px; 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: 405px 61.3px; transform-origin: 405px 61.3px; 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 92.4px 8.5px; tab-size: 4; transform-origin: 92.4px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eN(1,1) = {[2, 3, 4, 5]};\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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 103.95px 8.5px; tab-size: 4; transform-origin: 103.95px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eN(2,1) = {[1, 3, 4, 5, 6]};\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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 92.4px 8.5px; tab-size: 4; transform-origin: 92.4px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eN(3,1) = {[1, 2, 4, 6]};\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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 103.95px 8.5px; tab-size: 4; transform-origin: 103.95px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eN(4,1) = {[1, 2, 3, 5, 6]};\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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 92.4px 8.5px; tab-size: 4; transform-origin: 92.4px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eN(5,1) = {[1, 2, 4, 6]};\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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 92.4px 8.5px; tab-size: 4; transform-origin: 92.4px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eN(6,1) = {[2, 3, 4, 5]};\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; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; 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: 382.583px 8px; transform-origin: 382.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIndeed vertex #2 is part of triangles [1, 2, 3], [1, 2, 5], [2, 3, 6], [2, 5, 6], [2, 3, 4], [2, 4, 5], [1, 2, 4], and [2, 4, 6], it then admit all the other vertices as neighbors ([1, 3, 4, 5, 6]).\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: 83.2px 8px; transform-origin: 83.2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHypothesis / conditions :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; 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: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.8667px; 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: 364px 20.4333px; text-align: left; transform-origin: 364px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\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: 108.875px 8px; transform-origin: 108.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003evertex is the neighbor of another\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 94.525px 8px; transform-origin: 94.525px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if they are linked with an edge\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\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: 93.7167px 8px; transform-origin: 93.7167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ein at least one same triangle\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 50.1583px 8px; transform-origin: 50.1583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. A vertex is not neighbor of itself.\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 96.425px 8px; transform-origin: 96.425px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput N row order is crucial\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 18.2833px 8px; transform-origin: 18.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e since\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\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: 190.142px 8px; transform-origin: 190.142px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003erow number actually corresponds to the vertex id / index.\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 285.433px 8px; transform-origin: 285.433px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOutput N cells content order doesn't matter, but it doesn't admit any duplicated index / value.\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: 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: 14.6417px 8px; transform-origin: 14.6417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTip :\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: 23.7333px 8px; transform-origin: 23.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e solving\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: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/players/8668631-nicolas-douillet/created\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003emy previous problems\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: 48.2417px 8px; transform-origin: 48.2417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and especially\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: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/problems/45256-query-a-vertex-neighbors\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003equery_vertex_neighbors\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: 145.875px 8px; transform-origin: 145.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will help you to fully understand and solve this one.\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: 288.867px 8px; transform-origin: 288.867px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNB : the question of unreferenced vertices is not tacled here. We just supposed there are not.\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 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: 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function N = query_every_vertices_neighbor_indices(T)\r\n N = num2cell(T);\r\nend","test_suite":"%% Filled octahedron\r\nT = [1, 2, 3;...\r\n 1, 3, 4;...\r\n 1, 4, 5;...\r\n 1, 2, 5;...\r\n 2, 3, 6;...\r\n 3, 4, 6;...\r\n 4, 5, 6;...\r\n 2, 5, 6;...\r\n 2, 3, 4;...\r\n 2, 4, 5;...\r\n 1, 2, 4;...\r\n 2, 4, 6];\r\n \r\nN = cell(6,1);\r\n\r\nN(1,1) = {[2, 3, 4, 5]};\r\nN(2,1) = {[1, 3, 4, 5, 6]};\r\nN(3,1) = {[1, 2, 4, 6]};\r\nN(4,1) = {[1, 2, 3, 5, 6]};\r\nN(5,1) = {[1, 2, 4, 6]};\r\nN(6,1) = {[2, 3, 4, 5]};\r\n\r\nassert(isequal(query_every_vertices_neighbor_indices(T),N))\r\n\r\n%% Triangulated cube\r\nT = [1, 2, 4;...\r\n 2, 3, 4;...\r\n 5, 6, 8;...\r\n 6, 7, 8;...\r\n 1, 2, 5;...\r\n 2, 5, 6;...\r\n 2, 3, 6;...\r\n 3, 6, 7;...\r\n 3, 4, 7;...\r\n 4, 7, 8;...\r\n 1, 4, 8;...\r\n 1, 5, 8];\r\n\r\nN = cell(8,1);\r\n\r\nN(1,1) = {[2, 4, 5, 8]};\r\nN(2,1) = {[1, 3, 4, 5, 6]};\r\nN(3,1) = {[2, 4, 6, 7]};\r\nN(4,1) = {[1, 2, 3, 7, 8]};\r\nN(5,1) = {[1, 2, 6, 8]};\r\nN(6,1) = {[2, 3, 5, 7, 8]};\r\nN(7,1) = {[3, 4, 6, 8]};\r\nN(8,1) = {[1 4 5 6 7]};\r\n\r\nassert(isequal(query_every_vertices_neighbor_indices(T),N))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('query_every_vertices_neighbor_indices.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:49:16.000Z","deleted_by":null,"deleted_at":null,"solvers_count":27,"test_suite_updated_at":"2025-07-09T05:51:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-10T08:35:13.000Z","updated_at":"2025-11-16T17:45:29.000Z","published_at":"2020-01-10T09:24:12.000Z","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\u003eInput T 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://fr.mathworks.com/help/matlab/ref/triangulation.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003etriangulation\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\u003eThe purpose of this function is to query at once the cell array N of all vertex neighbor indices... of every vertices, nothing less (!)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 N must be a cell array since of course each vertex may have a different number of neighbors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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, for an input filled octahedron whom triangulation 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[T = [1, 2, 3;...\\n 1, 3, 4;...\\n 1, 4, 5;...\\n 1, 2, 5;...\\n 2, 3, 6;...\\n 3, 4, 6;...\\n 4, 5, 6;...\\n 2, 5, 6;...\\n 2, 3, 4;...\\n 2, 4, 5;...\\n 1, 2, 4;...\\n 2, 4, 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\u003ethen the output N is a 6x1 cell array of integers row vectors, such that :\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[N(1,1) = {[2, 3, 4, 5]};\\nN(2,1) = {[1, 3, 4, 5, 6]};\\nN(3,1) = {[1, 2, 4, 6]};\\nN(4,1) = {[1, 2, 3, 5, 6]};\\nN(5,1) = {[1, 2, 4, 6]};\\nN(6,1) = {[2, 3, 4, 5]};]]\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\u003eIndeed vertex #2 is part of triangles [1, 2, 3], [1, 2, 5], [2, 3, 6], [2, 5, 6], [2, 3, 4], [2, 4, 5], [1, 2, 4], and [2, 4, 6], it then admit all the other vertices as neighbors ([1, 3, 4, 5, 6]).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\u003eHypothesis / conditions :\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\u003ea\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\u003evertex is the neighbor of another\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if they are linked with an edge\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 at least one same triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. A vertex is not neighbor of itself.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput N row order is crucial\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e since\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\u003erow number actually corresponds to the vertex id / index.\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\u003eOutput N cells content order doesn't matter, but it doesn't admit any duplicated index / value.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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\u003eTip :\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e solving\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://fr.mathworks.com/matlabcentral/cody/players/8668631-nicolas-douillet/created\\\"\u003e\u003cw:r\u003e\u003cw:t\u003emy previous problems\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and especially\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://fr.mathworks.com/matlabcentral/cody/problems/45256-query-a-vertex-neighbors\\\"\u003e\u003cw:r\u003e\u003cw:t\u003equery_vertex_neighbors\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e will help you to fully understand and solve this one.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNB : the question of unreferenced vertices is not tacled here. We just supposed there are not.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\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:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\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":45379,"title":"3rd side of a Triangle","description":"Given two sides of a triangle, find the minimum and maximum possible area of the triangle.\r\n\r\nthe length of the third side has to be of integer-valued.","description_html":"\u003cp\u003eGiven two sides of a triangle, find the minimum and maximum possible area of the triangle.\u003c/p\u003e\u003cp\u003ethe length of the third side has to be of integer-valued.\u003c/p\u003e","function_template":"function [max,min]=tri_side(a1,a2)","test_suite":"%%\r\n[mx,mn]=tri_side(20,10);\r\nassert(abs(mx-99.9199)\u003c.001)\r\nassert(abs(mn- 31.9756)\u003c.001)\r\n\r\n%%\r\n[mx,mn]=tri_side(50,50);\r\nassert(abs(mx-1249.9579)\u003c.001)\r\nassert(abs(mn-24.9987)\u003c.001)\r\n\r\n%%\r\n[mx,mn]=tri_side(1,3);\r\nassert(abs(mx-1.479)\u003c.001)\r\nassert(abs(mn- 1.479)\u003c.001)\r\n\r\n%%\r\n[mx,mn]=tri_side(1000,30);\r\nassert(abs(mx-14998.3124)\u003c.001)\r\nassert(abs(mn-3784.4461)\u003c.001)","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2020-03-24T18:55:45.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-03-23T14:24:55.000Z","updated_at":"2026-01-29T12:45:10.000Z","published_at":"2020-03-23T14:34:12.000Z","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 two sides of a triangle, find the minimum and maximum possible area of the triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 length of the third side has to be of integer-valued.\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":45271,"title":"Calculate triangle area","description":"Imagine that you want to calculate the areas of some triangles given in matrix form. First the coordinates of the vertices of the triangles are in a matrix called coords where the line number represents the vertex number and the column number is the dimension, in this case it is equal to 2 (x, y). The way the nodes connect are found in the lnods matrix where the line number is the triangle number and the column number is the vertex number that makes up each triangle (v_i, v_j, v_k).","description_html":"\u003cp\u003eImagine that you want to calculate the areas of some triangles given in matrix form. First the coordinates of the vertices of the triangles are in a matrix called coords where the line number represents the vertex number and the column number is the dimension, in this case it is equal to 2 (x, y). The way the nodes connect are found in the lnods matrix where the line number is the triangle number and the column number is the vertex number that makes up each triangle (v_i, v_j, v_k).\u003c/p\u003e","function_template":"function y =areas(coords,lnods)\r\n y = ?;\r\nend","test_suite":"%%\r\ncoords=[0 0;1 0; 1 1; 0 1];\r\nlnods=[ 1 2 4; 2 3 4];\r\ny_correct = [0.500;0.500];\r\nassert(isequal(areas(coords,lnods),y_correct))\r\n%%\r\ncoords=[0 0;1 0; 1 1; 0 1; 0.5 0.5];\r\nlnods=[ 1 2 5; 2 3 5;3 4 5;4 1 5];\r\ny_correct = [0.2500;0.2500;0.2500;0.2500];\r\nassert(isequal(areas(coords,lnods),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":396229,"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":"2020-01-19T02:12:33.000Z","updated_at":"2026-03-14T18:54:18.000Z","published_at":"2020-01-19T02:17:46.000Z","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\u003eImagine that you want to calculate the areas of some triangles given in matrix form. First the coordinates of the vertices of the triangles are in a matrix called coords where the line number represents the vertex number and the column number is the dimension, in this case it is equal to 2 (x, y). The way the nodes connect are found in the lnods matrix where the line number is the triangle number and the column number is the vertex number that makes up each triangle (v_i, v_j, v_k).\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":44037,"title":"Pascal's triangle","description":"\u003chttps://en.wikipedia.org/wiki/Pascal%27s_triangle\u003e\r\nif the order is: x = 3; the output will be:\r\n\r\n\r\n output = [0 0 0 1 0 0 0;\r\n 0 0 1 0 1 0 0;\r\n 0 1 0 2 0 1 0;\r\n 1 0 3 0 3 0 1]","description_html":"\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Pascal%27s_triangle\"\u003ehttps://en.wikipedia.org/wiki/Pascal%27s_triangle\u003c/a\u003e\r\nif the order is: x = 3; the output will be:\u003c/p\u003e\u003cpre\u003e output = [0 0 0 1 0 0 0;\r\n 0 0 1 0 1 0 0;\r\n 0 1 0 2 0 1 0;\r\n 1 0 3 0 3 0 1]\u003c/pre\u003e","function_template":"function y = stg_Pascal(x)\r\n y = [];\r\nend","test_suite":"%%\r\nx = 3;\r\ny_correct = [0 0 0 1 0 0 0;\r\n 0 0 1 0 1 0 0;\r\n 0 1 0 2 0 1 0;\r\n 1 0 3 0 3 0 1];\r\nassert(isequal(stg_Pascal(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = [0 0 0 0 1 0 0 0 0;\r\n 0 0 0 1 0 1 0 0 0;\r\n 0 0 1 0 2 0 1 0 0;\r\n 0 1 0 3 0 3 0 1 0;\r\n 1 0 4 0 6 0 4 0 1];\r\nassert(isequal(stg_Pascal(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = [0 0 1 0 0;\r\n 0 1 0 1 0;\r\n 1 0 2 0 1];\r\nassert(isequal(stg_Pascal(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":108804,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":38,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-01-23T15:05:29.000Z","updated_at":"2026-03-14T18:48:45.000Z","published_at":"2017-01-23T15:05:29.000Z","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/Pascal%27s_triangle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://en.wikipedia.org/wiki/Pascal%27s_triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt; if the order is: x = 3; the output will be:\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[ output = [0 0 0 1 0 0 0;\\n 0 0 1 0 1 0 0;\\n 0 1 0 2 0 1 0;\\n 1 0 3 0 3 0 1]]]\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":61086,"title":"Covering a four-pointed star polygon by rectangles","description":"Given the area, A, of a star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, find the rectangles that have the same area, A, and cover the distance between opposite vertices (cf. figure below).\r\nGiven (A, L), return the 2x2 matrix M, where \r\nthe first row returns the dimensions, y1×y2, of the rectangle that covers the minimum distance (cf. left figure);\r\nthe second row returns the dimensions, z1×z2, of the rectangle that covers the maximum distance (cf. right figure).\r\ninput: (A, L)\r\noutput: M = [y1 y2; z1 z2]\r\n","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: 635.675px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 317.837px; transform-origin: 408px 317.837px; 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; 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=\"\"\u003eGiven the area, \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; \"\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=\"\"\u003e, of a star polygon formed by the rectangle, with dimensions \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×\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; \"\u003e2L\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, and four triangles, with height \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; \"\u003eh\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 from their bases to the vertices, find the rectangles that have the same area, \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; \"\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=\"\"\u003e, and cover the distance between opposite vertices (cf. figure below).\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=\"\"\u003eGiven \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(A, L)\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, return the \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; \"\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=\"\"\u003ex\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; \"\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=\"\"\u003e 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=\"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, where \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; 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 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; 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=\"\"\u003ethe first row returns the dimensions, y\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\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; unicode-bidi: normal; \"\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey2\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of the rectangle that covers the minimum distance (cf. left figure);\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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=\"\"\u003ethe second row returns the dimensions, \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ez1\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×z\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of the rectangle that covers the maximum distance (cf. right figure).\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=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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 \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(A, L)\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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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 \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 = [y1 y2; z1 z2]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 411.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 205.9px; text-align: left; transform-origin: 384px 205.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"508\" height=\"406\" style=\"vertical-align: baseline;width: 508px;height: 406px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = covering_polygon(A,L)\r\n M = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nL = 3;\r\nM_correct = [5 5.4; 3.375 8];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nA = 36;\r\nL = 3;\r\nM_correct = [7 36/7; 3.6 10];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nfiletext = fileread('covering_polygon.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 48;\r\nL = 4;\r\nM_correct = [20/3 36/5; 4.5 32/3];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nA = 56;\r\nL = 4;\r\nM_correct = [8 7; 14/3 12];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-28T15:21:25.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-27T15:06:59.000Z","updated_at":"2026-03-21T13:41:00.000Z","published_at":"2025-11-28T15:21:25.000Z","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\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a star polygon formed by the rectangle, with dimensions \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×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, find the rectangles that have the same area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and cover the distance between opposite vertices (cf. figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, L)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the 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\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×z\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the rectangle that covers the maximum distance (cf. right figure).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\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(A, L)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":985,"title":"Make a Star Pyramid","description":"Create a star pyramid. First line will have 1 star, second will have two stars and so on... a basic program which is easily done in c programming.\r\n\r\nExample\r\n\r\n n = 3\r\n p = pyramid(n)\r\n\r\nreturns this string matrix in p\r\n\r\n '* '\r\n '** '\r\n '***'\r\n\r\nThe output p is an n-by-n string matrix with spaces (ASCII=32) in the blank spots and '*' as shown. ","description_html":"\u003cp\u003eCreate a star pyramid. First line will have 1 star, second will have two stars and so on... a basic program which is easily done in c programming.\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cpre\u003e n = 3\r\n p = pyramid(n)\u003c/pre\u003e\u003cp\u003ereturns this string matrix in p\u003c/p\u003e\u003cpre\u003e '* '\r\n '** '\r\n '***'\u003c/pre\u003e\u003cp\u003eThe output p is an n-by-n string matrix with spaces (ASCII=32) in the blank spots and '*' as shown.\u003c/p\u003e","function_template":"function p = pyramid(n)\r\n p = '*';\r\nend","test_suite":"%%\r\nn = 2;\r\np = ['* ';'**'];\r\nassert(isequal(pyramid(n),p));\r\n\r\n%%\r\nn = 3;\r\np = ['* ';'** ';'***'];\r\nassert(isequal(pyramid(n),p));\r\n\r\n%%\r\nn = 4;\r\np = ['* ';'** ';'*** ';'****'];\r\nassert(isequal(pyramid(n),p));\r\n\r\n%%\r\nn = 10;\r\np = ['* ';\r\n '** ';\r\n '*** ';\r\n '**** ';\r\n '***** ';\r\n '****** ';\r\n '******* ';\r\n '******** ';\r\n '********* ';\r\n '**********'];\r\nassert(isequal(pyramid(n),p));\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":7262,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":219,"test_suite_updated_at":"2012-10-12T14:45:22.000Z","rescore_all_solutions":false,"group_id":18,"created_at":"2012-10-10T08:06:01.000Z","updated_at":"2026-03-31T18:12:10.000Z","published_at":"2012-10-10T08:08:21.000Z","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\u003eCreate a star pyramid. First line will have 1 star, second will have two stars and so on... a basic program which is easily done in c programming.\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[ n = 3\\n p = pyramid(n)]]\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\u003ereturns this string matrix in p\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[ '* '\\n '** '\\n '***']]\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 output p is an n-by-n string matrix with spaces (ASCII=32) in the blank spots and '*' as shown.\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":49918,"title":"Splitting Triangle - Problem the first","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: 368px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 184px; transform-origin: 407px 184px; 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=\"\"\u003eConsider an equilateral triangle sitting in Quadrant I as depicted in an example below:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 245px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 122.5px; text-align: left; transform-origin: 384px 122.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"247\" height=\"239\" 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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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis triangle is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the triangle, determine the x coordinate of the line that splits the regions. The ratio between the regions (red to blue) is presented through the first two entries of the input. For example, if the ratio is 2 and 5, then these two numbers will be the first two numbers in the input. The last entry is the side of the triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = ratio_polygon(s)\r\n y = s;\r\nend","test_suite":"%%\r\ns=[1 1 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.5;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[1 3 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.3536;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[1 0 1];\r\ny=ratio_polygon(s);\r\ny_correct=1;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[3 1 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.6464;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[1 pi 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.3475;\r\nassert(abs(y-y_correct)\u003ceps)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-21T22:16:27.000Z","updated_at":"2025-12-04T15:18:46.000Z","published_at":"2021-01-21T22:18:44.000Z","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\u003eConsider an equilateral triangle sitting in Quadrant I as depicted in an example below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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=\\\"239\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"247\\\"/\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\u003eThis triangle is to be split into two regions (e.g., red and blue). 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of a four-pointed star polygon","description":"Given the area A, of a rectangle with dimensions l1xl2, where the side lengths are integers and form the smallest possible perimeter, and given the total area A_t of the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, h, from their bases to the apices, find the vector [l1 l2 h] such that l1\u003cl2.\r\n","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: 490.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 245.4px; transform-origin: 408px 245.4px; 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: 385px 31.5px; text-align: left; transform-origin: 385px 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=\"\"\u003eGiven the area \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; \"\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=\"\"\u003e, of a rectangle with dimensions \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; \"\u003el1xl2\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, where the side lengths are integers and form the smallest possible perimeter, and given the total area \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; \"\u003eA_t\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 the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, \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; \"\u003eh\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, from their bases to the apices, find 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[l1 l2 h]\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 such that \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; \"\u003el1\u0026lt;l2\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: 418.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 209.4px; text-align: left; transform-origin: 385px 209.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"508\" height=\"413\" style=\"vertical-align: baseline;width: 508px;height: 413px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = star_polygon(A,A_t)\r\n y = A;\r\nend","test_suite":"%%\r\nA = 10;\r\nA_t = 24;\r\ny_correct = [2 5 2];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 11;\r\nA_t = 23;\r\ny_correct = [1 11 1];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 72;\r\nA_t = 106;\r\ny_correct = [8 9 2];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nfiletext = fileread('star_polygon.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 156;\r\nA_t = 180;\r\ny_correct = [12 13 0.96];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 168;\r\nA_t = 190;\r\ny_correct = [12 14 11/13];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-14T17:36:31.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-13T17:02:46.000Z","updated_at":"2026-01-15T09:17:29.000Z","published_at":"2025-11-14T17:36:31.000Z","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\u003eGiven the area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a rectangle with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1xl2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where the side lengths are integers and form the smallest possible perimeter, and given the total area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_t\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, from their bases to the apices, find the vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[l1 l2 h]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1\u0026lt;l2\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"413\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"508\\\"/\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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the centroid of triangle","description":"Imagine that you want to calculate the *centroid* of some _triangles_ given in matrix form. First the coordinates of the vertices of the triangles are in a matrix called coords where the line number represents the vertex number and the column number is the dimension, in this case it is equal to 2 (x, y). The way the nodes connect are found in the lnods matrix where the line number is the triangle number and the column number is the vertex number that makes up each triangle (v_i, v_j, v_k).","description_html":"\u003cp\u003eImagine that you want to calculate the \u003cb\u003ecentroid\u003c/b\u003e of some \u003ci\u003etriangles\u003c/i\u003e given in matrix form. First the coordinates of the vertices of the triangles are in a matrix called coords where the line number represents the vertex number and the column number is the dimension, in this case it is equal to 2 (x, y). The way the nodes connect are found in the lnods matrix where the line number is the triangle number and the column number is the vertex number that makes up each triangle (v_i, v_j, v_k).\u003c/p\u003e","function_template":"function c = your_fcn_name(coords,lnods)\r\n c = x;\r\nend","test_suite":"%%\r\ncoords=[0 0;1 0; 1 1; 0 1];\r\nlnods=[ 1 2 4; 2 3 4];\r\ny_correct =[1/3 1/3;2/3 2/3];\r\nassert(isequal(your_fcn_name(coords,lnods),y_correct))\r\n%%\r\ncoords=[0 0;1 0; 1 1; 0 1; 0.5 0.5];\r\nlnods=[ 1 2 5; 2 3 5;3 4 5;4 1 5];\r\ny_correct =[1/2 1/6; 5/6 1/2 ;1/2 5/6;1/6 1/2];\r\nassert(isequal(your_fcn_name(coords,lnods),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":396229,"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":1,"created_at":"2020-01-19T13:43:13.000Z","updated_at":"2026-03-14T18:42:54.000Z","published_at":"2020-01-19T13:51:41.000Z","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\u003eImagine that you want to calculate 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\u003ecentroid\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of some\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\u003etriangles\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e given in matrix form. First the coordinates of the vertices of the triangles are in a matrix called coords where the line number represents the vertex number and the column number is the dimension, in this case it is equal to 2 (x, y). The way the nodes connect are found in the lnods matrix where the line number is the triangle number and the column number is the vertex number that makes up each triangle (v_i, v_j, v_k).\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":61071,"title":"Generalizing square area to triangle area","description":"Cody Problem 61070 asked for the height, h, of a right triangle that had the same area, A, of a square with side length, c, and the hypothenuse length was correlated to the square side by x = 2. \r\nNow, find the height, h, of the right triangle that has the same area, A, of a square with side length, c, and the hypothenuse length is xc, for an arbitrary number x \u003e 2. Here, the height stands for the smallest cathetus.\r\n","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: 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\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/61070-square-area-to-triangle-area\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 61070\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 asked for the height, \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; \"\u003eh\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 a right triangle that had the same area, \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; \"\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=\"\"\u003e, of a square with side length, \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; \"\u003ec\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, and the hypothenuse length was correlated to the square side by \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; \"\u003ex = 2\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; 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=\"\"\u003eNow, find the height, \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; \"\u003eh\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 the right triangle that has the same area, \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; \"\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=\"\"\u003e, of a square with side length, \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; \"\u003ec\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, and the hypothenuse length is \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; \"\u003exc\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, for an arbitrary number \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; \"\u003ex \u0026gt; 2\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. Here, the height stands for the smallest cathetus.\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=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function h = find_height(A,x)\r\n h = x;\r\nend","test_suite":"%%\r\nA = 9;\r\nx = sqrt(5);\r\nh_correct = 3;\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A,x)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 10;\r\nx = 3;\r\nh_correct = sqrt(5*(9-sqrt(65)));\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A,x)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 16;\r\nx = sqrt(5);\r\nh_correct = 4;\r\nassert(isequal(find_height(A,x),h_correct))\r\n\r\n%%\r\nfiletext = fileread('find_height.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 16;\r\nx = 3; \r\nh_correct = 4*sqrt((9-sqrt(65))/2);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A,x)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 16;\r\nx = 5; \r\nh_correct = 4*sqrt((25 - sqrt(609))/2);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A,x)-h_correct)\u003ctolerance)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":7,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-13T10:09:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":"2025-11-13T10:09:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-10T14:44:15.000Z","updated_at":"2026-03-23T21:14:52.000Z","published_at":"2025-11-12T17:58:52.000Z","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:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/61070-square-area-to-triangle-area\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 61070\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asked for the height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a right triangle that had the same area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a square with side length, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and the hypothenuse length was correlated to the square side by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex = 2\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\u003eNow, find the height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the right triangle that has the same area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a square with side length, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and the hypothenuse length is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003exc\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, for an arbitrary number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex \u0026gt; 2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Here, the height stands for the smallest cathetus.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\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":43599,"title":"Find the sides of an isosceles triangle when given its area and height from its base to apex","description":"Find the sides of an isosceles triangle when given its area and the height from its base to apex.\r\nFor example, with A=12 and h=4, the result will be [5 5 6].","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: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; 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: 299px 8px; transform-origin: 299px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the sides of an isosceles triangle when given its area and the height from its base to apex.\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: 180px 8px; transform-origin: 180px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, with A=12 and h=4, the result will be [5 5 6].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = sidesOfTheTriangle(A,h)\r\n y = h;\r\nend","test_suite":"filetext = fileread('sidesOfTheTriangle.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'assert') || ...\r\n contains(filetext, 'elseif');\r\nassert(~illegal)\r\n\r\n%%\r\nA = 12;\r\nh = 4;\r\ny_correct = [5 5 6];\r\nassert(sum(abs(sidesOfTheTriangle(A,h)-y_correct))\u003c1e-3)\r\n\r\n%%\r\nA = 60;\r\nh = 5;\r\ny_correct = [13 13 24];\r\nassert(sum(abs(sidesOfTheTriangle(A,h)-y_correct))\u003c1e-3)\r\n\r\n%%\r\nA = 120;\r\nh = 8;\r\ny_correct = [17 17 30];\r\nassert(sum(abs(sidesOfTheTriangle(A,h)-y_correct))\u003c1e-3)\r\n\r\n%%\r\nA = 50;\r\nh = 11;\r\ny_correct = [11.9021492607341 11.9021492607341 9.09090909090909];\r\nassert(sum(abs(sidesOfTheTriangle(A,h)-y_correct))\u003c1e-3)\r\n\r\n%%\r\nA = 5;\r\nh = 3;\r\ny_correct = [3.43187671366233 3.43187671366233 10/3];\r\nassert(sum(abs(sidesOfTheTriangle(A,h)-y_correct))\u003c1e-3)\r\n\r\n%%\r\nA = 150;\r\nh = 10;\r\ny_correct = [18.0277563773199 18.0277563773199 30];\r\nassert(sum(abs(sidesOfTheTriangle(A,h)-y_correct))\u003c1e-3)\r\n\r\n%%\r\nA = 5;\r\nh = 0.5;\r\ny_correct = [10.0124921972504 10.0124921972504 20];\r\nassert(sum(abs(sidesOfTheTriangle(A,h)-y_correct))\u003c1e-3)\r\n\r\n%%\r\nA = 42;\r\nh = pi;\r\ny_correct = [13.7331777948941 13.7331777948941 26.7380304394384];\r\nassert(sum(abs(sidesOfTheTriangle(A,h)-y_correct))\u003c1e-3)\r\n","published":true,"deleted":false,"likes_count":12,"comments_count":3,"created_by":90467,"edited_by":223089,"edited_at":"2023-02-02T06:57:50.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2147,"test_suite_updated_at":"2023-02-02T06:57:50.000Z","rescore_all_solutions":false,"group_id":37,"created_at":"2016-10-22T23:50:43.000Z","updated_at":"2026-04-04T19:12:10.000Z","published_at":"2016-12-02T18:59:27.000Z","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\u003eFind the sides of an isosceles triangle when given its area and the height from its base to apex.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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, with A=12 and h=4, the result will be [5 5 6].\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":49933,"title":"Splitting Triangle - Problem the second","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: 369px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 184.5px; transform-origin: 407px 184.5px; 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=\"\"\u003eConsider an equilateral triangle sitting in Quadrant I as depicted in an example below:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 225px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 112.5px; text-align: left; transform-origin: 384px 112.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"268\" height=\"219\" style=\"vertical-align: baseline;width: 268px;height: 219px\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 52.5px; text-align: left; transform-origin: 384px 52.5px; 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=\"\"\u003eThis equilateral triangle is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the equilateral triangle, determine the angle between the red line splitting the regions and the positive x-axis (in degrees). The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 11 to 12, then these two numbers will be the first two numbers in the input. The last entry is the side of the triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = ratio_polygon(s)\r\n y = s;\r\nend","test_suite":"%%\r\ns=[1 1 1];\r\ny=ratio_polygon(s);\r\ny_correct=30;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[1 0 1];\r\ny=ratio_polygon(s);\r\ny_correct=60;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[0 1 1];\r\ny=ratio_polygon(s);\r\ny_correct=0;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[pi 17 1];\r\ny=ratio_polygon(s);\r\ny_correct=8.3348;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[3 2 1];\r\ny=ratio_polygon(s);\r\ny_correct=36.5868;\r\nassert(abs(y-y_correct)\u003ceps)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":"2021-01-22T02:14:20.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-22T01:43:29.000Z","updated_at":"2025-12-04T16:12:19.000Z","published_at":"2021-01-22T02:14:20.000Z","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\u003eConsider an equilateral triangle sitting in Quadrant I as depicted in an example below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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=\\\"219\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"268\\\"/\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\u003eThis equilateral triangle is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the equilateral triangle, determine the angle between the red line splitting the regions and the positive x-axis (in degrees). The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 11 to 12, then these two numbers will be the first two numbers in the input. The last entry is the side of the 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edges from a vertex","description":"First input is T, a triplet list of indices. Second input is i, a single index (positive integer). The goal of this function is to find and return all the edges [e1 e2] this vertex belong to.\r\nFor example if inputs are\r\nT = [1 2 3 ;...\r\n 1 3 4 ;...\r\n 1 4 2 ;...\r\n 2 3 4]\r\nand\r\ni = 4\r\nthen the output is the 3 x 2\r\nmatrix edg_list= [1 4;...\r\n 3 4;...\r\n 2 4]\r\nsince vertex number 4 is linked with vertices number 1, 2, and 3 and then part of edges [1 4], [2 4], and [3 4]. Format of the output must be the following :\r\nsize(edg_list) = [number of edges, 2]\r\nEvery row of it is an edge at the format [e1, e2], sorted in ascending order, i.e. e1 \u003c e2, and e1, e2 positive integers.\r\nEach edge is present once and only once, no duplicated edge admitted\r\nOrder of rows / edges in the output doesn't matter .\r\nIf the vertex is not in the list, the function must of course return the empty set.\r\n\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","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: 632.2px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 316.1px; transform-origin: 408px 316.1px; 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: 375.725px 8px; transform-origin: 375.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFirst input is T, a triplet list of indices. Second input is i, a single index (positive integer). The goal of this function is to find and return all the edges [e1 e2] this vertex belong to.\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: 77.0167px 8px; transform-origin: 77.0167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example if inputs are\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: 405px 40.8667px; transform-origin: 405px 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 57.75px 8.5px; tab-size: 4; transform-origin: 57.75px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 46.2px 8.5px; transform-origin: 46.2px 8.5px; \"\u003eT = [1 2 3 ;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 57.75px 8.5px; tab-size: 4; transform-origin: 57.75px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 46.2px 8.5px; transform-origin: 46.2px 8.5px; \"\u003e 1 3 4 ;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 57.75px 8.5px; tab-size: 4; transform-origin: 57.75px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 46.2px 8.5px; transform-origin: 46.2px 8.5px; \"\u003e 1 4 2 ;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 42.35px 8.5px; tab-size: 4; transform-origin: 42.35px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 2 3 4]\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; 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: 405px 10.2167px; transform-origin: 405px 10.2167px; 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; text-wrap-mode: 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: 19.25px 8.5px; tab-size: 4; transform-origin: 19.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ei = 4\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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 82.45px 8px; transform-origin: 82.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen the output is the 3 x 2\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: 405px 30.65px; transform-origin: 405px 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 96.25px 8.5px; tab-size: 4; transform-origin: 96.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 26.95px 8.5px; transform-origin: 26.95px 8.5px; \"\u003ematrix \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 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 53.9px 8.5px; \"\u003eedg_list= [1 4\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 3.85px 8.5px; transform-origin: 3.85px 8.5px; \"\u003e;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 96.25px 8.5px; tab-size: 4; transform-origin: 96.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 84.7px 8.5px; transform-origin: 84.7px 8.5px; \"\u003e 3 4;\u003c/span\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); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\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: 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: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\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: 84.7px 8.5px; tab-size: 4; transform-origin: 84.7px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 2 4]\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; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; 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: 380.75px 8px; transform-origin: 380.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince vertex number 4 is linked with vertices number 1, 2, and 3 and then part of edges [1 4], [2 4], and [3 4]. Format of the output must be the following :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; 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: 392px 40.8667px; transform-origin: 392px 40.8667px; 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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 113.392px 8px; transform-origin: 113.392px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esize(edg_list) = [number of edges, 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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 240.742px 8px; transform-origin: 240.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEvery row of it is an edge at the format [e1, e2], sorted in ascending order, i.e.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\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: 23.5417px 8px; transform-origin: 23.5417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ee1 \u0026lt; e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 91.4083px 8px; transform-origin: 91.4083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and e1, e2 positive integers.\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 236.008px 8px; transform-origin: 236.008px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEach edge is present once and only once, no duplicated edge admitted\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: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 166.133px 8px; transform-origin: 166.133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOrder of rows / edges in the output doesn't matter\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e .\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; 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: 238.775px 8px; transform-origin: 238.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf the vertex is not in the list, the function must of course return the empty set.\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 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: 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\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; 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\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function edg_list = find_edges_from_vertex(T,i)\r\n edg_list = T;\r\nend","test_suite":"%% Tetrahedron\r\nT = [1 2 3;...\r\n 1 3 4;...\r\n 1 4 2;...\r\n 2 3 4];\r\n \r\ni = 4;\r\n\r\nedg_list = [1 4;...\r\n 2 4;...\r\n 3 4];\r\n \r\nassert(isequal(sortrows(find_edges_from_vertex(T,i)),edg_list))\r\n \r\n%% Triangulated cube\r\nT = [1 2 4;...\r\n 2 3 4;...\r\n 5 6 8;...\r\n 6 7 8;...\r\n 1 2 5;...\r\n 2 5 6;...\r\n 2 3 6;...\r\n 3 6 7;...\r\n 3 4 7;...\r\n 4 7 8;...\r\n 4 1 8;...\r\n 1 8 5];\r\n\r\ni = 7;\r\n\r\nedg_list = [3 7;...\r\n 4 7;...\r\n 6 7;...\r\n 7 8];\r\n\r\nassert(isequal(sortrows(find_edges_from_vertex(T,i)),edg_list)); \r\n\r\n%% Empty set test\r\nT = [2 3 5;...\r\n 3 5 7;...\r\n 5 7 11;...\r\n 7 11 13];\r\n \r\ni = 8;\r\n\r\nassert(isempty(find_edges_from_vertex(T,i)))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('find_edges_from_vertex.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:51:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":"2025-07-09T05:49:14.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-12-02T15:54:28.000Z","updated_at":"2025-11-18T16:58:11.000Z","published_at":"2019-12-03T07:32:15.000Z","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\u003eFirst input is T, a triplet list of indices. Second input is i, a single index (positive integer). The goal of this function is to find and return all the edges [e1 e2] this vertex belong to.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 if inputs are\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[T = [1 2 3 ;...\\n 1 3 4 ;...\\n 1 4 2 ;...\\n 2 3 4]]]\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\u003eand\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[i = 4]]\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\u003ethen the output is the 3 x 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[matrix edg_list= [1 4;...\\n 3 4;...\\n 2 4]]]\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 vertex number 4 is linked with vertices number 1, 2, and 3 and then part of edges [1 4], [2 4], and [3 4]. Format of the output must be the following :\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\u003esize(edg_list) = [number of edges, 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\u003eEvery row of it is an edge at the format [e1, e2], sorted in ascending order, i.e.\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\u003ee1 \u0026lt; e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and e1, e2 positive integers.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEach edge is present once and only once, no duplicated edge admitted\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOrder of rows / edges in the output doesn't matter\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\u003eIf the vertex is not in the list, the function must of course return the empty set.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\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:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\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":43294,"title":"Can we make a triangle?","description":"Given three positive number, check whether a triangle can be made with these sides length or not. remember that in a triangle sum of two sides should be greater than the third one. So with the lengths of 2,3 and 6 we can not make a triangle","description_html":"\u003cp\u003eGiven three positive number, check whether a triangle can be made with these sides length or not. remember that in a triangle sum of two sides should be greater than the third one. So with the lengths of 2,3 and 6 we can not make a triangle\u003c/p\u003e","function_template":"function flag = Is_Triangle(a, b, c)\r\n flag=false;\r\nend","test_suite":"%%\r\nassert(isequal(Is_Triangle(3,4,6),true))\r\n%%\r\nassert(isequal(Is_Triangle(6,4,3),true))\r\n%%\r\nassert(isequal(Is_Triangle(3,7,4),false))\r\n%%\r\nassert(isequal(Is_Triangle(4,3,7),false))\r\n%%\r\nassert(isequal(Is_Triangle(3,3,4),true))\r\n\r\n","published":true,"deleted":false,"likes_count":16,"comments_count":3,"created_by":94830,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2256,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-10T06:51:56.000Z","updated_at":"2026-04-04T19:14:04.000Z","published_at":"2016-10-10T06:51:56.000Z","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 three positive number, check whether a triangle can be made with these sides length or not. remember that in a triangle sum of two sides should be greater than the third one. So with the lengths of 2,3 and 6 we can not make a triangle\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":58354,"title":"Find the circle inscribed in 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 center and radius of a circle inscribed in the triangle (i.e., tangent to each of the three sides).","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: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; 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 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: 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 center and radius of a circle inscribed in the triangle (i.e., tangent to each of the three sides).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [x0,y0,r] = incircle(x,y)\r\n% x = vector of x-coordinates of the triangle's vertices\r\n% y = vector of y-coordinates of the triangle's vertices\r\n% (x0,y0) = coordinates of the incircle's center\r\n% r = radius of the incircle\r\n [x0,y0,r] = Delaunay(something(x),something(y));\r\nend","test_suite":"%%\r\nx = [0 1 0];\r\ny = [0 0 1];\r\nx0_correct = 0.29289321881;\r\ny0_correct = 0.29289321881;\r\nr_correct = 0.29289321881;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nth = pi/2:2*pi/3:11*pi/6;\r\nx = cos(th);\r\ny = sin(th);\r\nx0_correct = 0;\r\ny0_correct = 0;\r\nr_correct = 0.5;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [1 4 5];\r\ny = [2 3 6];\r\nx0_correct = 3.47213595500;\r\ny0_correct = 3.52786404500;\r\nr_correct = 0.66770107084;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [1 4 5];\r\ny = [2 3 6];\r\nx0_correct = 3.47213595500;\r\ny0_correct = 3.52786404500;\r\nr_correct = 0.66770107084;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [-1 4 5];\r\ny = [2 -3 6];\r\nx0_correct = 2.36290232380;\r\ny0_correct = 1.66700704764;\r\nr_correct = 2.14246946292;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [12 3 45];\r\ny = [6 78 9];\r\nx0_correct = 23.24160585487;\r\ny0_correct = 19.96162835361;\r\nr_correct = 12.88652365580;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [-1 0 1];\r\ny = [0 19 0];\r\nx0_correct = 0;\r\ny0_correct = 0.94875250476;\r\nr_correct = 0.94875250476;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [10 15 20];\r\ny = [30 45.1 60];\r\nx0_correct = 15.01499995500; \r\ny0_correct = 45.09499981499; \r\nr_correct = 0.01581137249;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nL = 100*rand;\r\nx = [0 L 0];\r\ny = [0 0 L];\r\nd_correct = L/(2+sqrt(2)); \r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-d_correct)\u003c1e-10)\r\nassert(abs(y0-d_correct)\u003c1e-10)\r\nassert(abs(r-d_correct)\u003c1e-10)\r\n\r\n%%\r\nfiletext = fileread('incircle.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-05-20T15:34:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-20T15:33:53.000Z","updated_at":"2023-05-20T15:34:18.000Z","published_at":"2023-05-20T15:34:18.000Z","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 x- and y-coordinates of three points describing the vertices of a triangle and returns the center and radius of a circle inscribed in the triangle (i.e., tangent to each of the three sides).\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":61090,"title":"Covering a 4-pointed star polygon by a circle sector","description":"Given the area, A, of a 4-pointed star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, consider the circle that covers the greater of the two distances between opposite vertices (cf. figure below).\r\nGiven (A,h), find\r\nthe width, L, of the rectangle;\r\nthe angle, α [in Radians], of the sector of the circle such that its area is equal to A;\r\nthe minimum slicing number n, corresponding to the number of congruent circle slices, such that the area of one slice does not exceed the above sector area.\r\ninput: (A, h)\r\noutput: y = [L alpha n]\r\n","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: 751.55px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 375.775px; transform-origin: 408px 375.775px; 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; 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=\"\"\u003eGiven the area, \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; \"\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=\"\"\u003e, of a 4-pointed star polygon formed by the rectangle, with dimensions \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×\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; \"\u003e2L\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, and four triangles, with height \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; \"\u003eh\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 from their bases to the vertices, consider the circle that covers the greater of the two distances between opposite vertices (cf. figure below).\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=\"\"\u003eGiven \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(A,h)\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, find\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.75px; 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 40.875px; transform-origin: 391px 40.875px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; 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=\"\"\u003ethe width, \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL,\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the rectangle;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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=\"\"\u003ethe angle, \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eα\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e [in Radians], of the sector of the circle such that its area is equal to \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; 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 20.4375px; text-align: left; transform-origin: 363px 20.4375px; 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=\"\"\u003ethe minimum slicing number \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; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, corresponding to the number of congruent circle slices, such that the area of one slice does not exceed the above sector area.\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=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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 \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(A, h)\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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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 \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; \"\u003ey = [L alpha n]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 486.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 243.4px; text-align: left; transform-origin: 384px 243.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"601\" height=\"481\" style=\"vertical-align: baseline;width: 601px;height: 481px\" 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\" alt=\"Covering by sector\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = covering_by_sector(A,h)\r\n y = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nh = 1;\r\ny_correct = [3 3.375 2];\r\nassert(isequal(covering_by_sector(A,h),y_correct))\r\n\r\n%%\r\nA = 36;\r\nh = 2;\r\ny_correct = [3 2.88 3];\r\nassert(isequal(covering_by_sector(A,h),y_correct))\r\n\r\n%%\r\nA = 45;\r\nh = 3;\r\ny_correct = [3 2.5 3];\r\nassert(isequal(covering_by_sector(A,h),y_correct))\r\n\r\n%%\r\nfiletext = fileread('covering_by_sector.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 56;\r\nh = 2; \r\ny_correct = [4 28/9 3];\r\nassert(all(isapprox(covering_by_sector(A,h),y_correct), 'all'))\r\n\r\n%%\r\nA = 50;\r\nh = 5; \r\ny_correct = [2.5 16/9 4];\r\nassert(all(isapprox(covering_by_sector(A,h),y_correct), 'all'))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-12-03T10:39:21.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-30T14:56:09.000Z","updated_at":"2026-03-23T10:36:12.000Z","published_at":"2025-12-03T10:39:21.000Z","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\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a 4-pointed star polygon formed by the rectangle, with dimensions \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×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, consider the circle that covers the greater of the two distances between opposite vertices (cf. figure 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":769,"title":"Calculate the area of a triangle between three points","description":"Calculate the area of a triangle between three points:\r\nP1(X1,Y1)\r\nP2(X2,Y2)\r\nP3(X3,Y3)\r\nthese three points are the vertices of the triangle.","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: 141px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 70.5px; transform-origin: 407px 70.5px; 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: 167.5px 8px; transform-origin: 167.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the area of a triangle between three points:\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=\"\"\u003eP1(X1,Y1)\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=\"\"\u003eP2(X2,Y2)\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=\"\"\u003eP3(X3,Y3)\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: 155.5px 8px; transform-origin: 155.5px 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