{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","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":"2025-12-14T00:00:00.000Z","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":55530,"title":"Jump Search - 01","description":"Find the number of leaps you need to take to find an element in an array using the jump search algorithm.\r\nFor example, \r\na=[ 2,5,6,9,12,14,15,16,17,19,31]\r\nTo find 16 with a jump step of 3, you follow,  2 -\u003e 9 -\u003e 15 -\u003e 19 -\u003e 17 -\u003e 16\r\nSo, total number of jumps = 5\r\nnb. to go forward, you take n-step jump; to go backwards, you jump only one step back. \r\nIf the jump step is larger than the array size, u jump to the last element of the array.","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: 201.438px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 100.713px; transform-origin: 407px 100.719px; 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=\"\"\u003eFind the number of leaps you need to take to find an element in an array using the jump search algorithm.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-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=\"\"\u003ea=[ 2,5,6,9,12,14,15,16,17,19,31]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-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=\"\"\u003eTo find 16 with a jump step of 3, you follow,  2 -\u0026gt; 9 -\u0026gt; 15 -\u0026gt; 19 -\u0026gt; 17 -\u0026gt; 16\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-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=\"\"\u003eSo, total number of jumps = 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: 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=\"\"\u003enb. to go forward, you take n-step jump; to go backwards, you jump only one step back. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIf the jump step is larger than the array size, u jump to the last element of the array.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = jump_search(a,x,n)\r\n  y = x;\r\nend","test_suite":"%%\r\na=[ 2,5,6,9,12,14,15,16,17,19,31];\r\nx=16;\r\nn=3;\r\ny_correct = 5;\r\nassert(isequal(jump_search(a,x,n),y_correct))\r\n\r\n%%\r\na=[ 2,5,6,9,12,14,15,16,17,19,31];\r\nx=15;\r\nn=1;\r\ny_correct = 6;\r\nassert(isequal(jump_search(a,x,n),y_correct))\r\n\r\n\r\n%%\r\na=[ 2,5,6,9,12,14,15,16,17,19,31];\r\nx=2;\r\nn=5;\r\ny_correct = 0;\r\nassert(isequal(jump_search(a,x,n),y_correct))\r\n\r\n\r\n%%\r\na=[ 2,5,6,9,12,14,15,16,17,19,31];\r\nx=31;\r\nn=12;\r\ny_correct = 1;\r\nassert(isequal(jump_search(a,x,n),y_correct))\r\n\r\n\r\n%%\r\na=[ 2,5,6,9,12,14,15,16,17,19,31];\r\nx=17;\r\nn=12;\r\ny_correct = 3;\r\nassert(isequal(jump_search(a,x,n),y_correct))\r\n\r\n%%\r\na=[1,5,9,14,17,18,23,33,36,38];\r\nx=38;\r\nn=2;\r\ny_correct = 5;\r\nassert(isequal(jump_search(a,x,n),y_correct))\r\n\r\n%%\r\na=[1,5,9,14,17,18,23,33,36,38];\r\nx=11;\r\nn=4;\r\ny_correct = nan;\r\nassert(isnan(jump_search(a,x,n)))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":4,"created_by":363598,"edited_by":363598,"edited_at":"2022-09-30T16:20:21.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2022-09-29T13:10:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-08T04:51:33.000Z","updated_at":"2025-12-15T02:19:46.000Z","published_at":"2022-09-28T12:58:17.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the number of leaps you need to take to find an element in an array using the jump search algorithm.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=[ 2,5,6,9,12,14,15,16,17,19,31]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo find 16 with a jump step of 3, you follow,  2 -\u0026gt; 9 -\u0026gt; 15 -\u0026gt; 19 -\u0026gt; 17 -\u0026gt; 16\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo, total number of jumps = 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\u003enb. to go forward, you take n-step jump; to go backwards, you jump only one step back. \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 jump step is larger than the array size, u jump to the last element of the array.\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":44756,"title":"Lights Out 5 - 5x5, 10 moves","description":"\u003chttps://en.wikipedia.org/wiki/Lights_Out_(game) Lights Out\u003e is a logic game wherein all lights need to be turned off to complete each board. See \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44751-lights-out-1-5x5-3-moves the first problem in the series\u003e for an introduction.\r\n\r\nThis problem contains boards that each require ten moves to solve. For example, if\r\n\r\n board = [0 1 1 0 1  \r\n          1 1 1 1 1  \r\n          1 1 1 1 1  \r\n          1 1 1 1 1  \r\n          0 1 1 0 1]\r\n\r\nan answer is:\r\n\r\n moves = [1 2 3 4 5 16 17 18 19 20]\r\n\r\nPrev.: \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44755-lights-out-4-5x5-8-moves 5x5, 8 moves\u003e — \r\nNext: \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44757-lights-out-6-5x5-13-moves 5x5, 13 moves\u003e","description_html":"\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Lights_Out_(game)\"\u003eLights Out\u003c/a\u003e is a logic game wherein all lights need to be turned off to complete each board. See \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44751-lights-out-1-5x5-3-moves\"\u003ethe first problem in the series\u003c/a\u003e for an introduction.\u003c/p\u003e\u003cp\u003eThis problem contains boards that each require ten moves to solve. For example, if\u003c/p\u003e\u003cpre\u003e board = [0 1 1 0 1  \r\n          1 1 1 1 1  \r\n          1 1 1 1 1  \r\n          1 1 1 1 1  \r\n          0 1 1 0 1]\u003c/pre\u003e\u003cp\u003ean answer is:\u003c/p\u003e\u003cpre\u003e moves = [1 2 3 4 5 16 17 18 19 20]\u003c/pre\u003e\u003cp\u003ePrev.: \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44755-lights-out-4-5x5-8-moves\"\u003e5x5, 8 moves\u003c/a\u003e — \r\nNext: \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44757-lights-out-6-5x5-13-moves\"\u003e5x5, 13 moves\u003c/a\u003e\u003c/p\u003e","function_template":"function moves = lights_out_5(board) % 5x5 board, 10 moves\r\n moves = board;\r\nend","test_suite":"%% \r\n board = [0 1 1 0 1  \r\n          1 1 1 1 1  \r\n          1 1 1 1 1  \r\n          1 1 1 1 1  \r\n          0 1 1 0 1];\r\nmoves = lights_out_5(board); % [1 2 3 4 5 16 17 18 19 20]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [0 0 0 0 0  \r\n          1 1 1 0 0  \r\n          0 0 0 0 1  \r\n          1 1 0 0 1  \r\n          0 0 1 0 1];\r\nmoves = lights_out_5(board); % [1 2 3 11 13 14 16 17 21 24]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [1 0 0 0 1  \r\n          0 1 1 0 0  \r\n          0 1 0 0 0  \r\n          0 0 0 0 0  \r\n          1 0 0 0 0];\r\nmoves = lights_out_5(board); % [1 2 3 4 6 7 8 11 12 16]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [1 1 0 1 1  \r\n          0 0 1 1 0  \r\n          1 1 0 1 0  \r\n          1 1 0 0 0  \r\n          0 1 0 0 0];\r\nmoves = lights_out_5(board); % [3 6:7 11 13:15 19 22:23]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [1 0 1 0 1  \r\n          0 1 1 0 0  \r\n          0 0 1 0 0  \r\n          0 1 0 1 0  \r\n          1 0 1 1 0];\r\nmoves = lights_out_5(board); % [2 3 9 10 14 16 17 20 23 24]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [1 0 0 1 1  \r\n          0 1 0 0 0  \r\n          0 0 1 0 0  \r\n          0 0 0 0 1  \r\n          1 1 1 0 1];\r\nmoves = lights_out_5(board); % [2 4 7 9 11 12 17 19 20 21]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [0 0 0 1 1  \r\n          1 0 1 0 0  \r\n          1 0 1 0 1  \r\n          1 0 0 1 0  \r\n          1 1 0 1 1];\r\nmoves = lights_out_5(board); % [1 4 6 12 14 15 18 21 23 24]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [0 1 1 1 1  \r\n          0 0 0 1 1  \r\n          1 1 0 0 0  \r\n          1 0 0 1 0  \r\n          1 1 1 1 0];\r\nmoves = lights_out_5(board); % on your own\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [0 1 1 1 1  \r\n          1 0 1 1 0  \r\n          0 1 1 1 0  \r\n          0 1 1 1 1  \r\n          1 1 0 0 1];\r\nmoves = lights_out_5(board);\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [1 1 1 1 0  \r\n          0 1 1 0 1  \r\n          0 1 0 1 0  \r\n          1 0 1 1 0  \r\n          0 1 1 1 1];\r\nmoves = lights_out_5(board);\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [0 1 0 1 0  \r\n          0 0 0 1 1  \r\n          1 0 1 0 0  \r\n          1 0 1 1 0  \r\n          0 1 1 0 0];\r\nmoves = lights_out_5(board);\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [1 0 0 1 1  \r\n          0 0 1 1 0  \r\n          0 1 0 0 0  \r\n          0 1 1 0 0  \r\n          0 0 0 0 0];\r\nmoves = lights_out_5(board);\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [0 1 1 0 1  \r\n          0 0 0 1 1  \r\n          0 1 1 0 0  \r\n          1 1 1 1 0  \r\n          0 0 1 1 0];\r\nmoves = lights_out_5(board);\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [0 0 1 1 1  \r\n          0 0 1 0 0  \r\n          0 0 1 0 0  \r\n          0 0 1 0 0  \r\n          0 0 1 1 1];\r\nmoves = lights_out_5(board);\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)","published":true,"deleted":false,"likes_count":3,"comments_count":8,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2018-11-13T13:07:28.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-10-29T18:53:12.000Z","updated_at":"2025-11-29T13:41:10.000Z","published_at":"2018-11-12T15:53:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Lights_Out_(game)\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLights Out\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a logic game wherein all lights need to be turned off to complete each board. See\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44751-lights-out-1-5x5-3-moves\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ethe first problem in the series\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for an introduction.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem contains boards that each require ten moves to solve. For example, if\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ board = [0 1 1 0 1  \\n          1 1 1 1 1  \\n          1 1 1 1 1  \\n          1 1 1 1 1  \\n          0 1 1 0 1]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ean answer is:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ moves = [1 2 3 4 5 16 17 18 19 20]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrev.:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44755-lights-out-4-5x5-8-moves\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e5x5, 8 moves\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e — Next:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44757-lights-out-6-5x5-13-moves\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e5x5, 13 moves\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":39,"title":"Which values occur exactly three times?","description":"Return a list of all values (sorted smallest to largest) that appear exactly three times in the input vector x. So if\n\n x = [1 2 5 2 2 7 8 3 3 1 3 8 8 8]\n\nthen \n\n y = [2 3]","description_html":"\u003cp\u003eReturn a list of all values (sorted smallest to largest) that appear exactly three times in the input vector x. So if\u003c/p\u003e\u003cpre\u003e x = [1 2 5 2 2 7 8 3 3 1 3 8 8 8]\u003c/pre\u003e\u003cp\u003ethen\u003c/p\u003e\u003cpre\u003e y = [2 3]\u003c/pre\u003e","function_template":"function y = threeTimes(x)\n  y = x\nend","test_suite":"%%\nx = [1 2 5 2 2 7 8 3 3 1 3 8 8 8];\ny_correct = [2 3];\nassert(isequal(threeTimes(x),y_correct))\n\n%%\n\nx = [1 1 1];\ny_correct = [1];\nassert(isequal(threeTimes(x),y_correct))\n\n%%\n\nx = [5 10 -3 10 -3 11 -3 5 5 7];\ny_correct = [-3 5];\nassert(isequal(threeTimes(x),y_correct))","published":true,"deleted":false,"likes_count":23,"comments_count":5,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5240,"test_suite_updated_at":"2012-01-18T01:00:22.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:22.000Z","updated_at":"2026-03-25T03:10:27.000Z","published_at":"2012-01-18T01:00:22.000Z","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\u003eReturn a list of all values (sorted smallest to largest) that appear exactly three times in the input vector x. So 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[ x = [1 2 5 2 2 7 8 3 3 1 3 8 8 8]]]\u003e\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\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ y = [2 3]]]\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":56040,"title":"A Binary Search","description":"One way to locate a target value in a sorted array, is to use a binary search algorithm. Here, you test if the midpoint in the array is the target value. If it is, great! You're done. If not, then you continually narrow your search area depending on whether the target is less than or greater than the midpoint. The algorithm is as follows:\r\nGiven an array of sorted values (X), and a target value you wish to locate (target)\r\nCalculate the index of the midpoint of the array X by taking the average of the largest and smallest indices and rounding to the nearest integer.  \r\nIf the value located at the midpoint matches your target, set found to true.\r\nIf the target is less than the value located at the midpoint of X, narrow your search to the lower half of X by setting the largest index in the array to the midpoint - 1. \r\nIf the target is greater than the value located at the midpoint of X, narrow your search to the upper half of X by setting the smallest index in the array to the midpoint + 1. \r\nRepeat the steps above until found is true.\r\n\r\nWrite a function that takes X and target as inputs, performs a binary search and outputs the index of target value as well as the number of iterations it took to find the target.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 926.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 463.233px; transform-origin: 407px 463.233px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.5px 8px; transform-origin: 383.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOne way to locate a target value in a sorted array, is to use a binary search algorithm. Here, you test if the midpoint in the array is the target value. If it is, great! You're done. If not, then you continually narrow your search area depending on whether the target is less than or greater than the midpoint. The algorithm is as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; 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: 104px 8px; transform-origin: 104px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven an array of sorted values (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\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: 126.5px 8px; transform-origin: 126.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e), and a target value you wish to locate (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; \"\u003etarget\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.5px 8px; transform-origin: 2.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 164.967px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 82.4833px; transform-origin: 391px 82.4833px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 41.3667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.6833px; text-align: left; transform-origin: 363px 20.6833px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 149px 8px; transform-origin: 149px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the index of the midpoint of the array \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003eX\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 195.5px 8px; transform-origin: 195.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by taking the average of the largest and smallest indices and rounding to the nearest integer.  \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 231px 8px; transform-origin: 231px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf the value located at the midpoint matches your target, set found to true.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 41.3667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.6833px; text-align: left; transform-origin: 363px 20.6833px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 188px 8px; transform-origin: 188px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf the target is less than the value located at the midpoint of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003eX\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 127px 8px; transform-origin: 127px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, narrow your search to the lower half of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003eX\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 34.5px 8px; transform-origin: 34.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by setting the largest index in the array to the midpoint - 1. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 41.3667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.6833px; text-align: left; transform-origin: 363px 20.6833px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 198.5px 8px; transform-origin: 198.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf the target is greater than the value located at the midpoint of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003eX\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 129px 8px; transform-origin: 129px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, narrow your search to the upper half of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003eX\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 11.5px 8px; transform-origin: 11.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by setting the smallest index in the array to the midpoint + 1. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 134px 8px; transform-origin: 134px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRepeat the steps above until found is true.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 556.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 278.25px; text-align: left; transform-origin: 384px 278.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 610px;height: 551px\" 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Eyedf2ybnk6ab2TTK15eD1/EXusTxeHP12PLqdpR1n/Svr7Q+LK6h42F6kV+eF9UFrH6TFkTszn97tVZ2MS2FzE/LJ9MruCX0Gi4fyI70r2LmFS7WRGbP4284Ki2i1O67eyz2q5FLGdjZfl+vOYtMLb6bbrsMXbONFUOB/VQtXLwSm6ZptxljdVpCvlQVQxb97o2hSLB4pkTWftsus61mX74VSva1qc53V6KU5tzz+7QRdemeGiG6anhlDOZdZdmfZrmSW16ekpkK4oAK6/NwxexQdmNpnaUvrK1/C30Y+exBc9e+GJtkbbXV8uy+mMzjZPpTP7lr2fjx5tTEptJy148ezacyyfzoJPxnDFtlNGpNIdT/EoZDfdP0+WjSal2++Hb7IaYf06p6bVsF6d021UfTX7vv2Hsot+3ZkGeVMTsvXB+z1v5Dtiw+m360/zbZz5ca3r4j/R54LbhpAyzKd4t0/iMf/vFv/Kzwuo0hfykNj3FyWMmt7k2heISlGNtyCKd2cQ9PU3xw5cPYWNF2/o0drwvm7/7qn5Azjy7Qxddm+HQ87FtRpPtB+3aaVon9Uum6eKsNnni2R06YBFTO5oWpJYz3j1S58luJqXtswWp5ZR9StPlyZZn0rzmpgowrk/HnQ9Vsf2n1bZ1eMtrqorTeXGCLtZVilj6sv4lJWPkSYyq0Band6u/Qnae7eKUbqv0a101k4rYZPtfabC9nlLEFmOlz+mbxCvelxcuGjT8LTh61/V34zJEPbadcMs0vtVoxZ2Ey9Kk7zlrZjGGlnODm1+bMo3Op69i1zXE+CpNn/L0NBamuJ8yrmmuaFufxp8Tk+U1SBeoJXh2hy66NnZsTafn6ngJyodwsnho21anaZ20vCjZXLbNoJxrOWARq+4WpX6kmdRi8jbk2xf1yDeZSlC5Oj/ZorGNZxr39Jn8yFWyBTt2cVpNZlJ8U/wVBDTpcj25iM0t4wmfvt2uiHkP2/rr9W0fp3QbpL87aebGVRSx7U3MdnpKEcvfMNPo8KW/jZt5+UqXDBrpbToYkdIopxk5PbYt3DKNbzZZc6E2ppnH+OngNqPJQTk3uOW1CdL4JUgDuImamO8VV7TSFdLYnCbT6vG8zRVN69PMQdziyCcfkLSrZk7ZeG2cPSrzpfFTpb+r6Q9XGXP+Ga76LG6dtLwo2ZxtlKZMOddyvCKWylDRUrwAqeGkJpPfavIFmk58mxVFzCbLMxUn9+livS/QdMBy5qct2mGS4g+K06JN1+upRczvhbmn9LCbFTHvYZsP6jsZpdtAOxZ9qyxim5uY7fOUIla+4y1GlvODVunSQSN6001RFgPZzYvY2jRpu8mKMWxjGh04P7TNaXJQzg1ueW3sZC77Qc9fgtWJrpQmzeo5PJ64uaJpfZrTL5dTP3747A5tvDbOjq1JUz5SiwdKS8MHsLY+TeOk5UXJ5myrNGXKuZbjFbGyRSW2SNunJpOmE/sVXWXl8To1LSpm8pMtYjhbNJ49n068EbYrlK3WpB98cWyTbqqZ87+VDEaX62pF7Gn/xpEOcu0ilnrY1l8jdpUiln1Q60XM//nJ9Jnlxs9wbZcnFDF7J8zegW02t+rNeXbBoJHer+vCl0aq5flPjW2VW6bxDf0DOX02lxafsDGNHdTNR7Y5TQ7KucEtr42dzGUn0JJJfdXipYErpPFnrj1A41N4XNdc0bQ+jT8t0m2fdPS0WGxR42Txszu08doYO3Fx7LwULU+qxSuui9mQJj5peVGyOdssTZlyruV4RcxmlmXH60uajNrT0soi5kdd1KF8V5ssk5wpYrZWk75pULXmIjacpn0kTHSxnlrE9vzRpH7B/uYe9pQiFn00OVyj6V8Bt8u18ZaYHewJRczeLbN34DScDIuG8XNlwchtHjTSgBSM1uldvBqpToxttZum+XL+XpStrZJWNqZRlsF0aJvR5KCcG9zy2gRpxhHcekhareUTX6rp066QRo/RbLoUzRUtG9J8mmpYmhwUT532A9J4doc2Xhtjh89PPF8vs3h6hxezaX2axknLi5LN2VZpypRzLQctYpoe+Rap1lyxiNnU8kzps8k07ZNFWSqTLtna6UTWuDSZ87/aefJvYKKUrtRAw/0TfEg3ep5yJN/fqApt0dot9bBvt/ewpxSxwYf0dxcaN762H9b2eEIRW7zh2RvjIL1t+nDhU2ttHTTSm/XyV4IO0khVj2K3LBvb04xsrSbbtqYZ8ug2y3ji8jTl3OCm16ZO4wHG0dsv3fLk6wNdIc34KE3mh7G5omF7Glf9uM2f/9zzqXBBGju6Jk1ZiYILEFzMltVpWictL0o2ZxulKVPOtRyuiJUlSnyLrIid/FRv/BeLNNssYuGZ8vblkz41KpJWbO2UrNq3lJpYdXZU/EIZDfdP89S/NulJjKrQFo3d9Hv3NbeJ72mUbrP0bxxppmRrtt07tENdXsTsjTD/D+H09jm+aebTq2wcNNLbf/0f4unrvdGpy7fxM26eZmQbnL1OG9Mk6dyaKVNkK5JbXpukSJPqxHi5lk8kY+vXPX2ukGbg88Y/Lc7O3FwRuyjNkGc4dnEJGg/I+edTYXua5WPh5/P/vkgfo9dP8eBiNqxO0zppGS67RLbRfE1sTpMnHLOIhdIOvnFcxOwfdJw/+puOX8xkJ4uLmB/gsiJmu+Y/RnXsXAp6slHC+HUyGu6fyJrY5r8POEtRBqpCW8S7pa+Hbf37konvapTuArZ32LfuXcTsPbIYK+wNcFpQrT1n26Dhb9DBCVIbDO5MFW/c5908zch2PbXebUszsZPr2MVpqmH/ltdmkqXx802DpV8lTUuwqOUKacyn+o1e1ZmbK0IXpqkekfgB8Qynn0+F7Wn8Z9X0wE84nq59BfKt2tamaZ7UpuerlD2lzzy7Q4crYj4TSjv4+rq/VL8Bfz5+MZOdLD7SE4pYvrltebpl+YlOdjUYu0xOw/1TPe1QnsSoCm0R7Xbx18Nc2nmgdBewYhreIbx3ERve78q3ZVswvYlvGtrNlkHD352j9357R269Dd+sbFyUZlSMIS1b0mSyn7j44W2mTHWza5PJz2HT85OnmHEb8lwhTc4ej/DMzRWFC9NU5SGMt+b5VNiexk6gSeNPbU2fuATrHq61adonLVbYjF45xfltZsU1oogNFv/kd3LPItYObbTRQtpHM2jyy2Q03D/V0w7lSYyq0BbBbpd/Pcz53kbpLtAsYnbYOxax+v3O3jKnJbb6bMHIbRg0UvMJbgykkaoxJKwbLeTmaUa2yR2KmIccz2PTZaxbXZtcfo4ijuVZjJzF6tOukCbjj1l05uaK0hPSFJcgirfq+VTYnGaZo4zRuGYnVhTWpmmf1K7AGM+Wj63szLM7RBFbfpr5+sXiQ8diJjtZcKTB3YpYOnxwMBT8MhkN90/U/lLUKp7EqAptUe+WPpa86Othznc3Sred/+XJVMSGyayRXXCdbI+Li5i9KZbvd/7WqLfDcqRdY/2gkQakxdA9SI2oedZ1o4XcLs2wPEvhe2u6bX2anCcYz2XTCpkPZ3Kja5Mr0uRxgjy+rabPuUaakS+NnkDNFUur03yZV/c6Tf2ApAi3ek2JPRT5aS3G/NC0zh9fzMraNO2T2hrN+DmnMDajXYJnd+iYRezEh3r1+qmHvX79Iq1YV8R8q45FLDsT2vwSGg33mw0FY/zdYSf/muAqvr9RFdpiudsPi98e9u3mTyh9f6N0qwwV64OuR/G3SG1a/8bkh/Ql/o3XyXa5uIjZe58mR94q7A05+s1I56x9m15+X/nLcTKdc3oP/nT5dmzrz48Wcrs0PlCkHJ+mva83hNnBPx0DpGRpxgIMbOwPz3mTa3MizRwn/F1qW+JcIc3n/uDoSZs/bZormtamSd0lxYleLdUVSNtMEapnd2j1tRnZOTSZ+Fk9SPqS3Pj0PvHQNq1O48cLTppePL5mcclOP7tDhytiZYmq+cZFfbIFwy5ZpdlQxKoz2UJVp2xSiqQZX96kjZYoYqv4JTQa7jfT7hmtuISOsK2I6Ytgs1S40l+XLPjy9bTXpp8oddGc+lYqZbm0fDXb5dIiZm94y7EgvWtOprfPVda+TWtUzKUVmsmM78dppJitGMNul2YZ5ppDWJ1mHpKK885X4K7XJhsgy/OWZ/Xn0dpnz9PTlE/bLEpzRdvaNIuXyuDMk1VzmexitqxNM7Jzlz/mMo1OevKhbVmdpnHSQXnZsqdIscuqR+pwRWzRmyq+cV7EUgkqCs26IhYUrUG2MJuUMulCvrVtmIW0v89Z3Xyz7SliZ/llMhruN6sKxrZvPpV0iG2VSbtkfHGfIjb/JlcZ/w5ptWLrdbJ9Li1i9oZXvflufzucrX2b3l59Lhk1bpemGoJXNI61aapj549B/uBo0W2vzck0zSF14KE0fdbT0xRr8iTNFW1r01RlY0zTekA0kzn/QK1PI8Fhy5xjypMPbcv6NPFJTX7iImn47D7lmEVsWY9e2MeOaQvfOO80fmOpLDnl8YuZ/GQ2tWxC+a6+Pk1KmXRhWDWdxkJlmcpAibfF5Q+Kil8mo+F+s/Qx2+QJn0sOdJBbFbGNn01qr23Xprwllv2LT+WF2n6dbK+nFDFNZrJhZMU4UVj7Nh1UnzRGaiajd/Bblo3tacZPM2XVZVqbZhFn8RcIpvNmI9str83pNNllWKzx/VY/fa6QZk6yOGtzRdPqNGWcOU3rAdFMZkX3WZ8mscNqcpIHmq9C+2K2bUgTn9TMTWxxzujZfcrxipgXq0VpsUXawjfOe1e2blQeopjJTxbVo7zW2eT6ImbrinNq0tn8onT5sShiZ/llMhruL/H9u9Qx3n0//RM+F/LDGFWhVdZ/NHmPIjY0Ln037N1wPbRIxgt10XWyHS8tYsMbYvjum74x8uX0b/istvZtuh6pzlafeTxNrjiEXZBm8Ln/bqphjFl5mdamGXyqr+x8+eXnVXlIX0aa/mEdd8NrMziVZoxT5nFfrh1NB9dIk5YHD0ZzRcuGNHOcIk1aNtOV0Fzmuo+Ui1/UerYursLJhza0KU18UtN6TKJn9wnHK2LpTlHRdvLO4tOni1g6wvkiduZMQXsqk5Zs3ZRruWfdLtPJ8x8EIb9ORsN9X8qy+UPE21CWHV2bi7+sf21bB43bIk0badpI07avNIcpYnMl8dKS15iisyw2DopY2rwsYvPh8i6VzpTtW1Y4n9F0ku+8ZAcbV9l2Re3yHYs9q58SMb9ORsN9X8pCEQtYEIpYiDRtpGkjTdu+0hyhiHn9WcxmrUXzmvN98yK27DjafD6gV55pvW+uudNn2ljE8o1tu/JmV+pd0zL9CtrGoZDxC2U03PelLBSxgAWhiIVI00aaNtK07SvNYYrY0FJe5N/HHzbw2jL+1vyxs/jKvOSUbSr7p47SgrEDvR4Ob3NFl9K+r5/ZgnHXceX2IlZ0v7KIjWdKP9P4E/oqnJQu1UDDfV/KQhELWBCKWIg0baRpI03bvtIcoYjNY606zlymJlP7qYrYvPXr8Z/8Tn9oddrD+BnLLqV+lJt7ls9qOil3LtiqoohpchSciR62hi4WRSygLBSxGoNGG2naSNNGmrZDFLGpKo0Fq2otc/nxbcu7Tcve9mxRmHyhsZlyVXWm/PfC+gJNJ4udc7ZqilXtOKj+Qcz4OFjQ1aKIBZSFIlZj0GgjTRtp2kjTdogiNlWpuWAVrUUfWTrftyxiadnI1nm9mjaaypbNLLvU+DFhUhzYl2g6We6cscDjGjthcLurPBM9bB1dL4pYQFkoYjUGjTbStJGmjUeq7RhFbKxD+bIX+qBx/OaY+IaLIjYs1f76xyaXHUpf/7ID+YZlCRpPPu488qWaToKdR/m2tlkV0Uw/Ey1sNb9gRsN9X8pCEQtYEIpYiDRtpGkjTdu+0jxkETuiYRCaaqS1rbCIYTsb3p2G+76UhSIWsCAUsRBp2kjTRpq2faWhiOHYvGgYDfd9KQtFLGBBKGIh0rSRpo00bftKQxHDsXnRMBru+1IWiljAglDEQqRpI00badr2lYYihmPzomE03PelLBSxgAWhiIVI00aaNtK07SsNRQzH5kXDaLjvS1koYgELQhELkaaNNG2kadtXGooYjs2LhtFw35eyUMQCFoQiFiJNG2naSNO2rzQUMRybFw2j4b4vZaGIBSwIRSxEmjbStJGmbV9pKGI4Ni8aRsN9X8pCEQtYEIpYiDRtpGkjTdu+0lDEcGxeNIyG+76UhSIWsCAUsRBp2kjTRpq2faWhiOHYvGgYDfd9KQtFLGBBKGIh0rSRpo00bftKQxHDsXnRMBru+1IWiljAglDEQqRpI00badr2lYYihmPzomE03PelLBSxgAWhiIVI00aaNtK07SsNRQzH5kXDaLjvS1koYgELQhELkaaNNG2kadtXGooYjs2LhtFw35eyUMQCFoQiFiJNG2naSNO2rzQUMRybFw2j4b4vZaGIBSwIRSxEmjbStJGmbV9pKGI4Ni8aRsN9X8pCEQtYEIpYiDRtpGkjTdu+0lDEcGxeNIyG+76UhSIWsCAUsRBp2kjTRpq2faWhiOHYvGgYDfd9KQtFLGBBKGIh0rSRpo00bftKQxHDsXnRMBru+1IWiljAglDEQqRpI00badr2lYYihmPzomE03PelLBSxgAWhiIVI00aaNtK07SsNRQzH5kXDaLjvS1koYgELQhELkaaNNG2kadtXGooYjs2LhtFw35eyUMQCFoQiFiJNG2naSNO2rzQUMRybFw2j4b4vZaGIBSwIRSxEmjbStJGmbV9pKGI4Ni8aRsN9X8pCEQtYEIpYiDRtpGkjTdu+0lDEcGxeNIyG+76UhSIWsCAUsRBp2kjTRpq2faWhiOHYvGgYDfd9/f/t3QuzI8d5JmhxaK5WY8q2pBVDMReT690wZxUMkTOMnaFCY2rGa9kyvfL+/3+z+DI/AFmFTBzgXJB1qp8nQmJdANTbierKtwvo05lFEeuIIIpYlzRj3qkxaca2lUYRY99K0Qg53c+VWRSxjgiiiHVJMybNmDRj20qjiLFvpWiEnO7nyiyKWEcEUcS6pBmTZkyasW2lUcTYt1I0Qk73c2UWRawjgihiXdKMSTMmzdi20ihi7FspGiGn+7kyiyLWEUEUsS5pxqQZk2ZsW2kUMfatFI2Q0/1cmUUR64ggiliXNGPSjEkztq00ihj7VopGyOl+rsyiiHVEEEWsS5oxacakGdtWGkWMfStFI+R0P1dmUcQ6Iogi1iXNmDRj0oxtK40ixr6VohFyup8rsyhiHRFEEeuSZkyaMWnGtpVGEWPfStEIOd3PlVkUsY4Iooh1STMmzZg0Y9tKo4ixb6VohJzu58osilhHBFHEuqQZk2ZMmrFtpVHE2LdSNEJO93NlFkWsI4IoYl3SjEkzJs3YttIoYuxbKRohp/u5Mosi1hFBFLEuacakGZNmbFtpFDH2rRSNkNP9XJlFEeuIIIpYlzRj0oxJM7atNIoY+1aKRsjpfq7Mooh1RBBFrEuaMWnGpBnbVhpFjH0rRSPkdD9XZlHEOiKIItYlzZg0Y9KMbSuNIsa+laIRcrqfK7MoYh0RRBHrkmZMmjFpxraVRhFj30rRCDndz5VZFLGOCKKIdUkzJs2YNGPbSqOIsW+laISc7ufKLIpYRwRRxLqkGZNmTJqxbaVRxNi3UjRCTvdzZRZFrCOCKGJd0oxJMybN2LbSKGLsWykaIaf7uTKLItYRQRSxLmnGpBmTZmxbaRQx9q0UjZDT/VyZRRHriCCKWJc0Y9KMSTO2rTSKGPtWikbI6X6uzKKIdUQQRaxLmjFpxqQZ21YaRYx9K0WDd6IUsbgozXa6TOf6XNKMSTMmzdi20gRFjP3KGZ53QRHrkmZMmjFpxraVJihi7FfO8LwLiliXNGPSjEkztq00QRFjv3KG511QxLqkGZNmTJqxbaUJihj7lTM878L//PuDv9iAf3fw7//DQa7PJc2Yd2pMmrFtpQn/VhFjt/7vnOJ5L/4urkez/dUvqr/M9bmkGZNmTJqxbaU5+rOctmBf/iand96L/yuvSVP9NC/TP831uaQZk2ZMmrFtpTn6Nzltwc78l5zfeR/+W16SJqt/YN7KH5elGZNmTJqxbaWp3BBjt/7mv+YUz/b93X/KS9J0P/2rX/zldv60LM2YNGPSjG0rzcGfuR8GAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAvHO/+d3vcmm6X/76t//j4Le/zvV5vv7++385+P7rz3PDbB/9uMi1KTLCyScf5Y65Pv6khPk4V2f5uIzJ0uxMP/poI4NzUJN8vI1zJuJ8kktLH5X38bEDdniXhscb5Xw7gyNu6FSCnfnN7/415Npsv44WVv02N81RSlj6fhtVLC6CB7k2xbqIzU1TfVRmh2ruHL/FItZkevR0vtIkmV/FaqXonb3NKf6gmLX49c+Ucc63Mj7idk4l2JUsYSG3zPXL7GDVb3+Zmx/v86xgR1toYsfrYK5OscEi1tSw2bWnmalO5iZavV8zC9DifZraxLJqhNzSWIzY28fMEhYuzpSrOd/EtSMuT6WN3AqHHcgOVuSmqZY97CC3P172r7P5Tex0Icz1KS6K2Ozr8SqQIraUIU7mvV2rsZl43mSCIjedrc6nt47Zjsr6TMnNRW56Y3mwIjedXPzOz+3Ay/wmO1iR26aq7evXcSOsfkQ569PJr0v5Kp9Ifp7LdcdEpz+s5voU5XI8t1ssHKeH+N7RR59s4sO3XD4oq1MHq87z5UtZdXHeAJ0On58kT2tibfe5/L1UtpbbPSXmW49XOVxanSnXc76Fq0esWzdxKsGu/HV2sCK3zVRuiJ0+jyzf2c/lRyvl63QTrDSx2bfEzn8izQ1TbKyI5aBsJVCZoXL5oEzluTxFHZ6sPIuVh2trzUMqztD5N9JBbjsp72Ab841PrXKMtDrU1Zxv4toRy77T55HTz2zYkd/867/+7jc/+lH5olhumima1/84fS+s1LJZf3fy6/YL+uULY7OLWFz6fjz9Aliux9spYpFmS19XObw/5zB17sqVKUqtOAUqa7Peuzj2aSxiZeotsfh7f93fSyVZLj+ibsTtwY8/6v+2upbzbVw5Ymw6v2UbuwzAHmypiDXNK26Jzf2bk6kUsa9zZZIyi35S/j+3TLGtK3CZMaZWnWseOIMOrE6XWJs0WsvzpuSafRb13p5ZMa/9tnr8aTQqYk3AeMhmf+PBu7SlItb8RcnNFLHyQeXcIlau1D+uf8UqN02xqSKWg5JrmxPh5k5W2yliJcnyhsrU8/igVzdmDdj7KGLN7zRFDF7bVorYL3+7+CgyetkWilj9URa5Mkm5Nn68niger84YM37iZUcOykaVMZqbbhlhZokuSc4TeaxNPY8PenVjta33kDex/SL20SeLfPEIRQxe01aK2FL5sv78n69//BuUuTbH8RbCNorY2dxrcYlwGJSYOD7ZzM9rP3r8BHopIhz7T33rJo1SOfiqiE1+w3rvT2xqzumH/XbbfhFbKo+Y1OlhpzZZxEoPaz+pnKD56fq5ZZJy4TtMXFsrYnObWAlw/rn6G5sYItLsmwZ1bGJg8geHzgq0bBrnWBOVELl8FJsUsSePWN+/yUUadmaLRaz2sHk/0TU0PWzu35ks1+mYIDZXxGZWjToqJUU1u/YslLdqejdshyfk5sdrj54n0TspYo/oG++riOVJlWvAq9hgEcseNveGWP1QMkz+xyZP173pRaxG2cbPdazHb22piT1+/uzKSTPNu4lR3qz6/hzLvCJ28q6KWJ5SbojBq9peEdtED/vR5xu5JXaeD8pS2TZLBDj+4K46o9blCU5F7DB1zv5x7Zcy2GTH0pPmjU8NEmfO6W1TxE7eUxHTw+BNbK6IbaOHFZ8f21iuT1Cu0nV6mF/EDo3nfAkucabNp8cZveaZ3ArX5g7N0aqHzW9iLUXs5B0VMT0M3sbGitgvN9TD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data-image-state=\"image-loaded\" width=\"610\" height=\"551\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.25px; text-align: left; transform-origin: 384px 21.25px; 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: 84.5px 8px; transform-origin: 84.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\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: 16px 8px; transform-origin: 16px 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: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; \"\u003etarget\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 255.5px 8px; transform-origin: 255.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as inputs, performs a binary search and outputs the index of target value as well as the number of iterations it took to find the target.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [loc,iter] = binarySearch(X,target)\r\n    found = false;\r\nend","test_suite":"%%\r\nsortedData = sort(randi(1000,[1 200]),'ascend');\r\ntarget = sortedData(randi(length(sortedData),1));\r\n[mid,iter] = binarySearch(sortedData,target);\r\nassert(isequal(target,sortedData(mid)))\r\nassert(iter \u003e 0)\r\n%%\r\nsortedData = sort(randi(1000,[1 200]),'ascend');\r\ntarget = sortedData(randi(length(sortedData),1));\r\n[mid,iter] = binarySearch(sortedData,target);\r\nassert(isequal(target,sortedData(mid)))\r\nassert(iter \u003e 0)\r\n%%\r\nsortedData = sort(randi(1000,[1 200]),'ascend');\r\ntarget = sortedData(randi(length(sortedData),1));\r\n[mid,iter] = binarySearch(sortedData,target);\r\nassert(isequal(target,sortedData(mid)))\r\nassert(iter \u003e 0)\r\n%%\r\nsortedData = sort(randi(1000,[1 200]),'ascend');\r\ntarget = sortedData(randi(length(sortedData),1)); \r\n[mid,iter] = binarySearch(sortedData,target);\r\nassert(isequal(target,sortedData(mid)))\r\nassert(iter \u003e 0)\r\n%%\r\nsortedData = [3 12 35 76 221 225 301 367 399 512 783 800];\r\ntarget = 12;\r\n[mid,iter] = binarySearch(sortedData,target);\r\nassert(isequal(target,sortedData(mid)))\r\nassert(isequal(iter,4))\r\n%%\r\nsortedData = 0:160;\r\ntarget = 5;\r\n[mid,iter] = binarySearch(sortedData,target);\r\nassert(isequal(target,sortedData(mid)))\r\nassert(isequal(iter,6))","published":true,"deleted":false,"likes_count":5,"comments_count":8,"created_by":140016,"edited_by":223089,"edited_at":"2023-01-05T19:14:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":111,"test_suite_updated_at":"2023-01-05T19:14:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-23T17:47:03.000Z","updated_at":"2026-04-03T06:52:58.000Z","published_at":"2022-10-17T14:02:13.000Z","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\u003eOne way to locate a target value in a sorted array, is to use a binary search algorithm. Here, you test if the midpoint in the array is the target value. If it is, great! You're done. If not, then you continually narrow your search area depending on whether the target is less than or greater than the midpoint. The algorithm is 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\u003eGiven an array of sorted values (\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\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e), and a target value you wish to locate (\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\u003etarget\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the index of the midpoint of the array \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\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e by taking the average of the largest and smallest indices and rounding to the nearest integer.  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf the value located at the midpoint matches your target, set found to true.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf the target is less than the value located at the midpoint of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, narrow your search to the lower half of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e by setting the largest index in the array to the midpoint - 1. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf the target is greater than the value located at the midpoint of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, narrow your search to the upper half of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e by setting the smallest index in the array to the midpoint + 1. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRepeat the steps above until found is 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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"551\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"610\\\"/\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\u003eWrite a function that takes \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\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and 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the flag(s)","description":"Flags are distributed randomly on a large board. Starting from the corner position your goal is to capture as many flags as possible in at most N moves.\r\nDescription:\r\nThe board is described by a matrix B with 1's at the flag positions, and 0's otherwise.\r\nE.g.\r\n B = [0 0 1 1; \r\n      0 0 1 1;\r\n      0 0 1 0];\r\n\r\n N = 6;\r\nYou are starting at the top-left corner (row=1, col=1) and are allowed N steps (steps are up/down/left/right movements, no diagonal movements allowed).\r\nReturn a trajectory attempting to maximize the number of flags captured. The output of your function should be a Nx2 matrix of the form [row, col] (not including the initial [1,1] position) visiting as many flags as possible.\r\nE.g.\r\n path = [1 2;\r\n         1 3;\r\n         1 4;\r\n         2 4;\r\n         2 3;\r\n         3 3];\r\nThis solution captures all 5 flags on the board.\r\nScoring:\r\nYour function will receive a score equal to the number of non-visited flags across all 50 of the testsuite problems. You need to leave at most 10,000 flags univisited (among 50,000 total flags) to pass this problem.\r\nNote:\r\nThe boards and number of movements allowed will be large. Optimizing over all possible trajectories is very likely to time out.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 676px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 338px; transform-origin: 401px 338px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 21px; text-align: left; transform-origin: 377px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFlags are distributed randomly on a large board. Starting from the corner position your goal is to capture as many flags as possible in at most N moves.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDescription\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe board is described by a matrix\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eB\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with 1's at the flag positions, and 0's otherwise.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eE.g.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 90px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 397px 45px; transform-origin: 397px 45px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e B = [0 0 1 1; \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e      0 0 1 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e      0 0 1 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e N = 6;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 21px; text-align: left; transform-origin: 377px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are starting at the top-left corner (row=1, col=1) and are allowed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e steps (steps are up/down/left/right movements, no diagonal movements allowed).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 21px; text-align: left; transform-origin: 377px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn a trajectory attempting to maximize the number of flags captured. The output of your function should be a\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eNx2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix of the form\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[row, col]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (not including the initial [1,1] position) visiting as many flags as possible.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eE.g.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 108px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 397px 54px; transform-origin: 397px 54px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e path = [1 2;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e         1 3;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e         1 4;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e         2 4;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e         2 3;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e         3 3];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis solution captures all 5 flags on the board.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eScoring\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 21px; text-align: left; transform-origin: 377px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour function will receive a score equal to the number of non-visited flags across all 50 of the testsuite problems. You need to leave at most 10,000 flags univisited (among 50,000 total flags) to pass this problem.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNote\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 21px; text-align: left; transform-origin: 377px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe boards and number of movements allowed will be large. Optimizing over all possible trajectories is very likely to time out.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function path = capture_the_flag(B,N)\r\npath=[1 2];\r\n","test_suite":"%%\r\n% test cases\r\n\r\nrandn('seed',0);\r\nrand('seed',0);\r\nN=randi([1000 4000],50,1);\r\nS=randi([1,50],50,1);\r\nBoards=arrayfun(@(s)convn(randn(100),ones(s)/s^2,'same'),S,'uni',0); \r\n\r\nFLAGSLEFT=0;\r\nDOPLOT=false;\r\ntic;\r\nfor board=1:50\r\n B=Boards{board};\r\n sB=sort(B(:));\r\n B=double(B\u003esB(round(numel(sB)*.9)));\r\n n=N(board);\r\n path=capture_the_flag(B,n);\r\n assert(size(path,1)\u003c=n,'too many steps');\r\n assert(all(sum(abs(diff([1,1;path])),2)\u003c=1),'no jumping allowed');\r\n if DOPLOT\r\n    imagesc(B);\r\n    hold on;\r\n    plot(path(:,2),path(:,1),'y-');\r\n    hold off;\r\n    axis equal;\r\n    axis off;\r\n    set(gcf,'color',0*[1 1 1]);\r\n    colormap(.5*gray);\r\n    drawnow;\r\n end\r\n B(1)=0;\r\n B((path-1)*[1;size(B,1)]+1)=0;\r\n fprintf('test %d; left %d flags\\n',board,nnz(B));\r\n FLAGSLEFT=FLAGSLEFT+nnz(B);\r\nend\r\ntoc;","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":43,"edited_by":1,"edited_at":"2026-02-11T16:03:17.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2026-02-11T16:03:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-10-01T05:38:22.000Z","updated_at":"2026-03-16T11:31:01.000Z","published_at":"2013-10-01T06:27:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFlags are distributed randomly on a large board. Starting from the corner position your goal is to capture as many flags as possible in at most N moves.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDescription\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe board is described by a matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with 1's at the flag positions, and 0's otherwise.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eE.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ B = [0 0 1 1; \\n      0 0 1 1;\\n      0 0 1 0];\\n\\n N = 6;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are starting at the top-left corner (row=1, col=1) and are allowed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e steps (steps are up/down/left/right movements, no diagonal movements allowed).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn a trajectory attempting to maximize the number of flags captured. The output of your function should be a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNx2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix of the form\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[row, col]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (not including the initial [1,1] position) visiting as many flags as possible.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eE.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ path = [1 2;\\n         1 3;\\n         1 4;\\n         2 4;\\n         2 3;\\n         3 3];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis solution captures all 5 flags on the board.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour function will receive a score equal to the number of non-visited flags across all 50 of the testsuite problems. You need to leave at most 10,000 flags univisited (among 50,000 total flags) to pass this problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNote\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe boards and number of movements allowed will be large. Optimizing over all possible trajectories is very likely to time out.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":196,"title":"love is an n-letter word","description":"Given a list of *N words*, return the *N-letter word* (choosing one letter from each word) with the property of having the least distance between each pair of two consecutive letters (if there are multiple optimal solutions return any one of them).\r\n\r\nExample: s1 = {'abcd','bcde','cdef','defg'}; should return s2 = 'dddd'; (with total letter-distance = 0)\r\n\r\nExample: s1={'aldfejk','czoa','vwy','abcde'}; should return s2='love'; (with total letter-distance = 27: _|'l'-'o'|_=3 + _|'o'-'v'|_=7 + _|'v'-'e'|_=17 ; compare for example to the possible word 'aave' which has a total letter-distance of 38)\r\n\r\n\r\n\r\n","description_html":"\u003cp\u003eGiven a list of \u003cb\u003eN words\u003c/b\u003e, return the \u003cb\u003eN-letter word\u003c/b\u003e (choosing one letter from each word) with the property of having the least distance between each pair of two consecutive letters (if there are multiple optimal solutions return any one of them).\u003c/p\u003e\u003cp\u003eExample: s1 = {'abcd','bcde','cdef','defg'}; should return s2 = 'dddd'; (with total letter-distance = 0)\u003c/p\u003e\u003cp\u003eExample: s1={'aldfejk','czoa','vwy','abcde'}; should return s2='love'; (with total letter-distance = 27: \u003ci\u003e\u003ctt\u003e'l'-'o'\u003c/tt\u003e\u003c/i\u003e=3 + \u003ci\u003e\u003ctt\u003e'o'-'v'\u003c/tt\u003e\u003c/i\u003e=7 + \u003ci\u003e\u003ctt\u003e'v'-'e'\u003c/tt\u003e\u003c/i\u003e=17 ; compare for example to the possible word 'aave' which has a total letter-distance of 38)\u003c/p\u003e","function_template":"function s2 = gobbledigook(s1)\r\n  s2 = '';\r\nend","test_suite":"%%\r\ns1 = {'abcd','bcde','cdef','defg'}; \r\nassert(isequal(gobbledigook(s1),'dddd'))\r\ns2_correct = 'dddd';\r\n%%\r\ns1 = {'aldfejk','czoa','vwy','abcde'}; \r\nassert(isequal(gobbledigook(s1),'love'))\r\ns2_correct = 'love';\r\n%%\r\ns1 = {'some','help','check','viterbi','algorithm'}; \r\nassert(isequal(gobbledigook(s1),'eeeeg'))\r\ns2_correct = 'eeeeg';\r\n%%\r\ns1 = {'ldjfac','deamv','fka','idlw','pqmfjavs'}; \r\nassert(isequal(gobbledigook(s1),'lmklm')|isequal(gobbledigook(s1),'aaadf'))\r\ns2_correct = 'lmklm';\r\ns2_correct = 'aaadf';\r\n%% \r\n% avoids look-up table hack\r\ns1 = cellfun(@(x)char('a'-1+randi(26,1,5)),cell(1,7),'uniformoutput',false);\r\nassert(all(any(bsxfun(@eq,gobbledigook(s1),cell2mat(cellfun(@(x)x',s1,'uniformoutput',false)))))\u0026all(sum(abs(diff(double(gobbledigook(s1)))))\u003c=sum(abs(diff(double(cell2mat(cellfun(@(x)x(randi(numel(x),1,1000))',s1,'uniformoutput',false))),1,2)),2)));","published":true,"deleted":false,"likes_count":3,"comments_count":5,"created_by":43,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":55,"test_suite_updated_at":"2012-03-08T02:36:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-31T08:36:36.000Z","updated_at":"2026-03-20T18:33:59.000Z","published_at":"2012-03-08T03:14:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a list of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN words\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN-letter word\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (choosing one letter from each word) with the property of having the least distance between each pair of two consecutive letters (if there are multiple optimal solutions return any one of them).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: s1 = {'abcd','bcde','cdef','defg'}; should return s2 = 'dddd'; (with total letter-distance = 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: s1={'aldfejk','czoa','vwy','abcde'}; should return s2='love'; (with total letter-distance = 27:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'l'-'o'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e=3 +\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'o'-'v'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e=7 +\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'v'-'e'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e=17 ; compare for example to the possible word 'aave' which has a total letter-distance of 38)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44787,"title":"What can you get for exactly amount of money(harder)","description":"Inspired by \"Problem 42996. what can you get for exactly amount of money\"\r\n\u003chttps://ww2.mathworks.cn/matlabcentral/cody/problems/42996-what-can-you-get-for-exactly-amount-of-money\u003e\r\nProblem 42996 is a good problem, but the test suit is too weak.\r\n\r\nYou go to store, where each product has price. Prices are in vector\r\n\r\nv = [ 195 125 260 440 395 290]\r\nand you have amount of money s=570\r\n\r\nQuestion is what can you buy, if you want to use whole amount of money\r\n\r\nFor this data answer is\r\n\r\nres=[ 125 125 125 195]\r\n\r\nThe answer may not be unique, return any feasible answer.\r\nDo not cheat please.\r\n\r\nIn this hard version, \r\n1 \u003c= length(v) \u003c= 50\r\n1 \u003c= s \u003c= 10000000019 (1e10 + 19)\r\n","description_html":"\u003cp\u003eInspired by \"Problem 42996. what can you get for exactly amount of money\" \u003ca href = \"https://ww2.mathworks.cn/matlabcentral/cody/problems/42996-what-can-you-get-for-exactly-amount-of-money\"\u003ehttps://ww2.mathworks.cn/matlabcentral/cody/problems/42996-what-can-you-get-for-exactly-amount-of-money\u003c/a\u003e\r\nProblem 42996 is a good problem, but the test suit is too weak.\u003c/p\u003e\u003cp\u003eYou go to store, where each product has price. Prices are in vector\u003c/p\u003e\u003cp\u003ev = [ 195 125 260 440 395 290]\r\nand you have amount of money s=570\u003c/p\u003e\u003cp\u003eQuestion is what can you buy, if you want to use whole amount of money\u003c/p\u003e\u003cp\u003eFor this data answer is\u003c/p\u003e\u003cp\u003eres=[ 125 125 125 195]\u003c/p\u003e\u003cp\u003eThe answer may not be unique, return any feasible answer.\r\nDo not cheat please.\u003c/p\u003e\u003cp\u003eIn this hard version, \r\n1 \u0026lt;= length(v) \u0026lt;= 50\r\n1 \u0026lt;= s \u0026lt;= 10000000019 (1e10 + 19)\u003c/p\u003e","function_template":"function res = buy(v, s)\r\nres = [1, 2, 3];\r\nend","test_suite":"%%\r\nv = [ 195 125 260 440 395 290];\r\ns = 570;\r\ntic\r\nres = buy(v, s);\r\ntoc\r\nassert(sum(res) == s);\r\nassert(all(ismember(res, v)))\r\n\t\r\n%%\r\nv = [ 150 180 60 40];\r\ns = 210;\r\ntic\r\nres = buy(v, s);\r\ntoc\r\nassert(sum(res) == s);\r\nassert(all(ismember(res, v)))\r\n\r\n%%\r\nv = [ 150 180 60 40];\r\ns = 1e10;\r\ntic\r\nres = buy(v, s);\r\ntoc\r\nassert(sum(res) == s);\r\nassert(all(ismember(res, v)))\r\n\r\n%%\r\nv = [123456, 963852, 753159, 7841, 122];\r\ns = 1e10+19;\r\ntic\r\nres = buy(v, s);\r\ntoc\r\nassert(sum(res) == s);\r\nassert(all(ismember(res, v)))\r\n\r\n%%\r\nv = [319,2770,462,972,8235,6949,3171,9503,345,4388,3816,7656,7952,1869,4898,4456,6464,7094,7547,2761,6798,6551,1627,1190,4984,9598,3404,5853,2239,7513];\r\ns = 1e10+19;\r\ntic;\r\nres = buy(v, s);\r\ntoc;\r\nassert(sum(res) == s);\r\nassert(all(ismember(res, v)))\r\n\r\n%%\r\nv = [3898,2417,4040,965,1320,9421,9562,5753,598,2348,3532,8212,155,431,1690,6492,7318,6478,4510,5471,2964,7447,1890,6868,1836,3685,6257,7803,812,9294,7758,4868,4359,4468,3064,5086,5108,8177,7949,6444,3787,8116,5329,3508,9391,8760,5502,6225,5871,2078];\r\ns = 1e10+19;\r\ntic;\r\nres = buy(v, s);\r\ntoc;\r\nassert(sum(res) == s);\r\nassert(all(ismember(res, v)))","published":true,"deleted":false,"likes_count":3,"comments_count":14,"created_by":8269,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":"2018-11-12T07:09:17.000Z","rescore_all_solutions":false,"group_id":71,"created_at":"2018-11-12T06:38:43.000Z","updated_at":"2025-12-14T23:03:12.000Z","published_at":"2018-11-12T06:39:22.000Z","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\u003eInspired by \\\"Problem 42996. what can you get for exactly amount of money\\\"\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://ww2.mathworks.cn/matlabcentral/cody/problems/42996-what-can-you-get-for-exactly-amount-of-money\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://ww2.mathworks.cn/matlabcentral/cody/problems/42996-what-can-you-get-for-exactly-amount-of-money\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt; Problem 42996 is a good problem, but the test suit is too weak.\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\u003eYou go to store, where each product has price. Prices are in 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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = [ 195 125 260 440 395 290] and you have amount of money s=570\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\u003eQuestion is what can you buy, if you want to use whole amount of money\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this data answer is\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\u003eres=[ 125 125 125 195]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe answer may not be unique, return any feasible answer. Do not cheat please.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this hard version, 1 \u0026lt;= length(v) \u0026lt;= 50 1 \u0026lt;= s \u0026lt;= 10000000019 (1e10 + 19)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":55530,"title":"Jump Search - 01","description":"Find the number of leaps you need to take to find an element in an array using the jump search algorithm.\r\nFor example, \r\na=[ 2,5,6,9,12,14,15,16,17,19,31]\r\nTo find 16 with a jump step of 3, you follow,  2 -\u003e 9 -\u003e 15 -\u003e 19 -\u003e 17 -\u003e 16\r\nSo, total number of jumps = 5\r\nnb. to go forward, you take n-step jump; to go backwards, you jump only one step back. \r\nIf the jump step is larger than the array size, u jump to the last element of the array.","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: 201.438px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 100.713px; transform-origin: 407px 100.719px; 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=\"\"\u003eFind the number of leaps you need to take to find an element in an array using the jump search algorithm.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-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=\"\"\u003ea=[ 2,5,6,9,12,14,15,16,17,19,31]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-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=\"\"\u003eTo find 16 with a jump step of 3, you follow,  2 -\u0026gt; 9 -\u0026gt; 15 -\u0026gt; 19 -\u0026gt; 17 -\u0026gt; 16\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-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=\"\"\u003eSo, total number of jumps = 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: 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=\"\"\u003enb. to go forward, you take n-step jump; to go backwards, you jump only one step back. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIf the jump step is larger than the array size, u jump to the last element of the array.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = jump_search(a,x,n)\r\n  y = x;\r\nend","test_suite":"%%\r\na=[ 2,5,6,9,12,14,15,16,17,19,31];\r\nx=16;\r\nn=3;\r\ny_correct = 5;\r\nassert(isequal(jump_search(a,x,n),y_correct))\r\n\r\n%%\r\na=[ 2,5,6,9,12,14,15,16,17,19,31];\r\nx=15;\r\nn=1;\r\ny_correct = 6;\r\nassert(isequal(jump_search(a,x,n),y_correct))\r\n\r\n\r\n%%\r\na=[ 2,5,6,9,12,14,15,16,17,19,31];\r\nx=2;\r\nn=5;\r\ny_correct = 0;\r\nassert(isequal(jump_search(a,x,n),y_correct))\r\n\r\n\r\n%%\r\na=[ 2,5,6,9,12,14,15,16,17,19,31];\r\nx=31;\r\nn=12;\r\ny_correct = 1;\r\nassert(isequal(jump_search(a,x,n),y_correct))\r\n\r\n\r\n%%\r\na=[ 2,5,6,9,12,14,15,16,17,19,31];\r\nx=17;\r\nn=12;\r\ny_correct = 3;\r\nassert(isequal(jump_search(a,x,n),y_correct))\r\n\r\n%%\r\na=[1,5,9,14,17,18,23,33,36,38];\r\nx=38;\r\nn=2;\r\ny_correct = 5;\r\nassert(isequal(jump_search(a,x,n),y_correct))\r\n\r\n%%\r\na=[1,5,9,14,17,18,23,33,36,38];\r\nx=11;\r\nn=4;\r\ny_correct = nan;\r\nassert(isnan(jump_search(a,x,n)))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":4,"created_by":363598,"edited_by":363598,"edited_at":"2022-09-30T16:20:21.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2022-09-29T13:10:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-08T04:51:33.000Z","updated_at":"2025-12-15T02:19:46.000Z","published_at":"2022-09-28T12:58:17.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the number of leaps you need to take to find an element in an array using the jump search algorithm.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=[ 2,5,6,9,12,14,15,16,17,19,31]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo find 16 with a jump step of 3, you follow,  2 -\u0026gt; 9 -\u0026gt; 15 -\u0026gt; 19 -\u0026gt; 17 -\u0026gt; 16\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo, total number of jumps = 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\u003enb. to go forward, you take n-step jump; to go backwards, you jump only one step back. \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 jump step is larger than the array size, u jump to the last element of the array.\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":44756,"title":"Lights Out 5 - 5x5, 10 moves","description":"\u003chttps://en.wikipedia.org/wiki/Lights_Out_(game) Lights Out\u003e is a logic game wherein all lights need to be turned off to complete each board. See \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44751-lights-out-1-5x5-3-moves the first problem in the series\u003e for an introduction.\r\n\r\nThis problem contains boards that each require ten moves to solve. For example, if\r\n\r\n board = [0 1 1 0 1  \r\n          1 1 1 1 1  \r\n          1 1 1 1 1  \r\n          1 1 1 1 1  \r\n          0 1 1 0 1]\r\n\r\nan answer is:\r\n\r\n moves = [1 2 3 4 5 16 17 18 19 20]\r\n\r\nPrev.: \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44755-lights-out-4-5x5-8-moves 5x5, 8 moves\u003e — \r\nNext: \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44757-lights-out-6-5x5-13-moves 5x5, 13 moves\u003e","description_html":"\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Lights_Out_(game)\"\u003eLights Out\u003c/a\u003e is a logic game wherein all lights need to be turned off to complete each board. See \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44751-lights-out-1-5x5-3-moves\"\u003ethe first problem in the series\u003c/a\u003e for an introduction.\u003c/p\u003e\u003cp\u003eThis problem contains boards that each require ten moves to solve. For example, if\u003c/p\u003e\u003cpre\u003e board = [0 1 1 0 1  \r\n          1 1 1 1 1  \r\n          1 1 1 1 1  \r\n          1 1 1 1 1  \r\n          0 1 1 0 1]\u003c/pre\u003e\u003cp\u003ean answer is:\u003c/p\u003e\u003cpre\u003e moves = [1 2 3 4 5 16 17 18 19 20]\u003c/pre\u003e\u003cp\u003ePrev.: \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44755-lights-out-4-5x5-8-moves\"\u003e5x5, 8 moves\u003c/a\u003e — \r\nNext: \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44757-lights-out-6-5x5-13-moves\"\u003e5x5, 13 moves\u003c/a\u003e\u003c/p\u003e","function_template":"function moves = lights_out_5(board) % 5x5 board, 10 moves\r\n moves = board;\r\nend","test_suite":"%% \r\n board = [0 1 1 0 1  \r\n          1 1 1 1 1  \r\n          1 1 1 1 1  \r\n          1 1 1 1 1  \r\n          0 1 1 0 1];\r\nmoves = lights_out_5(board); % [1 2 3 4 5 16 17 18 19 20]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [0 0 0 0 0  \r\n          1 1 1 0 0  \r\n          0 0 0 0 1  \r\n          1 1 0 0 1  \r\n          0 0 1 0 1];\r\nmoves = lights_out_5(board); % [1 2 3 11 13 14 16 17 21 24]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [1 0 0 0 1  \r\n          0 1 1 0 0  \r\n          0 1 0 0 0  \r\n          0 0 0 0 0  \r\n          1 0 0 0 0];\r\nmoves = lights_out_5(board); % [1 2 3 4 6 7 8 11 12 16]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [1 1 0 1 1  \r\n          0 0 1 1 0  \r\n          1 1 0 1 0  \r\n          1 1 0 0 0  \r\n          0 1 0 0 0];\r\nmoves = lights_out_5(board); % [3 6:7 11 13:15 19 22:23]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [1 0 1 0 1  \r\n          0 1 1 0 0  \r\n          0 0 1 0 0  \r\n          0 1 0 1 0  \r\n          1 0 1 1 0];\r\nmoves = lights_out_5(board); % [2 3 9 10 14 16 17 20 23 24]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [1 0 0 1 1  \r\n          0 1 0 0 0  \r\n          0 0 1 0 0  \r\n          0 0 0 0 1  \r\n          1 1 1 0 1];\r\nmoves = lights_out_5(board); % [2 4 7 9 11 12 17 19 20 21]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [0 0 0 1 1  \r\n          1 0 1 0 0  \r\n          1 0 1 0 1  \r\n          1 0 0 1 0  \r\n          1 1 0 1 1];\r\nmoves = lights_out_5(board); % [1 4 6 12 14 15 18 21 23 24]\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [0 1 1 1 1  \r\n          0 0 0 1 1  \r\n          1 1 0 0 0  \r\n          1 0 0 1 0  \r\n          1 1 1 1 0];\r\nmoves = lights_out_5(board); % on your own\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [0 1 1 1 1  \r\n          1 0 1 1 0  \r\n          0 1 1 1 0  \r\n          0 1 1 1 1  \r\n          1 1 0 0 1];\r\nmoves = lights_out_5(board);\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [1 1 1 1 0  \r\n          0 1 1 0 1  \r\n          0 1 0 1 0  \r\n          1 0 1 1 0  \r\n          0 1 1 1 1];\r\nmoves = lights_out_5(board);\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [0 1 0 1 0  \r\n          0 0 0 1 1  \r\n          1 0 1 0 0  \r\n          1 0 1 1 0  \r\n          0 1 1 0 0];\r\nmoves = lights_out_5(board);\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [1 0 0 1 1  \r\n          0 0 1 1 0  \r\n          0 1 0 0 0  \r\n          0 1 1 0 0  \r\n          0 0 0 0 0];\r\nmoves = lights_out_5(board);\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [0 1 1 0 1  \r\n          0 0 0 1 1  \r\n          0 1 1 0 0  \r\n          1 1 1 1 0  \r\n          0 0 1 1 0];\r\nmoves = lights_out_5(board);\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)\r\n\r\n%% \r\n board = [0 0 1 1 1  \r\n          0 0 1 0 0  \r\n          0 0 1 0 0  \r\n          0 0 1 0 0  \r\n          0 0 1 1 1];\r\nmoves = lights_out_5(board);\r\nb1 = diag(ones(1,5),0) + diag(ones(1,4),1) + diag(ones(1,4),-1); b2 = eye(5); b3 = zeros(5);\r\nb_map = [b1,b2,b3,b3,b3;b2,b1,b2,b3,b3;b3,b2,b1,b2,b3;b3,b3,b2,b1,b2;b3,b3,b3,b2,b1];\r\nfor i = 1:numel(moves)\r\n\tboard = mod(board + reshape(b_map(moves(i),:),[5,5]),2); %remove semicolon to display progress\r\nend\r\nassert(sum(abs(board(:)))==0)\r\nassert(numel(moves)==10)","published":true,"deleted":false,"likes_count":3,"comments_count":8,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2018-11-13T13:07:28.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-10-29T18:53:12.000Z","updated_at":"2025-11-29T13:41:10.000Z","published_at":"2018-11-12T15:53:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Lights_Out_(game)\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLights Out\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a logic game wherein all lights need to be turned off to complete each board. See\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44751-lights-out-1-5x5-3-moves\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ethe first problem in the series\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for an introduction.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem contains boards that each require ten moves to solve. For example, if\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ board = [0 1 1 0 1  \\n          1 1 1 1 1  \\n          1 1 1 1 1  \\n          1 1 1 1 1  \\n          0 1 1 0 1]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ean answer is:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ moves = [1 2 3 4 5 16 17 18 19 20]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrev.:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44755-lights-out-4-5x5-8-moves\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e5x5, 8 moves\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e — Next:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44757-lights-out-6-5x5-13-moves\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e5x5, 13 moves\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":39,"title":"Which values occur exactly three times?","description":"Return a list of all values (sorted smallest to largest) that appear exactly three times in the input vector x. So if\n\n x = [1 2 5 2 2 7 8 3 3 1 3 8 8 8]\n\nthen \n\n y = [2 3]","description_html":"\u003cp\u003eReturn a list of all values (sorted smallest to largest) that appear exactly three times in the input vector x. So if\u003c/p\u003e\u003cpre\u003e x = [1 2 5 2 2 7 8 3 3 1 3 8 8 8]\u003c/pre\u003e\u003cp\u003ethen\u003c/p\u003e\u003cpre\u003e y = [2 3]\u003c/pre\u003e","function_template":"function y = threeTimes(x)\n  y = x\nend","test_suite":"%%\nx = [1 2 5 2 2 7 8 3 3 1 3 8 8 8];\ny_correct = [2 3];\nassert(isequal(threeTimes(x),y_correct))\n\n%%\n\nx = [1 1 1];\ny_correct = [1];\nassert(isequal(threeTimes(x),y_correct))\n\n%%\n\nx = [5 10 -3 10 -3 11 -3 5 5 7];\ny_correct = [-3 5];\nassert(isequal(threeTimes(x),y_correct))","published":true,"deleted":false,"likes_count":23,"comments_count":5,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5240,"test_suite_updated_at":"2012-01-18T01:00:22.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:22.000Z","updated_at":"2026-03-25T03:10:27.000Z","published_at":"2012-01-18T01:00:22.000Z","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\u003eReturn a list of all values (sorted smallest to largest) that appear exactly three times in the input vector x. So 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[ x = [1 2 5 2 2 7 8 3 3 1 3 8 8 8]]]\u003e\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\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ y = [2 3]]]\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":56040,"title":"A Binary Search","description":"One way to locate a target value in a sorted array, is to use a binary search algorithm. Here, you test if the midpoint in the array is the target value. If it is, great! You're done. If not, then you continually narrow your search area depending on whether the target is less than or greater than the midpoint. The algorithm is as follows:\r\nGiven an array of sorted values (X), and a target value you wish to locate (target)\r\nCalculate the index of the midpoint of the array X by taking the average of the largest and smallest indices and rounding to the nearest integer.  \r\nIf the value located at the midpoint matches your target, set found to true.\r\nIf the target is less than the value located at the midpoint of X, narrow your search to the lower half of X by setting the largest index in the array to the midpoint - 1. \r\nIf the target is greater than the value located at the midpoint of X, narrow your search to the upper half of X by setting the smallest index in the array to the midpoint + 1. \r\nRepeat the steps above until found is true.\r\n\r\nWrite a function that takes X and target as inputs, performs a binary search and outputs the index of target value as well as the number of iterations it took to find the target.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 926.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 463.233px; transform-origin: 407px 463.233px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.5px 8px; transform-origin: 383.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOne way to locate a target value in a sorted array, is to use a binary search algorithm. Here, you test if the midpoint in the array is the target value. If it is, great! You're done. If not, then you continually narrow your search area depending on whether the target is less than or greater than the midpoint. The algorithm is as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; 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: 104px 8px; transform-origin: 104px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven an array of sorted values (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\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: 126.5px 8px; transform-origin: 126.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e), and a target value you wish to locate (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; \"\u003etarget\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.5px 8px; transform-origin: 2.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 164.967px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 82.4833px; transform-origin: 391px 82.4833px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 41.3667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.6833px; text-align: left; transform-origin: 363px 20.6833px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 149px 8px; transform-origin: 149px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the index of the midpoint of the array \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003eX\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 195.5px 8px; transform-origin: 195.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by taking the average of the largest and smallest indices and rounding to the nearest integer.  \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 231px 8px; transform-origin: 231px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf the value located at the midpoint matches your target, set found to true.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 41.3667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.6833px; text-align: left; transform-origin: 363px 20.6833px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 188px 8px; transform-origin: 188px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf the target is less than the value located at the midpoint of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003eX\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 127px 8px; transform-origin: 127px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, narrow your search to the lower half of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003eX\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 34.5px 8px; transform-origin: 34.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by setting the largest index in the array to the midpoint - 1. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 41.3667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.6833px; text-align: left; transform-origin: 363px 20.6833px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 198.5px 8px; transform-origin: 198.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf the target is greater than the value located at the midpoint of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003eX\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 129px 8px; transform-origin: 129px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, narrow your search to the upper half of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003eX\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 11.5px 8px; transform-origin: 11.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by setting the smallest index in the array to the midpoint + 1. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 134px 8px; transform-origin: 134px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRepeat the steps above until found is true.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 556.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 278.25px; text-align: left; transform-origin: 384px 278.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 610px;height: 551px\" 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data-image-state=\"image-loaded\" width=\"610\" height=\"551\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.25px; text-align: left; transform-origin: 384px 21.25px; 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: 84.5px 8px; transform-origin: 84.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\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: 16px 8px; transform-origin: 16px 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: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; \"\u003etarget\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 255.5px 8px; transform-origin: 255.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as inputs, performs a binary search and outputs the index of target value as well as the number of iterations it took to find the target.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [loc,iter] = binarySearch(X,target)\r\n    found = false;\r\nend","test_suite":"%%\r\nsortedData = sort(randi(1000,[1 200]),'ascend');\r\ntarget = sortedData(randi(length(sortedData),1));\r\n[mid,iter] = binarySearch(sortedData,target);\r\nassert(isequal(target,sortedData(mid)))\r\nassert(iter \u003e 0)\r\n%%\r\nsortedData = sort(randi(1000,[1 200]),'ascend');\r\ntarget = sortedData(randi(length(sortedData),1));\r\n[mid,iter] = binarySearch(sortedData,target);\r\nassert(isequal(target,sortedData(mid)))\r\nassert(iter \u003e 0)\r\n%%\r\nsortedData = sort(randi(1000,[1 200]),'ascend');\r\ntarget = sortedData(randi(length(sortedData),1));\r\n[mid,iter] = binarySearch(sortedData,target);\r\nassert(isequal(target,sortedData(mid)))\r\nassert(iter \u003e 0)\r\n%%\r\nsortedData = sort(randi(1000,[1 200]),'ascend');\r\ntarget = sortedData(randi(length(sortedData),1)); \r\n[mid,iter] = binarySearch(sortedData,target);\r\nassert(isequal(target,sortedData(mid)))\r\nassert(iter \u003e 0)\r\n%%\r\nsortedData = [3 12 35 76 221 225 301 367 399 512 783 800];\r\ntarget = 12;\r\n[mid,iter] = binarySearch(sortedData,target);\r\nassert(isequal(target,sortedData(mid)))\r\nassert(isequal(iter,4))\r\n%%\r\nsortedData = 0:160;\r\ntarget = 5;\r\n[mid,iter] = binarySearch(sortedData,target);\r\nassert(isequal(target,sortedData(mid)))\r\nassert(isequal(iter,6))","published":true,"deleted":false,"likes_count":5,"comments_count":8,"created_by":140016,"edited_by":223089,"edited_at":"2023-01-05T19:14:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":111,"test_suite_updated_at":"2023-01-05T19:14:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-23T17:47:03.000Z","updated_at":"2026-04-03T06:52:58.000Z","published_at":"2022-10-17T14:02:13.000Z","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\u003eOne way to locate a target value in a sorted array, is to use a binary search algorithm. Here, you test if the midpoint in the array is the target value. If it is, great! You're done. If not, then you continually narrow your search area depending on whether the target is less than or greater than the midpoint. The algorithm is 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\u003eGiven an array of sorted values (\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\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e), and a target value you wish to locate (\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\u003etarget\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the index of the midpoint of the array \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\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e by taking the average of the largest and smallest indices and rounding to the nearest integer.  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf the value located at the midpoint matches your target, set found to true.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf the target is less than the value located at the midpoint of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, narrow your search to the lower half of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e by setting the largest index in the array to the midpoint - 1. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf the target is greater than the value located at the midpoint of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, narrow your search to the upper half of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e by setting the smallest index in the array to the midpoint + 1. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRepeat the steps above until found is 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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"551\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"610\\\"/\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\u003eWrite a function that takes \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\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and 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the flag(s)","description":"Flags are distributed randomly on a large board. Starting from the corner position your goal is to capture as many flags as possible in at most N moves.\r\nDescription:\r\nThe board is described by a matrix B with 1's at the flag positions, and 0's otherwise.\r\nE.g.\r\n B = [0 0 1 1; \r\n      0 0 1 1;\r\n      0 0 1 0];\r\n\r\n N = 6;\r\nYou are starting at the top-left corner (row=1, col=1) and are allowed N steps (steps are up/down/left/right movements, no diagonal movements allowed).\r\nReturn a trajectory attempting to maximize the number of flags captured. The output of your function should be a Nx2 matrix of the form [row, col] (not including the initial [1,1] position) visiting as many flags as possible.\r\nE.g.\r\n path = [1 2;\r\n         1 3;\r\n         1 4;\r\n         2 4;\r\n         2 3;\r\n         3 3];\r\nThis solution captures all 5 flags on the board.\r\nScoring:\r\nYour function will receive a score equal to the number of non-visited flags across all 50 of the testsuite problems. You need to leave at most 10,000 flags univisited (among 50,000 total flags) to pass this problem.\r\nNote:\r\nThe boards and number of movements allowed will be large. Optimizing over all possible trajectories is very likely to time out.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 676px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 338px; transform-origin: 401px 338px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 21px; text-align: left; transform-origin: 377px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFlags are distributed randomly on a large board. Starting from the corner position your goal is to capture as many flags as possible in at most N moves.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDescription\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe board is described by a matrix\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eB\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with 1's at the flag positions, and 0's otherwise.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eE.g.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 90px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 397px 45px; transform-origin: 397px 45px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e B = [0 0 1 1; \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e      0 0 1 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e      0 0 1 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e N = 6;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 21px; text-align: left; transform-origin: 377px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are starting at the top-left corner (row=1, col=1) and are allowed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e steps (steps are up/down/left/right movements, no diagonal movements allowed).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 21px; text-align: left; transform-origin: 377px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn a trajectory attempting to maximize the number of flags captured. The output of your function should be a\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eNx2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix of the form\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[row, col]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (not including the initial [1,1] position) visiting as many flags as possible.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eE.g.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 108px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 397px 54px; transform-origin: 397px 54px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e path = [1 2;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e         1 3;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e         1 4;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e         2 4;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e         2 3;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18.004px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 397px 9px; text-wrap-mode: nowrap; transform-origin: 397px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e         3 3];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis solution captures all 5 flags on the board.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eScoring\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 21px; text-align: left; transform-origin: 377px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour function will receive a score equal to the number of non-visited flags across all 50 of the testsuite problems. You need to leave at most 10,000 flags univisited (among 50,000 total flags) to pass this problem.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNote\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 21px; text-align: left; transform-origin: 377px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe boards and number of movements allowed will be large. Optimizing over all possible trajectories is very likely to time out.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function path = capture_the_flag(B,N)\r\npath=[1 2];\r\n","test_suite":"%%\r\n% test cases\r\n\r\nrandn('seed',0);\r\nrand('seed',0);\r\nN=randi([1000 4000],50,1);\r\nS=randi([1,50],50,1);\r\nBoards=arrayfun(@(s)convn(randn(100),ones(s)/s^2,'same'),S,'uni',0); \r\n\r\nFLAGSLEFT=0;\r\nDOPLOT=false;\r\ntic;\r\nfor board=1:50\r\n B=Boards{board};\r\n sB=sort(B(:));\r\n B=double(B\u003esB(round(numel(sB)*.9)));\r\n n=N(board);\r\n path=capture_the_flag(B,n);\r\n assert(size(path,1)\u003c=n,'too many steps');\r\n assert(all(sum(abs(diff([1,1;path])),2)\u003c=1),'no jumping allowed');\r\n if DOPLOT\r\n    imagesc(B);\r\n    hold on;\r\n    plot(path(:,2),path(:,1),'y-');\r\n    hold off;\r\n    axis equal;\r\n    axis off;\r\n    set(gcf,'color',0*[1 1 1]);\r\n    colormap(.5*gray);\r\n    drawnow;\r\n end\r\n B(1)=0;\r\n B((path-1)*[1;size(B,1)]+1)=0;\r\n fprintf('test %d; left %d flags\\n',board,nnz(B));\r\n FLAGSLEFT=FLAGSLEFT+nnz(B);\r\nend\r\ntoc;","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":43,"edited_by":1,"edited_at":"2026-02-11T16:03:17.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2026-02-11T16:03:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-10-01T05:38:22.000Z","updated_at":"2026-03-16T11:31:01.000Z","published_at":"2013-10-01T06:27:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFlags are distributed randomly on a large board. Starting from the corner position your goal is to capture as many flags as possible in at most N moves.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDescription\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe board is described by a matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with 1's at the flag positions, and 0's otherwise.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eE.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ B = [0 0 1 1; \\n      0 0 1 1;\\n      0 0 1 0];\\n\\n N = 6;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are starting at the top-left corner (row=1, col=1) and are allowed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e steps (steps are up/down/left/right movements, no diagonal movements allowed).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn a trajectory attempting to maximize the number of flags captured. The output of your function should be a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNx2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix of the form\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[row, col]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (not including the initial [1,1] position) visiting as many flags as possible.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eE.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ path = [1 2;\\n         1 3;\\n         1 4;\\n         2 4;\\n         2 3;\\n         3 3];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis solution captures all 5 flags on the board.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour function will receive a score equal to the number of non-visited flags across all 50 of the testsuite problems. You need to leave at most 10,000 flags univisited (among 50,000 total flags) to pass this problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNote\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe boards and number of movements allowed will be large. Optimizing over all possible trajectories is very likely to time out.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":196,"title":"love is an n-letter word","description":"Given a list of *N words*, return the *N-letter word* (choosing one letter from each word) with the property of having the least distance between each pair of two consecutive letters (if there are multiple optimal solutions return any one of them).\r\n\r\nExample: s1 = {'abcd','bcde','cdef','defg'}; should return s2 = 'dddd'; (with total letter-distance = 0)\r\n\r\nExample: s1={'aldfejk','czoa','vwy','abcde'}; should return s2='love'; (with total letter-distance = 27: _|'l'-'o'|_=3 + _|'o'-'v'|_=7 + _|'v'-'e'|_=17 ; compare for example to the possible word 'aave' which has a total letter-distance of 38)\r\n\r\n\r\n\r\n","description_html":"\u003cp\u003eGiven a list of \u003cb\u003eN words\u003c/b\u003e, return the \u003cb\u003eN-letter word\u003c/b\u003e (choosing one letter from each word) with the property of having the least distance between each pair of two consecutive letters (if there are multiple optimal solutions return any one of them).\u003c/p\u003e\u003cp\u003eExample: s1 = {'abcd','bcde','cdef','defg'}; should return s2 = 'dddd'; (with total letter-distance = 0)\u003c/p\u003e\u003cp\u003eExample: s1={'aldfejk','czoa','vwy','abcde'}; should return s2='love'; (with total letter-distance = 27: \u003ci\u003e\u003ctt\u003e'l'-'o'\u003c/tt\u003e\u003c/i\u003e=3 + \u003ci\u003e\u003ctt\u003e'o'-'v'\u003c/tt\u003e\u003c/i\u003e=7 + \u003ci\u003e\u003ctt\u003e'v'-'e'\u003c/tt\u003e\u003c/i\u003e=17 ; compare for example to the possible word 'aave' which has a total letter-distance of 38)\u003c/p\u003e","function_template":"function s2 = gobbledigook(s1)\r\n  s2 = '';\r\nend","test_suite":"%%\r\ns1 = {'abcd','bcde','cdef','defg'}; \r\nassert(isequal(gobbledigook(s1),'dddd'))\r\ns2_correct = 'dddd';\r\n%%\r\ns1 = {'aldfejk','czoa','vwy','abcde'}; \r\nassert(isequal(gobbledigook(s1),'love'))\r\ns2_correct = 'love';\r\n%%\r\ns1 = {'some','help','check','viterbi','algorithm'}; \r\nassert(isequal(gobbledigook(s1),'eeeeg'))\r\ns2_correct = 'eeeeg';\r\n%%\r\ns1 = {'ldjfac','deamv','fka','idlw','pqmfjavs'}; \r\nassert(isequal(gobbledigook(s1),'lmklm')|isequal(gobbledigook(s1),'aaadf'))\r\ns2_correct = 'lmklm';\r\ns2_correct = 'aaadf';\r\n%% \r\n% avoids look-up table hack\r\ns1 = cellfun(@(x)char('a'-1+randi(26,1,5)),cell(1,7),'uniformoutput',false);\r\nassert(all(any(bsxfun(@eq,gobbledigook(s1),cell2mat(cellfun(@(x)x',s1,'uniformoutput',false)))))\u0026all(sum(abs(diff(double(gobbledigook(s1)))))\u003c=sum(abs(diff(double(cell2mat(cellfun(@(x)x(randi(numel(x),1,1000))',s1,'uniformoutput',false))),1,2)),2)));","published":true,"deleted":false,"likes_count":3,"comments_count":5,"created_by":43,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":55,"test_suite_updated_at":"2012-03-08T02:36:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-31T08:36:36.000Z","updated_at":"2026-03-20T18:33:59.000Z","published_at":"2012-03-08T03:14:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a list of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN words\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN-letter word\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (choosing one letter from each word) with the property of having the least distance between each pair of two consecutive letters (if there are multiple optimal solutions return any one of them).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: s1 = {'abcd','bcde','cdef','defg'}; should return s2 = 'dddd'; (with total letter-distance = 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: s1={'aldfejk','czoa','vwy','abcde'}; should return s2='love'; (with total letter-distance = 27:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'l'-'o'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e=3 +\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'o'-'v'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e=7 +\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'v'-'e'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e=17 ; compare for example to the possible word 'aave' which has a total letter-distance of 38)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44787,"title":"What can you get for exactly amount of money(harder)","description":"Inspired by \"Problem 42996. what can you get for exactly amount of money\"\r\n\u003chttps://ww2.mathworks.cn/matlabcentral/cody/problems/42996-what-can-you-get-for-exactly-amount-of-money\u003e\r\nProblem 42996 is a good problem, but the test suit is too weak.\r\n\r\nYou go to store, where each product has price. Prices are in vector\r\n\r\nv = [ 195 125 260 440 395 290]\r\nand you have amount of money s=570\r\n\r\nQuestion is what can you buy, if you want to use whole amount of money\r\n\r\nFor this data answer is\r\n\r\nres=[ 125 125 125 195]\r\n\r\nThe answer may not be unique, return any feasible answer.\r\nDo not cheat please.\r\n\r\nIn this hard version, \r\n1 \u003c= length(v) \u003c= 50\r\n1 \u003c= s \u003c= 10000000019 (1e10 + 19)\r\n","description_html":"\u003cp\u003eInspired by \"Problem 42996. what can you get for exactly amount of money\" \u003ca href = \"https://ww2.mathworks.cn/matlabcentral/cody/problems/42996-what-can-you-get-for-exactly-amount-of-money\"\u003ehttps://ww2.mathworks.cn/matlabcentral/cody/problems/42996-what-can-you-get-for-exactly-amount-of-money\u003c/a\u003e\r\nProblem 42996 is a good problem, but the test suit is too weak.\u003c/p\u003e\u003cp\u003eYou go to store, where each product has price. Prices are in vector\u003c/p\u003e\u003cp\u003ev = [ 195 125 260 440 395 290]\r\nand you have amount of money s=570\u003c/p\u003e\u003cp\u003eQuestion is what can you buy, if you want to use whole amount of money\u003c/p\u003e\u003cp\u003eFor this data answer is\u003c/p\u003e\u003cp\u003eres=[ 125 125 125 195]\u003c/p\u003e\u003cp\u003eThe answer may not be unique, return any feasible answer.\r\nDo not cheat please.\u003c/p\u003e\u003cp\u003eIn this hard version, \r\n1 \u0026lt;= length(v) \u0026lt;= 50\r\n1 \u0026lt;= s \u0026lt;= 10000000019 (1e10 + 19)\u003c/p\u003e","function_template":"function res = buy(v, s)\r\nres = [1, 2, 3];\r\nend","test_suite":"%%\r\nv = [ 195 125 260 440 395 290];\r\ns = 570;\r\ntic\r\nres = buy(v, s);\r\ntoc\r\nassert(sum(res) == s);\r\nassert(all(ismember(res, v)))\r\n\t\r\n%%\r\nv = [ 150 180 60 40];\r\ns = 210;\r\ntic\r\nres = buy(v, s);\r\ntoc\r\nassert(sum(res) == s);\r\nassert(all(ismember(res, v)))\r\n\r\n%%\r\nv = [ 150 180 60 40];\r\ns = 1e10;\r\ntic\r\nres = buy(v, s);\r\ntoc\r\nassert(sum(res) == s);\r\nassert(all(ismember(res, v)))\r\n\r\n%%\r\nv = [123456, 963852, 753159, 7841, 122];\r\ns = 1e10+19;\r\ntic\r\nres = buy(v, s);\r\ntoc\r\nassert(sum(res) == s);\r\nassert(all(ismember(res, v)))\r\n\r\n%%\r\nv = [319,2770,462,972,8235,6949,3171,9503,345,4388,3816,7656,7952,1869,4898,4456,6464,7094,7547,2761,6798,6551,1627,1190,4984,9598,3404,5853,2239,7513];\r\ns = 1e10+19;\r\ntic;\r\nres = buy(v, s);\r\ntoc;\r\nassert(sum(res) == s);\r\nassert(all(ismember(res, v)))\r\n\r\n%%\r\nv = [3898,2417,4040,965,1320,9421,9562,5753,598,2348,3532,8212,155,431,1690,6492,7318,6478,4510,5471,2964,7447,1890,6868,1836,3685,6257,7803,812,9294,7758,4868,4359,4468,3064,5086,5108,8177,7949,6444,3787,8116,5329,3508,9391,8760,5502,6225,5871,2078];\r\ns = 1e10+19;\r\ntic;\r\nres = buy(v, s);\r\ntoc;\r\nassert(sum(res) == s);\r\nassert(all(ismember(res, v)))","published":true,"deleted":false,"likes_count":3,"comments_count":14,"created_by":8269,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":"2018-11-12T07:09:17.000Z","rescore_all_solutions":false,"group_id":71,"created_at":"2018-11-12T06:38:43.000Z","updated_at":"2025-12-14T23:03:12.000Z","published_at":"2018-11-12T06:39:22.000Z","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\u003eInspired by \\\"Problem 42996. what can you get for exactly amount of money\\\"\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://ww2.mathworks.cn/matlabcentral/cody/problems/42996-what-can-you-get-for-exactly-amount-of-money\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://ww2.mathworks.cn/matlabcentral/cody/problems/42996-what-can-you-get-for-exactly-amount-of-money\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt; Problem 42996 is a good problem, but the test suit is too weak.\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\u003eYou go to store, where each product has price. Prices are in 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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = [ 195 125 260 440 395 290] and you have amount of money s=570\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\u003eQuestion is what can you buy, if you want to use whole amount of money\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this data answer is\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\u003eres=[ 125 125 125 195]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe answer may not be unique, return any feasible answer. Do not cheat please.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this hard version, 1 \u0026lt;= length(v) \u0026lt;= 50 1 \u0026lt;= s \u0026lt;= 10000000019 (1e10 + 19)\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\"}]}"}],"term":"tag:\"search\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"search\"","current_player":null,"sort":"map(difficulty_value,0,0,999) 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