{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-26T00:14:02.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-26T00:00:00.000Z","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":44080,"title":"Construct a \"diagAdiag\" matrix","description":"Construct a matrix whose elements begin from 1 and end at n^2 with the order of arrangement as shown below:\r\n\r\nFor:\r\n\r\n  n = 4\r\n\r\noutput\r\n\r\n  M = \r\n[1   2   6   7;\r\n 3   5   8   13;\r\n 4   9   12  14;\r\n 10  11  15  16]\r\n\r\nNote the elements increase and decrease along alternating diagonals with the last element being always n^2.\r\n","description_html":"\u003cp\u003eConstruct a matrix whose elements begin from 1 and end at n^2 with the order of arrangement as shown below:\u003c/p\u003e\u003cp\u003eFor:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003en = 4\r\n\u003c/pre\u003e\u003cp\u003eoutput\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eM = \r\n[1   2   6   7;\r\n3   5   8   13;\r\n4   9   12  14;\r\n10  11  15  16]\r\n\u003c/pre\u003e\u003cp\u003eNote the elements increase and decrease along alternating diagonals with the last element being always n^2.\u003c/p\u003e","function_template":"function y = diagAdiag(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 3;\r\ny_correct = [1 2 6; 3 5 7;4 8 9];\r\nassert(isequal(diagAdiag(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = [1   2   6   7; 3   5   8   13;4   9   12  14;10  11  15  16];\r\nassert(isequal(diagAdiag(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = [1 2 6 7 15;3 5 8 14 16;4 9 13 17 22;10 12 18 21 23;11 19 20 24 25];\r\nassert(isequal(diagAdiag(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = [ 1  2  6  7 15 16;\r\n              3  5  8 14 17 26;\r\n              4  9 13 18 25 27;\r\n             10 12 19 24 28 33;\r\n             11 20 23 29 32 34;\r\n             21 22 30 31 35 36];\r\nassert(isequal(diagAdiag(x),y_correct))\r\n\r\n%%\r\nx = 7;\r\ny_correct = [ 1  2  6  7 15 16 28;\r\n              3  5  8 14 17 27 29;\r\n              4  9 13 18 26 30 39;\r\n             10 12 19 25 31 38 40;\r\n             11 20 24 32 37 41 46;\r\n             21 23 33 36 42 45 47;\r\n             22 34 35 43 44 48 49];\r\nassert(isequal(diagAdiag(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":98103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":90,"test_suite_updated_at":"2017-04-19T17:09:18.000Z","rescore_all_solutions":false,"group_id":24,"created_at":"2017-03-04T19:12:05.000Z","updated_at":"2026-04-16T15:49:35.000Z","published_at":"2017-03-04T19:15:05.000Z","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\u003eConstruct a matrix whose elements begin from 1 and end at n^2 with the order of arrangement as shown below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[n = 4]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eoutput\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[M = \\n[1   2   6   7;\\n3   5   8   13;\\n4   9   12  14;\\n10  11  15  16]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote the elements increase and decrease along alternating diagonals with the last element being always n^2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42504,"title":"Data Regularization","description":"Provided is an m-by-n integer data matrix A whose elements are drawn arbitrarily from a set *S* = [1,2,3,...,S] for any large integer number S \u003e 1. The \"arbitrary\" manner of drawing integer numbers implies that each column of A might contain only a subset of integer numbers from *S*. Our objective is to regularize the data in A subject to the following rules: \r\n\r\nFor each column in A, \r\n\r\n* The smallest number or numbers (if there are more than one such number) are mapped to 1; \r\n* The 2nd-smallest number or numbers (if there are more than one such number) are mapped to 2;\r\n* The _k_ th-smallest number or numbers (if there are more than one such number) are mapped to _k_ .\r\n\r\nFor example, *S* = [1:8] with S = 8. Suppose the input data matrix A is \r\n \r\n  A = [2  6\r\n       5  3\r\n       5  6\r\n       3  7]\r\n\r\nThen the output matrix B is \r\n\r\n  B = [1  2 \r\n       3  1\r\n       3  2\r\n       2  3]\r\n\r\nPlease try to avoid for or while loops. Vectorized code will be more appreciated. ","description_html":"\u003cp\u003eProvided is an m-by-n integer data matrix A whose elements are drawn arbitrarily from a set \u003cb\u003eS\u003c/b\u003e = [1,2,3,...,S] for any large integer number S \u0026gt; 1. The \"arbitrary\" manner of drawing integer numbers implies that each column of A might contain only a subset of integer numbers from \u003cb\u003eS\u003c/b\u003e. Our objective is to regularize the data in A subject to the following rules:\u003c/p\u003e\u003cp\u003eFor each column in A,\u003c/p\u003e\u003cul\u003e\u003cli\u003eThe smallest number or numbers (if there are more than one such number) are mapped to 1;\u003c/li\u003e\u003cli\u003eThe 2nd-smallest number or numbers (if there are more than one such number) are mapped to 2;\u003c/li\u003e\u003cli\u003eThe \u003ci\u003ek\u003c/i\u003e th-smallest number or numbers (if there are more than one such number) are mapped to \u003ci\u003ek\u003c/i\u003e .\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eFor example, \u003cb\u003eS\u003c/b\u003e = [1:8] with S = 8. Suppose the input data matrix A is\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eA = [2  6\r\n     5  3\r\n     5  6\r\n     3  7]\r\n\u003c/pre\u003e\u003cp\u003eThen the output matrix B is\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eB = [1  2 \r\n     3  1\r\n     3  2\r\n     2  3]\r\n\u003c/pre\u003e\u003cp\u003ePlease try to avoid for or while loops. Vectorized code will be more appreciated.\u003c/p\u003e","function_template":"function B = regular(A)\r\n  B = A;\r\nend","test_suite":"%%\r\nfiletext = fileread('regular.m');\r\nassert(isempty(strfind(filetext, 'for')))\r\nassert(isempty(strfind(filetext, 'while')))\r\n\r\n%%\r\nA = 1;\r\nB = 1;\r\nassert(isequal(regular(A),B));\r\n\r\n%%\r\nA = [2     6\r\n     5     3\r\n     5     6\r\n     3     7];\r\nB = [1     2\r\n     3     1\r\n     3     2\r\n     2     3];\r\nassert(isequal(regular(A),B));\r\n\r\n%%\r\nA = [10    2     4     4     2\r\n     4     5     6     8     1\r\n     6     5    10     3     9\r\n     9     9     5     5     5\r\n     9    10     3     7     8];\r\nB = [4     1     2     2     2\r\n     1     2     4     5     1\r\n     2     2     5     1     5\r\n     3     3     3     3     3\r\n     3     4     1     4     4];\r\nassert(isequal(regular(A),B));\r\n\r\n%%\r\nA = randi(100,80,100);\r\nB = zeros(size(A));\r\nfor iter = 1:size(A,2)\r\n    [~, ~, B(:, iter)] = unique(A(:,iter)); \r\nend\r\nassert(isequal(regular(A),B));\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":6,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":50,"test_suite_updated_at":"2015-08-12T07:02:47.000Z","rescore_all_solutions":false,"group_id":24,"created_at":"2015-08-12T00:30:34.000Z","updated_at":"2026-04-22T09:33:39.000Z","published_at":"2015-08-12T00:56:23.000Z","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\u003eProvided is an m-by-n integer data matrix A whose elements are drawn arbitrarily from a set\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\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = [1,2,3,...,S] for any large integer number S \u0026gt; 1. The \\\"arbitrary\\\" manner of drawing integer numbers implies that each column of A might contain only a subset of integer numbers from\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\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Our objective is to regularize the data in A subject to the following rules:\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 each column in A,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe smallest number or numbers (if there are more than one such number) are mapped to 1;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe 2nd-smallest number or numbers (if there are more than one such number) are mapped to 2;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e th-smallest number or numbers (if there are more than one such number) are mapped to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\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\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = [1:8] with S = 8. Suppose the input data matrix A 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[A = [2  6\\n     5  3\\n     5  6\\n     3  7]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen the output matrix B 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[B = [1  2 \\n     3  1\\n     3  2\\n     2  3]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease try to avoid for or while loops. Vectorized code will be more appreciated.\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":44080,"title":"Construct a \"diagAdiag\" matrix","description":"Construct a matrix whose elements begin from 1 and end at n^2 with the order of arrangement as shown below:\r\n\r\nFor:\r\n\r\n  n = 4\r\n\r\noutput\r\n\r\n  M = \r\n[1   2   6   7;\r\n 3   5   8   13;\r\n 4   9   12  14;\r\n 10  11  15  16]\r\n\r\nNote the elements increase and decrease along alternating diagonals with the last element being always n^2.\r\n","description_html":"\u003cp\u003eConstruct a matrix whose elements begin from 1 and end at n^2 with the order of arrangement as shown below:\u003c/p\u003e\u003cp\u003eFor:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003en = 4\r\n\u003c/pre\u003e\u003cp\u003eoutput\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eM = \r\n[1   2   6   7;\r\n3   5   8   13;\r\n4   9   12  14;\r\n10  11  15  16]\r\n\u003c/pre\u003e\u003cp\u003eNote the elements increase and decrease along alternating diagonals with the last element being always n^2.\u003c/p\u003e","function_template":"function y = diagAdiag(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 3;\r\ny_correct = [1 2 6; 3 5 7;4 8 9];\r\nassert(isequal(diagAdiag(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = [1   2   6   7; 3   5   8   13;4   9   12  14;10  11  15  16];\r\nassert(isequal(diagAdiag(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = [1 2 6 7 15;3 5 8 14 16;4 9 13 17 22;10 12 18 21 23;11 19 20 24 25];\r\nassert(isequal(diagAdiag(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = [ 1  2  6  7 15 16;\r\n              3  5  8 14 17 26;\r\n              4  9 13 18 25 27;\r\n             10 12 19 24 28 33;\r\n             11 20 23 29 32 34;\r\n             21 22 30 31 35 36];\r\nassert(isequal(diagAdiag(x),y_correct))\r\n\r\n%%\r\nx = 7;\r\ny_correct = [ 1  2  6  7 15 16 28;\r\n              3  5  8 14 17 27 29;\r\n              4  9 13 18 26 30 39;\r\n             10 12 19 25 31 38 40;\r\n             11 20 24 32 37 41 46;\r\n             21 23 33 36 42 45 47;\r\n             22 34 35 43 44 48 49];\r\nassert(isequal(diagAdiag(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":98103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":90,"test_suite_updated_at":"2017-04-19T17:09:18.000Z","rescore_all_solutions":false,"group_id":24,"created_at":"2017-03-04T19:12:05.000Z","updated_at":"2026-04-16T15:49:35.000Z","published_at":"2017-03-04T19:15:05.000Z","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\u003eConstruct a matrix whose elements begin from 1 and end at n^2 with the order of arrangement as shown below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[n = 4]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eoutput\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[M = \\n[1   2   6   7;\\n3   5   8   13;\\n4   9   12  14;\\n10  11  15  16]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote the elements increase and decrease along alternating diagonals with the last element being always n^2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42504,"title":"Data Regularization","description":"Provided is an m-by-n integer data matrix A whose elements are drawn arbitrarily from a set *S* = [1,2,3,...,S] for any large integer number S \u003e 1. The \"arbitrary\" manner of drawing integer numbers implies that each column of A might contain only a subset of integer numbers from *S*. Our objective is to regularize the data in A subject to the following rules: \r\n\r\nFor each column in A, \r\n\r\n* The smallest number or numbers (if there are more than one such number) are mapped to 1; \r\n* The 2nd-smallest number or numbers (if there are more than one such number) are mapped to 2;\r\n* The _k_ th-smallest number or numbers (if there are more than one such number) are mapped to _k_ .\r\n\r\nFor example, *S* = [1:8] with S = 8. Suppose the input data matrix A is \r\n \r\n  A = [2  6\r\n       5  3\r\n       5  6\r\n       3  7]\r\n\r\nThen the output matrix B is \r\n\r\n  B = [1  2 \r\n       3  1\r\n       3  2\r\n       2  3]\r\n\r\nPlease try to avoid for or while loops. Vectorized code will be more appreciated. ","description_html":"\u003cp\u003eProvided is an m-by-n integer data matrix A whose elements are drawn arbitrarily from a set \u003cb\u003eS\u003c/b\u003e = [1,2,3,...,S] for any large integer number S \u0026gt; 1. The \"arbitrary\" manner of drawing integer numbers implies that each column of A might contain only a subset of integer numbers from \u003cb\u003eS\u003c/b\u003e. Our objective is to regularize the data in A subject to the following rules:\u003c/p\u003e\u003cp\u003eFor each column in A,\u003c/p\u003e\u003cul\u003e\u003cli\u003eThe smallest number or numbers (if there are more than one such number) are mapped to 1;\u003c/li\u003e\u003cli\u003eThe 2nd-smallest number or numbers (if there are more than one such number) are mapped to 2;\u003c/li\u003e\u003cli\u003eThe \u003ci\u003ek\u003c/i\u003e th-smallest number or numbers (if there are more than one such number) are mapped to \u003ci\u003ek\u003c/i\u003e .\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eFor example, \u003cb\u003eS\u003c/b\u003e = [1:8] with S = 8. Suppose the input data matrix A is\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eA = [2  6\r\n     5  3\r\n     5  6\r\n     3  7]\r\n\u003c/pre\u003e\u003cp\u003eThen the output matrix B is\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eB = [1  2 \r\n     3  1\r\n     3  2\r\n     2  3]\r\n\u003c/pre\u003e\u003cp\u003ePlease try to avoid for or while loops. Vectorized code will be more appreciated.\u003c/p\u003e","function_template":"function B = regular(A)\r\n  B = A;\r\nend","test_suite":"%%\r\nfiletext = fileread('regular.m');\r\nassert(isempty(strfind(filetext, 'for')))\r\nassert(isempty(strfind(filetext, 'while')))\r\n\r\n%%\r\nA = 1;\r\nB = 1;\r\nassert(isequal(regular(A),B));\r\n\r\n%%\r\nA = [2     6\r\n     5     3\r\n     5     6\r\n     3     7];\r\nB = [1     2\r\n     3     1\r\n     3     2\r\n     2     3];\r\nassert(isequal(regular(A),B));\r\n\r\n%%\r\nA = [10    2     4     4     2\r\n     4     5     6     8     1\r\n     6     5    10     3     9\r\n     9     9     5     5     5\r\n     9    10     3     7     8];\r\nB = [4     1     2     2     2\r\n     1     2     4     5     1\r\n     2     2     5     1     5\r\n     3     3     3     3     3\r\n     3     4     1     4     4];\r\nassert(isequal(regular(A),B));\r\n\r\n%%\r\nA = randi(100,80,100);\r\nB = zeros(size(A));\r\nfor iter = 1:size(A,2)\r\n    [~, ~, B(:, iter)] = unique(A(:,iter)); \r\nend\r\nassert(isequal(regular(A),B));\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":6,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":50,"test_suite_updated_at":"2015-08-12T07:02:47.000Z","rescore_all_solutions":false,"group_id":24,"created_at":"2015-08-12T00:30:34.000Z","updated_at":"2026-04-22T09:33:39.000Z","published_at":"2015-08-12T00:56:23.000Z","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\u003eProvided is an m-by-n integer data matrix A whose elements are drawn arbitrarily from a set\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\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = [1,2,3,...,S] for any large integer number S \u0026gt; 1. The \\\"arbitrary\\\" manner of drawing integer numbers implies that each column of A might contain only a subset of integer numbers from\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\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Our objective is to regularize the data in A subject to the following rules:\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 each column in A,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe smallest number or numbers (if there are more than one such number) are mapped to 1;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe 2nd-smallest number or numbers (if there are more than one such number) are mapped to 2;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e th-smallest number or numbers (if there are more than one such number) are mapped to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\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\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = [1:8] with S = 8. Suppose the input data matrix A 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[A = [2  6\\n     5  3\\n     5  6\\n     3  7]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen the output matrix B 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[B = [1  2 \\n     3  1\\n     3  2\\n     2  3]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease try to avoid for or while loops. Vectorized code will be more appreciated.\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":"group:\"Matrix Manipulation III\" 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