{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-06-05T00:10:21.000Z","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":"2026-06-05T00:00:00.000Z","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":2732,"title":"Construct a precedence graph from a code segment","description":"A hypothetical MATLAB code segment containing n lines is given in the form of a cell array. The i-th cell contains the i-th line of the code. Each of the lines contains simple arithmetic expressions.\r\n\r\nNow, construct an adjacency matrix of a graph containing n-vertices. The i-th vertex will represent the i-th line of the code. There should be a directed edge from i-th vertex to j-th vertex only if the values generated at i-th line are used in the j-th line.\r\n\r\nAll the variables in the code will have single letter names (e.g.: a,b,x,y etc).\r\n\r\nExample:\r\n\r\n  C = {'a=1;'\r\n       'b=1;'\r\n       'c=a+b;'\r\n       'c=c+1;'};\r\n\r\nHere, the cell array C contains a code segment. The first two lines are independent in the sense that they do not use values generated at any other lines. The third line uses information generated at line 1 and 2. The fourth line uses information generated at line 1,2 and 3.\r\n\r\nThus the resulting adjacency matrix will be as follows:\r\n\r\n  \r\n  mat = [0 0 1 1;\r\n         0 0 1 1;\r\n         0 0 0 1;\r\n         0 0 0 0];\r\n\r\n\r\n\r\n\r\nDefinition of adjacency matrix:\r\n\u003chttp://en.wikipedia.org/wiki/Adjacency_matrix\u003e","description_html":"\u003cp\u003eA hypothetical MATLAB code segment containing n lines is given in the form of a cell array. The i-th cell contains the i-th line of the code. Each of the lines contains simple arithmetic expressions.\u003c/p\u003e\u003cp\u003eNow, construct an adjacency matrix of a graph containing n-vertices. The i-th vertex will represent the i-th line of the code. There should be a directed edge from i-th vertex to j-th vertex only if the values generated at i-th line are used in the j-th line.\u003c/p\u003e\u003cp\u003eAll the variables in the code will have single letter names (e.g.: a,b,x,y etc).\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eC = {'a=1;'\r\n     'b=1;'\r\n     'c=a+b;'\r\n     'c=c+1;'};\r\n\u003c/pre\u003e\u003cp\u003eHere, the cell array C contains a code segment. The first two lines are independent in the sense that they do not use values generated at any other lines. The third line uses information generated at line 1 and 2. The fourth line uses information generated at line 1,2 and 3.\u003c/p\u003e\u003cp\u003eThus the resulting adjacency matrix will be as follows:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003emat = [0 0 1 1;\r\n       0 0 1 1;\r\n       0 0 0 1;\r\n       0 0 0 0];\r\n\u003c/pre\u003e\u003cp\u003eDefinition of adjacency matrix: \u003ca href = \"http://en.wikipedia.org/wiki/Adjacency_matrix\"\u003ehttp://en.wikipedia.org/wiki/Adjacency_matrix\u003c/a\u003e\u003c/p\u003e","function_template":"function y = pGraph(x)\r\n\r\n\r\n\r\n\r\nend","test_suite":"%%\r\nC = {'a=1;'\r\n     'b=1;'\r\n     'c=a+b;'\r\n     'c=c+1;'};\r\nmat = [0 0 1 1;\r\n       0 0 1 1;\r\n       0 0 0 1;\r\n       0 0 0 0];\r\nassert(isequal(pGraph(C),mat))\r\n\r\n\r\n\r\n%%\r\nC = {'a=1;'\r\n     'a=1;'\r\n     'c=1;'\r\n     'c=1;'};\r\nmat = [0 0 0 0;\r\n       0 0 0 0;\r\n       0 0 0 0;\r\n       0 0 0 0];\r\nassert(isequal(pGraph(C),mat))\r\n\r\n%%\r\nC = {'a=1;'\r\n     'a=1;'\r\n     'c=a+1;'\r\n     'c=a+1;'};\r\nmat = [0 0 0 0;\r\n       0 0 1 1;\r\n       0 0 0 0;\r\n       0 0 0 0];\r\nassert(isequal(pGraph(C),mat))\r\n\r\n%%\r\nC = {'a=1;'\r\n     'b=a+2;'\r\n     'c=b+1;'\r\n     'd=c+1;'};\r\nmat = double(~tril(ones(4)))\r\nassert(isequal(pGraph(C),mat))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":17203,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2014-12-06T07:56:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-12-06T07:54:40.000Z","updated_at":"2026-05-31T16:51:08.000Z","published_at":"2014-12-06T07:54:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA hypothetical MATLAB code segment containing n lines is given in the form of a cell array. The i-th cell contains the i-th line of the code. Each of the lines contains simple arithmetic expressions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNow, construct an adjacency matrix of a graph containing n-vertices. The i-th vertex will represent the i-th line of the code. There should be a directed edge from i-th vertex to j-th vertex only if the values generated at i-th line are used in the j-th line.\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\u003eAll the variables in the code will have single letter names (e.g.: a,b,x,y etc).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[C = {'a=1;'\\n     'b=1;'\\n     'c=a+b;'\\n     'c=c+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\u003eHere, the cell array C contains a code segment. The first two lines are independent in the sense that they do not use values generated at any other lines. The third line uses information generated at line 1 and 2. The fourth line uses information generated at line 1,2 and 3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThus the resulting adjacency matrix will be as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[mat = [0 0 1 1;\\n       0 0 1 1;\\n       0 0 0 1;\\n       0 0 0 0];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDefinition of adjacency matrix:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Adjacency_matrix\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://en.wikipedia.org/wiki/Adjacency_matrix\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\"}]}"}],"problem_search":{"problems":[{"id":2732,"title":"Construct a precedence graph from a code segment","description":"A hypothetical MATLAB code segment containing n lines is given in the form of a cell array. The i-th cell contains the i-th line of the code. Each of the lines contains simple arithmetic expressions.\r\n\r\nNow, construct an adjacency matrix of a graph containing n-vertices. The i-th vertex will represent the i-th line of the code. There should be a directed edge from i-th vertex to j-th vertex only if the values generated at i-th line are used in the j-th line.\r\n\r\nAll the variables in the code will have single letter names (e.g.: a,b,x,y etc).\r\n\r\nExample:\r\n\r\n  C = {'a=1;'\r\n       'b=1;'\r\n       'c=a+b;'\r\n       'c=c+1;'};\r\n\r\nHere, the cell array C contains a code segment. The first two lines are independent in the sense that they do not use values generated at any other lines. The third line uses information generated at line 1 and 2. The fourth line uses information generated at line 1,2 and 3.\r\n\r\nThus the resulting adjacency matrix will be as follows:\r\n\r\n  \r\n  mat = [0 0 1 1;\r\n         0 0 1 1;\r\n         0 0 0 1;\r\n         0 0 0 0];\r\n\r\n\r\n\r\n\r\nDefinition of adjacency matrix:\r\n\u003chttp://en.wikipedia.org/wiki/Adjacency_matrix\u003e","description_html":"\u003cp\u003eA hypothetical MATLAB code segment containing n lines is given in the form of a cell array. The i-th cell contains the i-th line of the code. Each of the lines contains simple arithmetic expressions.\u003c/p\u003e\u003cp\u003eNow, construct an adjacency matrix of a graph containing n-vertices. The i-th vertex will represent the i-th line of the code. There should be a directed edge from i-th vertex to j-th vertex only if the values generated at i-th line are used in the j-th line.\u003c/p\u003e\u003cp\u003eAll the variables in the code will have single letter names (e.g.: a,b,x,y etc).\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eC = {'a=1;'\r\n     'b=1;'\r\n     'c=a+b;'\r\n     'c=c+1;'};\r\n\u003c/pre\u003e\u003cp\u003eHere, the cell array C contains a code segment. The first two lines are independent in the sense that they do not use values generated at any other lines. The third line uses information generated at line 1 and 2. The fourth line uses information generated at line 1,2 and 3.\u003c/p\u003e\u003cp\u003eThus the resulting adjacency matrix will be as follows:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003emat = [0 0 1 1;\r\n       0 0 1 1;\r\n       0 0 0 1;\r\n       0 0 0 0];\r\n\u003c/pre\u003e\u003cp\u003eDefinition of adjacency matrix: \u003ca href = \"http://en.wikipedia.org/wiki/Adjacency_matrix\"\u003ehttp://en.wikipedia.org/wiki/Adjacency_matrix\u003c/a\u003e\u003c/p\u003e","function_template":"function y = pGraph(x)\r\n\r\n\r\n\r\n\r\nend","test_suite":"%%\r\nC = {'a=1;'\r\n     'b=1;'\r\n     'c=a+b;'\r\n     'c=c+1;'};\r\nmat = [0 0 1 1;\r\n       0 0 1 1;\r\n       0 0 0 1;\r\n       0 0 0 0];\r\nassert(isequal(pGraph(C),mat))\r\n\r\n\r\n\r\n%%\r\nC = {'a=1;'\r\n     'a=1;'\r\n     'c=1;'\r\n     'c=1;'};\r\nmat = [0 0 0 0;\r\n       0 0 0 0;\r\n       0 0 0 0;\r\n       0 0 0 0];\r\nassert(isequal(pGraph(C),mat))\r\n\r\n%%\r\nC = {'a=1;'\r\n     'a=1;'\r\n     'c=a+1;'\r\n     'c=a+1;'};\r\nmat = [0 0 0 0;\r\n       0 0 1 1;\r\n       0 0 0 0;\r\n       0 0 0 0];\r\nassert(isequal(pGraph(C),mat))\r\n\r\n%%\r\nC = {'a=1;'\r\n     'b=a+2;'\r\n     'c=b+1;'\r\n     'd=c+1;'};\r\nmat = double(~tril(ones(4)))\r\nassert(isequal(pGraph(C),mat))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":17203,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2014-12-06T07:56:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-12-06T07:54:40.000Z","updated_at":"2026-05-31T16:51:08.000Z","published_at":"2014-12-06T07:54:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA hypothetical MATLAB code segment containing n lines is given in the form of a cell array. The i-th cell contains the i-th line of the code. Each of the lines contains simple arithmetic expressions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNow, construct an adjacency matrix of a graph containing n-vertices. The i-th vertex will represent the i-th line of the code. There should be a directed edge from i-th vertex to j-th vertex only if the values generated at i-th line are used in the j-th line.\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\u003eAll the variables in the code will have single letter names (e.g.: a,b,x,y etc).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[C = {'a=1;'\\n     'b=1;'\\n     'c=a+b;'\\n     'c=c+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\u003eHere, the cell array C contains a code segment. The first two lines are independent in the sense that they do not use values generated at any other lines. The third line uses information generated at line 1 and 2. The fourth line uses information generated at line 1,2 and 3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThus the resulting adjacency matrix will be as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[mat = [0 0 1 1;\\n       0 0 1 1;\\n       0 0 0 1;\\n       0 0 0 0];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDefinition of adjacency matrix:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Adjacency_matrix\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://en.wikipedia.org/wiki/Adjacency_matrix\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\"}]}"}],"errors":[],"facets":[[],[{"value":"medium","count":1,"selected":false}]],"term":"tag:\"precedence\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}