{"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":695,"title":"Parse string and identify specific string sequence in algebraic equation","description":"Given a string S that defines an algebraic expression such as: \r\n\r\nS= 'X= A1 + A2*(Y1 + A3*Y3)*exp( A4*Y12 + Y1) ;' \r\n\r\nreturn a cell array {'Y1', 'Y12', 'Y123'}\r\n\r\ni.e. parse the string S and identify the unique variables in the expression that start with the letter \"Y\".\r\n","description_html":"\u003cp\u003eGiven a string S that defines an algebraic expression such as:\u003c/p\u003e\u003cp\u003eS= 'X= A1 + A2*(Y1 + A3*Y3)*exp( A4*Y12 + Y1) ;'\u003c/p\u003e\u003cp\u003ereturn a cell array {'Y1', 'Y12', 'Y123'}\u003c/p\u003e\u003cp\u003ei.e. parse the string S and identify the unique variables in the expression that start with the letter \"Y\".\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 'X= A1 + A2*(Y1 + A3*Y123) ;' ;\r\ny_correct = {'Y1', 'Y123'} ;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%% \r\nx= 'X= A + B*Y1*exp( C + D*Y12**2)' ;\r\ny_correct = {'Y1', 'Y12'} ;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%% \r\nx= 'X= A + B*log( Y1 + 2) ; Z= atan( C + D*Y3*exp( C + D*Y12**2)' ;\r\ny_correct = {'Y1', 'Y12', 'Y3'} ;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":2949,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":60,"test_suite_updated_at":"2012-05-17T01:12:07.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-05-17T00:32:36.000Z","updated_at":"2026-03-31T12:54:13.000Z","published_at":"2012-05-17T00:41:24.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a string S that defines an algebraic expression such as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eS= 'X= A1 + A2*(Y1 + A3*Y3)*exp( A4*Y12 + Y1) ;'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ereturn a cell array {'Y1', 'Y12', 'Y123'}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ei.e. parse the string S and identify the unique variables in the expression that start with the letter \\\"Y\\\".\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":221,"title":"Boolean algebra","description":"Your contractor from Elbonia has sent you the prototype of the new logical unit. It turns out that the only logical relation it understands is \"nand\":\r\n\r\n  nand(a,b) := ~(a\u0026b)\r\n\r\nYour team has been developing code using the usual logical operators following MATLAB syntax: |~,\u0026| and |||. To save the project you need to write a translator that expresses MATLAB logical expressions using only the |nand| function.\r\n\r\nInput\r\n\r\n* expr: a string containing a valid logical expression in MATLAB, that relates the two logical variables |a| and |b|\r\n\r\nOutput\r\n\r\n* out: a string containing an equivalent logical expression that may only use the function |nand(a,b)|.\r\n\r\nExample 1:\r\n\r\n    expr = 'a|(~b)'\r\n  =\u003eout  = 'nand(nand(a,a),b)'\r\n\r\nExample 2:\r\n\r\n    expr = '(a \u0026 ~a) | ~(a|b)'\r\n  =\u003eout  = 'nand(nand(nand(a,a),nand(b,b)),nand(nand(a,a),nand(b,b)))'\r\n\r\nRemarks:\r\n\r\nIt is not necessary to provide the shortest solution. A solution always exists. The input string is non-empty and always evaluates to true or false, if |a| and |b| are logical variables. All substrings in the output that are not 'a','b','0','1','true','false','(',')' or'nand' will be ignored.","description_html":"\u003cp\u003eYour contractor from Elbonia has sent you the prototype of the new logical unit. It turns out that the only logical relation it understands is \"nand\":\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003enand(a,b) := ~(a\u0026b)\r\n\u003c/pre\u003e\u003cp\u003eYour team has been developing code using the usual logical operators following MATLAB syntax: \u003ctt\u003e~,\u0026\u003c/tt\u003e and \u003ctt\u003e|\u003c/tt\u003e. To save the project you need to write a translator that expresses MATLAB logical expressions using only the \u003ctt\u003enand\u003c/tt\u003e function.\u003c/p\u003e\u003cp\u003eInput\u003c/p\u003e\u003cul\u003e\u003cli\u003eexpr: a string containing a valid logical expression in MATLAB, that relates the two logical variables \u003ctt\u003ea\u003c/tt\u003e and \u003ctt\u003eb\u003c/tt\u003e\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eOutput\u003c/p\u003e\u003cul\u003e\u003cli\u003eout: a string containing an equivalent logical expression that may only use the function \u003ctt\u003enand(a,b)\u003c/tt\u003e.\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eExample 1:\u003c/p\u003e\u003cpre\u003e    expr = 'a|(~b)'\r\n  =\u003eout  = 'nand(nand(a,a),b)'\u003c/pre\u003e\u003cp\u003eExample 2:\u003c/p\u003e\u003cpre\u003e    expr = '(a \u0026 ~a) | ~(a|b)'\r\n  =\u003eout  = 'nand(nand(nand(a,a),nand(b,b)),nand(nand(a,a),nand(b,b)))'\u003c/pre\u003e\u003cp\u003eRemarks:\u003c/p\u003e\u003cp\u003eIt is not necessary to provide the shortest solution. A solution always exists. The input string is non-empty and always evaluates to true or false, if \u003ctt\u003ea\u003c/tt\u003e and \u003ctt\u003eb\u003c/tt\u003e are logical variables. All substrings in the output that are not 'a','b','0','1','true','false','(',')' or'nand' will be ignored.\u003c/p\u003e","function_template":"function out = mat2nand(expr)\r\n  out = '';\r\nend","test_suite":"%% is ~(a\u0026b) == nand(a,b)?\r\nnand = @(x,y) (~(x\u0026y));\r\nexpr = '~(a\u0026b)';\r\nsol = regexprep(mat2nand(expr),'[^(nand)ab\\(\\),01(true)(false)]*','');\r\nfor a=[0 1], for b=[0 1]\r\n   res(a+1,b+1) = eval(sol);\r\nend; end\r\nif isempty(strfind(which('isequal'),'built-in')) || isempty(strfind(which('assert'),'built-in'))\r\n   error('test-suite manipulation attempt detected')\r\nend\r\nassert(isequal(res , logical([1 1; 1 0])))\r\n\r\n%% a complicated \"and\"\r\nnand = @(x,y) (~(x\u0026y));\r\nexpr = '(a\u0026~a)|(b\u0026~b)|((a\u0026b)\u0026(a|~a))';\r\nsol = regexprep(mat2nand(expr),'[^(nand)ab\\(\\),01(true)(false)]*','');\r\nfor a=[0 1], for b=[0 1]\r\n   res(a+1,b+1) = eval(sol);\r\nend; end\r\nif isempty(strfind(which('isequal'),'built-in')) || isempty(strfind(which('assert'),'built-in'))\r\n   error('test-suite manipulation attempt detected')\r\nend\r\nassert(isequal(res , logical([0 0; 0 1])))\r\n\r\n%% a randomized test (repeated 5times)\r\nnand = @(x,y) (~(x\u0026y));\r\nrules ={{'a','~(a|b)'},{'b','(~b\u0026a)\u0026a'},{'a','(a\u0026~a)|(~(b\u0026~b))\u0026b'},{'b','a\u0026b|~a\u0026~b'}};\r\nfor nrep=1:5\r\n   expr='a|b';\r\n   for l=1:randi(10)+5\r\n      rn=randi(4);\r\n      expr = regexprep(expr,rules{rn}(1),rules{rn}(2),'once');\r\n   end\r\n   sol = regexprep(mat2nand(expr),'[^(nand)ab\\(\\),01(true)(false)]*','');\r\n   for a=[0 1], for b=[0 1]\r\n      res(a+1,b+1) = eval(sol);\r\n      cor(a+1,b+1) = eval(expr);\r\n   end; end\r\n   if isempty(strfind(which('isequal'),'built-in')) || isempty(strfind(which('assert'),'built-in'))\r\n      error('test-suite manipulation attempt detected')\r\n   end\r\n   assert(isequal(res , cor))\r\nend","published":true,"deleted":false,"likes_count":4,"comments_count":10,"created_by":203,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2013-01-24T14:41:51.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-01T23:36:17.000Z","updated_at":"2025-01-01T21:28:37.000Z","published_at":"2012-02-02T13:42:48.000Z","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\u003eYour contractor from Elbonia has sent you the prototype of the new logical unit. It turns out that the only logical relation it understands is \\\"nand\\\":\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[nand(a,b) := ~(a\u0026b)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour team has been developing code using the usual logical operators following MATLAB syntax:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e~,\u0026amp;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e|. To save the project you need to write a translator that expresses MATLAB logical expressions using only the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function.\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\u003eInput\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\u003eexpr: a string containing a valid logical expression in MATLAB, that relates the two logical variables\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\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=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eout: a string containing an equivalent logical expression that may only use the function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enand(a,b)\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\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    expr = 'a|(~b)'\\n  =\u003eout  = 'nand(nand(a,a),b)']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    expr = '(a \u0026 ~a) | ~(a|b)'\\n  =\u003eout  = 'nand(nand(nand(a,a),nand(b,b)),nand(nand(a,a),nand(b,b)))']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRemarks:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt is not necessary to provide the shortest solution. A solution always exists. The input string is non-empty and always evaluates to true or false, if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are logical variables. All substrings in the output that are not 'a','b','0','1','true','false','(',')' or'nand' will be ignored.\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":695,"title":"Parse string and identify specific string sequence in algebraic equation","description":"Given a string S that defines an algebraic expression such as: \r\n\r\nS= 'X= A1 + A2*(Y1 + A3*Y3)*exp( A4*Y12 + Y1) ;' \r\n\r\nreturn a cell array {'Y1', 'Y12', 'Y123'}\r\n\r\ni.e. parse the string S and identify the unique variables in the expression that start with the letter \"Y\".\r\n","description_html":"\u003cp\u003eGiven a string S that defines an algebraic expression such as:\u003c/p\u003e\u003cp\u003eS= 'X= A1 + A2*(Y1 + A3*Y3)*exp( A4*Y12 + Y1) ;'\u003c/p\u003e\u003cp\u003ereturn a cell array {'Y1', 'Y12', 'Y123'}\u003c/p\u003e\u003cp\u003ei.e. parse the string S and identify the unique variables in the expression that start with the letter \"Y\".\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 'X= A1 + A2*(Y1 + A3*Y123) ;' ;\r\ny_correct = {'Y1', 'Y123'} ;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%% \r\nx= 'X= A + B*Y1*exp( C + D*Y12**2)' ;\r\ny_correct = {'Y1', 'Y12'} ;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%% \r\nx= 'X= A + B*log( Y1 + 2) ; Z= atan( C + D*Y3*exp( C + D*Y12**2)' ;\r\ny_correct = {'Y1', 'Y12', 'Y3'} ;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":2949,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":60,"test_suite_updated_at":"2012-05-17T01:12:07.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-05-17T00:32:36.000Z","updated_at":"2026-03-31T12:54:13.000Z","published_at":"2012-05-17T00:41:24.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a string S that defines an algebraic expression such as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eS= 'X= A1 + A2*(Y1 + A3*Y3)*exp( A4*Y12 + Y1) ;'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ereturn a cell array {'Y1', 'Y12', 'Y123'}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ei.e. parse the string S and identify the unique variables in the expression that start with the letter \\\"Y\\\".\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":221,"title":"Boolean algebra","description":"Your contractor from Elbonia has sent you the prototype of the new logical unit. It turns out that the only logical relation it understands is \"nand\":\r\n\r\n  nand(a,b) := ~(a\u0026b)\r\n\r\nYour team has been developing code using the usual logical operators following MATLAB syntax: |~,\u0026| and |||. To save the project you need to write a translator that expresses MATLAB logical expressions using only the |nand| function.\r\n\r\nInput\r\n\r\n* expr: a string containing a valid logical expression in MATLAB, that relates the two logical variables |a| and |b|\r\n\r\nOutput\r\n\r\n* out: a string containing an equivalent logical expression that may only use the function |nand(a,b)|.\r\n\r\nExample 1:\r\n\r\n    expr = 'a|(~b)'\r\n  =\u003eout  = 'nand(nand(a,a),b)'\r\n\r\nExample 2:\r\n\r\n    expr = '(a \u0026 ~a) | ~(a|b)'\r\n  =\u003eout  = 'nand(nand(nand(a,a),nand(b,b)),nand(nand(a,a),nand(b,b)))'\r\n\r\nRemarks:\r\n\r\nIt is not necessary to provide the shortest solution. A solution always exists. The input string is non-empty and always evaluates to true or false, if |a| and |b| are logical variables. All substrings in the output that are not 'a','b','0','1','true','false','(',')' or'nand' will be ignored.","description_html":"\u003cp\u003eYour contractor from Elbonia has sent you the prototype of the new logical unit. It turns out that the only logical relation it understands is \"nand\":\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003enand(a,b) := ~(a\u0026b)\r\n\u003c/pre\u003e\u003cp\u003eYour team has been developing code using the usual logical operators following MATLAB syntax: \u003ctt\u003e~,\u0026\u003c/tt\u003e and \u003ctt\u003e|\u003c/tt\u003e. To save the project you need to write a translator that expresses MATLAB logical expressions using only the \u003ctt\u003enand\u003c/tt\u003e function.\u003c/p\u003e\u003cp\u003eInput\u003c/p\u003e\u003cul\u003e\u003cli\u003eexpr: a string containing a valid logical expression in MATLAB, that relates the two logical variables \u003ctt\u003ea\u003c/tt\u003e and \u003ctt\u003eb\u003c/tt\u003e\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eOutput\u003c/p\u003e\u003cul\u003e\u003cli\u003eout: a string containing an equivalent logical expression that may only use the function \u003ctt\u003enand(a,b)\u003c/tt\u003e.\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eExample 1:\u003c/p\u003e\u003cpre\u003e    expr = 'a|(~b)'\r\n  =\u003eout  = 'nand(nand(a,a),b)'\u003c/pre\u003e\u003cp\u003eExample 2:\u003c/p\u003e\u003cpre\u003e    expr = '(a \u0026 ~a) | ~(a|b)'\r\n  =\u003eout  = 'nand(nand(nand(a,a),nand(b,b)),nand(nand(a,a),nand(b,b)))'\u003c/pre\u003e\u003cp\u003eRemarks:\u003c/p\u003e\u003cp\u003eIt is not necessary to provide the shortest solution. A solution always exists. The input string is non-empty and always evaluates to true or false, if \u003ctt\u003ea\u003c/tt\u003e and \u003ctt\u003eb\u003c/tt\u003e are logical variables. All substrings in the output that are not 'a','b','0','1','true','false','(',')' or'nand' will be ignored.\u003c/p\u003e","function_template":"function out = mat2nand(expr)\r\n  out = '';\r\nend","test_suite":"%% is ~(a\u0026b) == nand(a,b)?\r\nnand = @(x,y) (~(x\u0026y));\r\nexpr = '~(a\u0026b)';\r\nsol = regexprep(mat2nand(expr),'[^(nand)ab\\(\\),01(true)(false)]*','');\r\nfor a=[0 1], for b=[0 1]\r\n   res(a+1,b+1) = eval(sol);\r\nend; end\r\nif isempty(strfind(which('isequal'),'built-in')) || isempty(strfind(which('assert'),'built-in'))\r\n   error('test-suite manipulation attempt detected')\r\nend\r\nassert(isequal(res , logical([1 1; 1 0])))\r\n\r\n%% a complicated \"and\"\r\nnand = @(x,y) (~(x\u0026y));\r\nexpr = '(a\u0026~a)|(b\u0026~b)|((a\u0026b)\u0026(a|~a))';\r\nsol = regexprep(mat2nand(expr),'[^(nand)ab\\(\\),01(true)(false)]*','');\r\nfor a=[0 1], for b=[0 1]\r\n   res(a+1,b+1) = eval(sol);\r\nend; end\r\nif isempty(strfind(which('isequal'),'built-in')) || isempty(strfind(which('assert'),'built-in'))\r\n   error('test-suite manipulation attempt detected')\r\nend\r\nassert(isequal(res , logical([0 0; 0 1])))\r\n\r\n%% a randomized test (repeated 5times)\r\nnand = @(x,y) (~(x\u0026y));\r\nrules ={{'a','~(a|b)'},{'b','(~b\u0026a)\u0026a'},{'a','(a\u0026~a)|(~(b\u0026~b))\u0026b'},{'b','a\u0026b|~a\u0026~b'}};\r\nfor nrep=1:5\r\n   expr='a|b';\r\n   for l=1:randi(10)+5\r\n      rn=randi(4);\r\n      expr = regexprep(expr,rules{rn}(1),rules{rn}(2),'once');\r\n   end\r\n   sol = regexprep(mat2nand(expr),'[^(nand)ab\\(\\),01(true)(false)]*','');\r\n   for a=[0 1], for b=[0 1]\r\n      res(a+1,b+1) = eval(sol);\r\n      cor(a+1,b+1) = eval(expr);\r\n   end; end\r\n   if isempty(strfind(which('isequal'),'built-in')) || isempty(strfind(which('assert'),'built-in'))\r\n      error('test-suite manipulation attempt detected')\r\n   end\r\n   assert(isequal(res , cor))\r\nend","published":true,"deleted":false,"likes_count":4,"comments_count":10,"created_by":203,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2013-01-24T14:41:51.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-01T23:36:17.000Z","updated_at":"2025-01-01T21:28:37.000Z","published_at":"2012-02-02T13:42:48.000Z","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\u003eYour contractor from Elbonia has sent you the prototype of the new logical unit. It turns out that the only logical relation it understands is \\\"nand\\\":\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[nand(a,b) := ~(a\u0026b)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour team has been developing code using the usual logical operators following MATLAB syntax:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e~,\u0026amp;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e|. To save the project you need to write a translator that expresses MATLAB logical expressions using only the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function.\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\u003eInput\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\u003eexpr: a string containing a valid logical expression in MATLAB, that relates the two logical variables\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\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=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eout: a string containing an equivalent logical expression that may only use the function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enand(a,b)\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\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    expr = 'a|(~b)'\\n  =\u003eout  = 'nand(nand(a,a),b)']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    expr = '(a \u0026 ~a) | ~(a|b)'\\n  =\u003eout  = 'nand(nand(nand(a,a),nand(b,b)),nand(nand(a,a),nand(b,b)))']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRemarks:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt is not necessary to provide the shortest solution. A solution always exists. The input string is non-empty and always evaluates to true or false, if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are logical variables. 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