{"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":1885,"title":"Minimum Sum thru a Lower Triangle","description":"This Challenge is to find the minimum cumulative sum that traverses from row-1 thru row-N via vertical/diagonal adjacent elements of adjacent rows.\r\n\r\nThe input is a series of values of length n*(n+1)/2.\r\n\r\n*Input:* S  [Series that can be converted into a lower triangle]\r\n\r\n*Output:* MinSum  [Minimum cost path from top to bottom]\r\n\r\n*Example:*\r\n\r\n[5 7 6 3 2 5] becomes\r\n\r\n  5 0 0\r\n  7 6 0\r\n  3 2 5\r\n\r\nCreates a MinSum of 13 [5+6+2].  The 5 can only see 6, 3 sees 7 and 6, while 2 sees 7 6 0.\r\n ","description_html":"\u003cp\u003eThis Challenge is to find the minimum cumulative sum that traverses from row-1 thru row-N via vertical/diagonal adjacent elements of adjacent rows.\u003c/p\u003e\u003cp\u003eThe input is a series of values of length n*(n+1)/2.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e S  [Series that can be converted into a lower triangle]\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e MinSum  [Minimum cost path from top to bottom]\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cp\u003e[5 7 6 3 2 5] becomes\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e5 0 0\r\n7 6 0\r\n3 2 5\r\n\u003c/pre\u003e\u003cp\u003eCreates a MinSum of 13 [5+6+2].  The 5 can only see 6, 3 sees 7 and 6, while 2 sees 7 6 0.\u003c/p\u003e","function_template":"function MinSum=Find_MinSum(s)\r\n MinSum=0;\r\nend","test_suite":"%%\r\ns=[5 7 6 3 2 5];\r\nMinSum=Find_MinSum(s);\r\nexp=13;\r\nassert(exp==MinSum)\r\n%%\r\ns=[7 9 8 3 2 6 7 1 5   5 9   4   8   2   4 6   3   2   9   7   5 7   2   4   8   5   1   9 4   2   9   3   8   5   2   8  8   2   4   8   5   9   2   7   3];\r\nMinSum=Find_MinSum(s);\r\nexp=30;\r\nassert(exp==MinSum)\r\n%%\r\ns=[21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1];\r\nMinSum=Find_MinSum(s);\r\nexp=76;\r\nassert(exp==MinSum)\r\n%%\r\ns=1:28;\r\nMinSum=Find_MinSum(s);\r\nexp=63;\r\nassert(exp==MinSum)\r\n%%\r\ns=[82 91 13 92 64 10 28 55 96 97 16 98 96 49 81 15 43 92 80 96 66 4 85 94 68 76 75 40 66 18 71 4 28 5 10 83 ];\r\nMinSum=Find_MinSum(s);\r\nexp=213;\r\nassert(exp==MinSum)\r\n%%\r\ns=[348 159 476 18 220 191 383 398 94 245 223 324 355 378 139 340 328 82 60 250 480 171 293 112 376 128 253 350 446 480 274 70 75 129 421 128 ];\r\nMinSum=Find_MinSum(s);\r\nexp=1409;\r\nassert(exp==MinSum)\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-09-21T02:45:50.000Z","updated_at":"2025-12-04T12:10:46.000Z","published_at":"2013-09-21T03:00:18.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to find the minimum cumulative sum that traverses from row-1 thru row-N via vertical/diagonal adjacent elements of adjacent rows.\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 input is a series of values of length n*(n+1)/2.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e S [Series that can be converted into a lower triangle]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e MinSum [Minimum cost path from top to bottom]\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[5 7 6 3 2 5] becomes\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[5 0 0\\n7 6 0\\n3 2 5]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreates a MinSum of 13 [5+6+2]. The 5 can only see 6, 3 sees 7 and 6, while 2 sees 7 6 0.\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":1885,"title":"Minimum Sum thru a Lower Triangle","description":"This Challenge is to find the minimum cumulative sum that traverses from row-1 thru row-N via vertical/diagonal adjacent elements of adjacent rows.\r\n\r\nThe input is a series of values of length n*(n+1)/2.\r\n\r\n*Input:* S  [Series that can be converted into a lower triangle]\r\n\r\n*Output:* MinSum  [Minimum cost path from top to bottom]\r\n\r\n*Example:*\r\n\r\n[5 7 6 3 2 5] becomes\r\n\r\n  5 0 0\r\n  7 6 0\r\n  3 2 5\r\n\r\nCreates a MinSum of 13 [5+6+2].  The 5 can only see 6, 3 sees 7 and 6, while 2 sees 7 6 0.\r\n ","description_html":"\u003cp\u003eThis Challenge is to find the minimum cumulative sum that traverses from row-1 thru row-N via vertical/diagonal adjacent elements of adjacent rows.\u003c/p\u003e\u003cp\u003eThe input is a series of values of length n*(n+1)/2.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e S  [Series that can be converted into a lower triangle]\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e MinSum  [Minimum cost path from top to bottom]\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cp\u003e[5 7 6 3 2 5] becomes\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e5 0 0\r\n7 6 0\r\n3 2 5\r\n\u003c/pre\u003e\u003cp\u003eCreates a MinSum of 13 [5+6+2].  The 5 can only see 6, 3 sees 7 and 6, while 2 sees 7 6 0.\u003c/p\u003e","function_template":"function MinSum=Find_MinSum(s)\r\n MinSum=0;\r\nend","test_suite":"%%\r\ns=[5 7 6 3 2 5];\r\nMinSum=Find_MinSum(s);\r\nexp=13;\r\nassert(exp==MinSum)\r\n%%\r\ns=[7 9 8 3 2 6 7 1 5   5 9   4   8   2   4 6   3   2   9   7   5 7   2   4   8   5   1   9 4   2   9   3   8   5   2   8  8   2   4   8   5   9   2   7   3];\r\nMinSum=Find_MinSum(s);\r\nexp=30;\r\nassert(exp==MinSum)\r\n%%\r\ns=[21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1];\r\nMinSum=Find_MinSum(s);\r\nexp=76;\r\nassert(exp==MinSum)\r\n%%\r\ns=1:28;\r\nMinSum=Find_MinSum(s);\r\nexp=63;\r\nassert(exp==MinSum)\r\n%%\r\ns=[82 91 13 92 64 10 28 55 96 97 16 98 96 49 81 15 43 92 80 96 66 4 85 94 68 76 75 40 66 18 71 4 28 5 10 83 ];\r\nMinSum=Find_MinSum(s);\r\nexp=213;\r\nassert(exp==MinSum)\r\n%%\r\ns=[348 159 476 18 220 191 383 398 94 245 223 324 355 378 139 340 328 82 60 250 480 171 293 112 376 128 253 350 446 480 274 70 75 129 421 128 ];\r\nMinSum=Find_MinSum(s);\r\nexp=1409;\r\nassert(exp==MinSum)\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-09-21T02:45:50.000Z","updated_at":"2025-12-04T12:10:46.000Z","published_at":"2013-09-21T03:00:18.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to find the minimum cumulative sum that traverses from row-1 thru row-N via vertical/diagonal adjacent elements of adjacent rows.\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 input is a series of values of length n*(n+1)/2.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e S [Series that can be converted into a lower triangle]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e MinSum [Minimum cost path from top to bottom]\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[5 7 6 3 2 5] becomes\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[5 0 0\\n7 6 0\\n3 2 5]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreates a MinSum of 13 [5+6+2]. The 5 can only see 6, 3 sees 7 and 6, while 2 sees 7 6 0.\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:\"create lower 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