{"id":28992,"date":"2023-01-04T20:37:07","date_gmt":"2023-01-04T15:07:07","guid":{"rendered":"https:\/\/jassweb.com\/solved\/solved-finding-subsets-of-a-set-of-vectors-that-fulfill-some-conditions\/"},"modified":"2023-01-04T20:37:07","modified_gmt":"2023-01-04T15:07:07","slug":"solved-finding-subsets-of-a-set-of-vectors-that-fulfill-some-conditions","status":"publish","type":"post","link":"https:\/\/jassweb.com\/solved\/solved-finding-subsets-of-a-set-of-vectors-that-fulfill-some-conditions\/","title":{"rendered":"[Solved] Finding subsets of a set of vectors that fulfill some conditions"},"content":{"rendered":"

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The question is a bit complicated and hard to follow.. Anyways I tried writing some code to the best of my understanding of the problem. Here is the part that finds the possible combinations:<\/p>\n

% input matrix\nA=[1   2 0 1 2 0 0   0\n   2   1 1 1 0 2 2   0\n   3   0 0 0 0 1 1   1\n   4   0 2 0 1 1 1   2\n   5   0 0 0 0 0 1   0\n   6   1 0 1 1 2 0   2\n   7   1 1 2 2 2 1   1\n   8   0 1 1 2 2 0   0\n   9   0 1 1 2 2 0   0\n  10   2 2 2 2 0 0   1];\n\n% start by considering all rows\nrowsIndices = (1:size(A,1))';\nrIdx = true(size(rowsIndices));\n\n% exclude 7th row (i.e rows with no zeros in columns 2:7)\n%idx(~any(A(:,2:7)==0,2)) = false;\nrIdx(7) = false;\n\n% exclude rows that dont have zero in column 8\nrIdx(A(:,8) ~= 0) = false;\n\n% for each possible n-combinations\nN = sum(rIdx);\ncombs = cell(1,N);\nfor k=2:N\n    % all combinations of k-rows\n    combsK = nchoosek(rowsIndices(rIdx), k);\n\n    % must involve first row\n    combsK = combsK(any(combsK==1,2),:);\n\n    % exclude from current k-combinations if there are smaller ones\n    if k > 2\n        combsKIdx = true(size(combsK,1),1);\n        for kk=2:k-1\n            if isempty(combs{kk}), continue, end\n            for i=1:size(combs{kk},1)\n                combsKIdx(sum(ismember(combsK,combs{kk}(i,:)),2)==kk) = false;\n            end\n        end\n        combsK = combsK(combsKIdx,:);\n    end\n\n    % for every possible combination, each column 2:7 must not be all zeros\n    combsKIdx = true(size(combsK,1),1);\n    for i=1:size(combsK,1)\n        combsKIdx(i) = all(any(A(combsK(i,:),2:7),1));\n    end\n    combsK = combsK(combsKIdx,:);\n\n    % store combinations found\n    combs{k} = combsK;\nend\n\n% display results\ncelldisp(combs)\n<\/code><\/pre>\n
Here are the combinations I got:<\/p>\n
combs{1} =\n     []\ncombs{2} =\n     1     2\ncombs{3} =\n     1     5     8\n     1     5     9\ncombs{4} =\n     []\ncombs{5} =\n     []\n<\/code><\/pre>\n
in other words three combinations; first with rows [1 2], second [1 5 8], and third with rows [1 5 9].<\/p>\n
The part I left out is the final step of computing the “scores” of each combination found. Honestly I didn’t understand how, the description was confusing! So I’ll leave that part to you..<\/p>\n<\/p><\/div>\n
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            7<\/span> <\/p><\/div>\n<\/div>\n
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solved Finding subsets of a set of vectors that fulfill some conditions <\/p>\n","protected":false},"excerpt":{"rendered":"
[ad_1] The question is a bit complicated and hard to follow.. Anyways I tried writing some code to the best of my understanding of the problem. Here is the part that finds the possible combinations: % input matrix A=[1 2 0 1 2 0 0 0 2 1 1 1 0 2 2 0 3 … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[320],"tags":[457,516,1331],"class_list":["post-28992","post","type-post","status-publish","format-standard","hentry","category-solved","tag-algorithm","tag-matlab","tag-matrix"],"yoast_head":"\n[Solved] Finding subsets of a set of vectors that fulfill some conditions - JassWeb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/jassweb.com\/solved\/solved-finding-subsets-of-a-set-of-vectors-that-fulfill-some-conditions\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"[Solved] Finding subsets of a set of vectors that fulfill some conditions - JassWeb\" \/>\n<meta property=\"og:description\" content=\"[ad_1] The question is a bit complicated and hard to follow.. 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