# [Solved] Finding subsets of a set of vectors that fulfill some conditions

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   0 0 0 0 1 1   1
4   0 2 0 1 1 1   2
5   0 0 0 0 0 1   0
6   1 0 1 1 2 0   2
7   1 1 2 2 2 1   1
8   0 1 1 2 2 0   0
9   0 1 1 2 2 0   0
10   2 2 2 2 0 0   1];

% start by considering all rows
rowsIndices = (1:size(A,1))';
rIdx = true(size(rowsIndices));

% exclude 7th row (i.e rows with no zeros in columns 2:7)
%idx(~any(A(:,2:7)==0,2)) = false;
rIdx(7) = false;

% exclude rows that dont have zero in column 8
rIdx(A(:,8) ~= 0) = false;

% for each possible n-combinations
N = sum(rIdx);
combs = cell(1,N);
for k=2:N
% all combinations of k-rows
combsK = nchoosek(rowsIndices(rIdx), k);

% must involve first row
combsK = combsK(any(combsK==1,2),:);

% exclude from current k-combinations if there are smaller ones
if k > 2
combsKIdx = true(size(combsK,1),1);
for kk=2:k-1
if isempty(combs{kk}), continue, end
for i=1:size(combs{kk},1)
combsKIdx(sum(ismember(combsK,combs{kk}(i,:)),2)==kk) = false;
end
end
combsK = combsK(combsKIdx,:);
end

% for every possible combination, each column 2:7 must not be all zeros
combsKIdx = true(size(combsK,1),1);
for i=1:size(combsK,1)
combsKIdx(i) = all(any(A(combsK(i,:),2:7),1));
end
combsK = combsK(combsKIdx,:);

% store combinations found
combs{k} = combsK;
end

% display results
celldisp(combs)
``````

Here are the combinations I got:

``````combs{1} =
[]
combs{2} =
1     2
combs{3} =
1     5     8
1     5     9
combs{4} =
[]
combs{5} =
[]
``````

in other words three combinations; first with rows [1 2], second [1 5 8], and third with rows [1 5 9].

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..

solved Finding subsets of a set of vectors that fulfill some conditions