For each vector of the cell A, How to find all possible combinations of its components that are not contained in vectors of the cell B?

Question

For each vector of the cell A , How to find all possible combinations of its components that are not contained in vectors of the cell B ?

   A = {[2 3 6 21],[66 4 2 7],[84 56 66 47 45]};
   B = {[5 6 9 20 21],[7 85 14 2 3],[5 66 84 10 23 35 56],[5 6 87 14 21 29]};

For A{1} , all possible combinations which satisfy the condition:

{[2 6],[2 21],[3 6],[3 21],[2 6 21],[2 3 6],[2 3 21],[3 6 21],[2 3 6 21]}

[2 3] is contained in B{2}

[6 21] is contained in B{1}

Answer 1

Try this:

C = cell(1, numel(A));
for ii = 1:numel(A)
    aux = arrayfun(@(x) num2cell(nchoosek(A{ii}, x), 2)', 1:numel(A{ii}), 'Un', 0);
    aux = [aux{:}];
    C{ii} = aux(~cellfun(@(a) any(cellfun(@(b) all(ismember(a, b)), B)), aux));
end

The result will be in C . Run celldisp(C{1}) to see the result for A{1} , for example.

This code takes every vector in A and find all possible combinations using nchoosek . Then, it checks if any combination has all values contained on any vector of B , returning the remaining combinations which are ont in B and putting them into C .