MATLAB: Building all such vectors

algorithm

How to build all vector with A elements equal to 1, B elements equal to 2, and C elements equal to 3 ?
I'm looking for an algorithm or a function building all such vectors.

Best Answer

This is a problem in combinations, not permutations, and can be performed using matlab's 'nchoosek' function. Note that the number of possible combinations in your problem is
 (A+B+C)!/A!/B!/C! = (A+B+C)!/A!/(B+C)! * (B+C)!/B!/C!
The code:
 p1 = nchoosek(1:A+B+C,B+C); % Choose B+C indices out of 1:A+B+C
 p2 = nchoosek(1:B+C,C); % Choose C indices out of 1:B+C
 m = size(p1,1);
 n = size(p2,1);
 V = ones(m*n,A+B+C); % Start with all 1's
 for ix = 1:m
   V((1:n)+n*(ix-1),p1(ix,:)) = 2; % Reset B+C of them to 2's
   for jx = 1:n
     V(jx+n*(ix-1),p1(ix,p2(jx,:))) = 3; % Of these, reset C to 3's
   end
 end
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