How can I generate all combinations of n elements in an array?

Question

I have n states like 10, 15, 18, ... and I want to generate all possible combinations of my states in an array with length of m.

For example, if m=5 and n=2 (states={10,15}), I want to generate all possible combinations like this example:

comb = { 10 10 10 10 15

         10 10 10 15 10

         10 10 10 15 15

         ...

         15 15 15 15 10 }

Each row should consist of one possible combination of 10, 15. How to generate this array in MATLAB?

From your suggested output, it looks like you want at least one of each possible state in each of your combination (that is you don't want the combination `10 10 10 10 10` or `15 15 15 15 15`) if that is the case please add that requirement to your question! — Jens Boldsen, Nov 24 '14 at 09:17
Try the linked answer with input `vectors = { [10 15] [10 15] [10 15] [10 15] [10 15] };` — Luis Mendo, Nov 24 '14 at 12:02

score 0 · Answer 1 · answered Nov 24 '14 at 09:40

One approach is:

m = 4;
n = 2;
states = [10, 15];
v = mod(perms(1:(2*(m-1))),n) + 1;
ind = unique(v(:,1:m),'rows');
comb = states(ind)

comb =

    10    10    10    15
    10    10    15    10
    10    10    15    15
    10    15    10    10
    10    15    10    15
    10    15    15    10
    10    15    15    15
    15    10    10    10
    15    10    10    15
    15    10    15    10
    15    10    15    15
    15    15    10    10
    15    15    10    15
    15    15    15    10

Note that this has horrible performance for high values of m and n).

score 0 · Answer 2 · answered Nov 24 '14 at 10:16

Try something like:

n = 5;
states = [10,15];
m = numel(states);
sz = m*ones(1,n);
idx = {0};
idx = repmat(idx,1,n);
comb = zeros(m^n,n);
for i = 1:(m^n)
[idx{:}] = ind2sub(sz,i);
comb(i,:) =states([idx{:}]);
end

This will give you all possible combinations and put them in the matrix comb; then you can sort out all the unwanted combinations afterwards - it is unclear which combinations you aren't interested in (it could for example be the combinations with not all elements of the same state, or the combinations with at least one of each of the states represented).

How can I generate all combinations of n elements in an array?

2 Answers2