Question

I would like to generate all possible integer arrays of a given length L, up to a maximum element size M.

The minimum element size is 1.

If M = 3, and L = 2, the output would be the following:

[1,1]
[1,2]
[1,3]
[2,1]
[2,2]
[2,3]
[3,1]
[3,2]
[3,3]

There are M^L different combinations, so I guess the Matlab code would look something like this:

function [arrays] = allArrays(M,L)
  for i = 1:(M^L)
    arrays(i) = % Something here that translates i to the desired array.
  end
end

I’m not sure what should go in the middle of the loop, any help would be much appreciated!

Answer 1

You should use ndgrid:

[y x]=ndgrid(1:3,1:3);
resu=[y(:) x(:)];

If you want to give M and L as input, you should do the following trick:

arg=repmat((1:M)',1,L);
arg=mat2cell(arg,M,ones(1,L));
resu=cell(1,L);
[resu{:}]=ndgrid(arg{:});
resu=cell2mat(cellfun(@(x) x(:), resu,'UniformOutput',0));

result:

 resu =  
     1     1
     2     1
     3     1
     1     2
     2     2
     3     2
     1     3
     2     3
     3     3