How to generate N number of loops

Input: cell array of characters (e.g. 'IHQ')

Each individual character in the array is a variable in the code. For example,

I = {'AUU','AUC','AUA'}

H = {'CAU','CAC'}

Q = {'CAA','CAG'}

Output: all combinations of the elements of the arrays

For example:

B =

    'AUUCAUCAA'
    'AUUCAUCAG'
    'AUUCACCAA'
    'AUUCACCAG'
    'AUCCAUCAA'
    'AUCCAUCAG'
    'AUCCACCAA'
    'AUCCACCAG'
    'AUACAUCAA'
    'AUACAUCAG'
    'AUACACCAA'
    'AUACACCAG'

The way my code generates the combinations is in the following way:

k=1;  
for i=1:length(I)
      for j=1:length(H)
          for m=1:length(Q)
          B(k) = strcat(I(i), H(j), Q(m));
          k=k+1;
          end
      end
  end

This is, however, specific for the example input 'IHQ'. I want to code a more general way where the input can be of any length. Using this way, the number of for loops involved depends on the length of the input. I guess, is there any way I can make a for loop specifying the number of for loops. Or perhaps a different way to approach the output? Thanks!

Answer 1

[Andrei Bobrov]

I = {'AUU','AUC','AUA'};
H = {'CAU','CAC'};
Q = {'CAA','CAG'};
A = {I,H,Q};

A = A(:)';
n = cellfun('length',A);
nn = numel(n);
i0 = arrayfun(@(x)1:x,n,'un',0);
idx = cell(1,nn);
[idx{:}] = ndgrid(i0{end:-1:1});
i1 = fliplr(reshape(cat(nn,idx{:}),[],nn));
A1 = [A{:}];
ii = bsxfun(@plus,i1,[0,cumsum(n(1:end-1))]);
A2 = num2cell(A1(ii),1);
out = strcat(A2{:});

or

I = {'AUU','AUC','AUA'};
H = {'CAU','CAC'};
Q = {'CAA','CAG'};

A = {I,H,Q};

A = A(:)';
n = cellfun('length',A);
i0 = fullfact(n);
ii = bsxfun(@plus,i0,[0,cumsum(n(1:end-1))]);
A1 = [A{:}];
A2 = num2cell(A1(ii),1);
out = strcat(A2{:});

Answer 2

[Azzi Abdelmalek]

%or more general

I = {'AUU','AUC','AUA'};
H = {'CAU','CAC'};
Q = {'CAA','CAG'};
L={'s1','s2','s3'};
v={I,H,Q,L}
v0=v{1};
for k=1:numel(v)-1
  v1=v{k+1};
  [ii1,ii2]=ndgrid(1:numel(v0),1:numel(v1));
  v0= strcat(v0(ii1(:)),v1(ii2(:)));
end
out=v0'