MATLAB: Permutations of array retaining sub-array groups together

algorithmarraygroupsMATLABpermutationrestrictedtogethervector

How can I obtain in an efficient way all the permutations of an array with n elements such that all the sub-array groups defined are always together?
For example: Consider the array [ 1 (2 3) 4 ]. Here (2,3) is one sub-group and the parentheses are just put for clarity. Output expected is then: [ 1 (2 3) 4 ; 1 (3 2) 4 ; 1 4 (2 3) ; 1 4 (3 2) ; … so on].
There can be multiple such groups and the groups can be comprised of more than 2 elements as well. So, let's say A = [ 1 2 3 4 5 6 7 8] is the array to be permuted and there is another vector of same size containing information about the groups like G = [ 1 2 2 2 3 4 5 5 ] implying that I need to permute [1 (2 3 4) 5 6 (7 8)]. This way of describing the arrays to approach the problem is just a suggestion but I am open to better suggestions. Thanks a lot for your time.

Best Answer

Try this:
A = [ 1 2 3 4 5 6 7 8]
G = [ 1 2 2 2 3 4 5 5 ]
l = diff(find([true,diff(G)>0,true]));
Ag = mat2cell(A, 1, l);
Ap = cellfun(@perms, Ag, 'unif',0);
I = cellfun(@(x) 1:size(x,1), Ap, 'unif',0);
[I{:}] = ndgrid(I{:});
AP = cellfun(@(Ap,r) Ap(r,:), Ap, I, 'unif',0);
c = perms(unique(G));
AP = arrayfun(@(i) cell2mat(AP(:,c(i,:))), 1:size(c,1), 'unif', 0);
AP = cat(1, AP{:})
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