# Find all possible combinations of string array

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Christos Traianos on 7 Dec 2021
Commented: Adam Danz on 9 Dec 2021
Hi,
i have a struct that contains cells of different dimensions. I need a way to find all possible combinations of all cells.
The cells containing string variable e.g: matrix(1).elements = {'500A', '600B', '700C',''}, matrix(2).elements = {'100AC', '300D', '200CA','60G'}, matrix(3).elements = {'100BC', '300DF', '200AA','60GR'}...(some cells have less variables and for this reason i have " at the last element of matrix(1))
The total number of combinations in the example above is: 4*4*4=64
The results that i would like is a mat like: 1) 500A,100AC, 100BC,
2) 500A,100AC, 300DF
3) 500A,100AC, 200AA...
I tried allcomb function but it doesn't work
Any idea on that?

Adam Danz on 7 Dec 2021
Edited: Adam Danz on 9 Dec 2021
Here are two options.
Use combvec() from the Deep Learning Toolbox
a = {'a','b','c','d'};
b = {'qq','rrr','ss'};
c = {'tuv','xyz'};
m = combvec(1:numel(a), 1:numel(b), 1:numel(c))
m = 3×24
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 1 1 1 2 2 2 2 3 3 3 3 1 1 1 1 2 2 2 2 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2
combStr = [a(m(1,:)); b(m(2,:)); c(m(3,:))]'
combStr = 24×3 cell array
{'a'} {'qq' } {'tuv'} {'b'} {'qq' } {'tuv'} {'c'} {'qq' } {'tuv'} {'d'} {'qq' } {'tuv'} {'a'} {'rrr'} {'tuv'} {'b'} {'rrr'} {'tuv'} {'c'} {'rrr'} {'tuv'} {'d'} {'rrr'} {'tuv'} {'a'} {'ss' } {'tuv'} {'b'} {'ss' } {'tuv'} {'c'} {'ss' } {'tuv'} {'d'} {'ss' } {'tuv'} {'a'} {'qq' } {'xyz'} {'b'} {'qq' } {'xyz'} {'c'} {'qq' } {'xyz'} {'d'} {'qq' } {'xyz'} {'a'} {'rrr'} {'xyz'} {'b'} {'rrr'} {'xyz'} {'c'} {'rrr'} {'xyz'} {'d'} {'rrr'} {'xyz'} {'a'} {'ss' } {'xyz'} {'b'} {'ss' } {'xyz'} {'c'} {'ss' } {'xyz'} {'d'} {'ss' } {'xyz'}
Use ndgrid, no toolboxes needed
[ai,bi,ci] = ndgrid(1:numel(a), 1:numel(b), 1:numel(c));
m = [ai(:),bi(:),ci(:)]'
m = 3×24
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 1 1 1 2 2 2 2 3 3 3 3 1 1 1 1 2 2 2 2 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2
combStr2 = [a(m(1,:)); b(m(2,:)); c(m(3,:))]'
combStr2 = 24×3 cell array
{'a'} {'qq' } {'tuv'} {'b'} {'qq' } {'tuv'} {'c'} {'qq' } {'tuv'} {'d'} {'qq' } {'tuv'} {'a'} {'rrr'} {'tuv'} {'b'} {'rrr'} {'tuv'} {'c'} {'rrr'} {'tuv'} {'d'} {'rrr'} {'tuv'} {'a'} {'ss' } {'tuv'} {'b'} {'ss' } {'tuv'} {'c'} {'ss' } {'tuv'} {'d'} {'ss' } {'tuv'} {'a'} {'qq' } {'xyz'} {'b'} {'qq' } {'xyz'} {'c'} {'qq' } {'xyz'} {'d'} {'qq' } {'xyz'} {'a'} {'rrr'} {'xyz'} {'b'} {'rrr'} {'xyz'} {'c'} {'rrr'} {'xyz'} {'d'} {'rrr'} {'xyz'} {'a'} {'ss' } {'xyz'} {'b'} {'ss' } {'xyz'} {'c'} {'ss' } {'xyz'} {'d'} {'ss' } {'xyz'}
Compare results
isequal(combStr, combStr2)
ans = logical
1
Use ndgrid with a variable number of vectors / cell arrays
% Concatenate all cell arrays into a since
% cell array of cells (data in this example).
a = {'a','b','c','d'};
b = {'qq','rrr','ss'};
c = {'tuv','xyz'};
d = {'1','2','3','4','5'};
data = {a,b,c,d}
data = 1×4 cell array
{1×4 cell} {1×3 cell} {1×2 cell} {1×5 cell}
% Combine all nested cell arrays in 'data'.
indices = cellfun(@(c){1:numel(c)},data);
ndg = cell(size(data));
[ndg{:}] = ndgrid(indices{:});
combStrCellArray = cellfun(@(str,ind){str(ind)},data,ndg);
combStrCell = cellfun(@(c){c(:)}, combStrCellArray);
combStr = horzcat(combStrCell{:})'
combStr = 4×120 cell array
{'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'a' } {'b' } {'c' } {'d' } {'qq' } {'qq' } {'qq' } {'qq' } {'rrr'} {'rrr'} {'rrr'} {'rrr'} {'ss' } {'ss' } {'ss' } {'ss' } {'qq' } {'qq' } {'qq' } {'qq' } {'rrr'} {'rrr'} {'rrr'} {'rrr'} {'ss' } {'ss' } {'ss' } {'ss' } {'qq' } {'qq' } {'qq' } {'qq' } {'rrr'} {'rrr'} {'rrr'} {'rrr'} {'ss' } {'ss' } {'ss' } {'ss' } {'qq' } {'qq' } {'qq' } {'qq' } {'rrr'} {'rrr'} {'rrr'} {'rrr'} {'ss' } {'ss' } {'ss' } {'ss' } {'qq' } {'qq' } {'qq' } {'qq' } {'rrr'} {'rrr'} {'rrr'} {'rrr'} {'ss' } {'ss' } {'ss' } {'ss' } {'qq' } {'qq' } {'qq' } {'qq' } {'rrr'} {'rrr'} {'rrr'} {'rrr'} {'ss' } {'ss' } {'ss' } {'ss' } {'qq' } {'qq' } {'qq' } {'qq' } {'rrr'} {'rrr'} {'rrr'} {'rrr'} {'ss' } {'ss' } {'ss' } {'ss' } {'qq' } {'qq' } {'qq' } {'qq' } {'rrr'} {'rrr'} {'rrr'} {'rrr'} {'ss' } {'ss' } {'ss' } {'ss' } {'qq' } {'qq' } {'qq' } {'qq' } {'rrr'} {'rrr'} {'rrr'} {'rrr'} {'ss' } {'ss' } {'ss' } {'ss' } {'qq' } {'qq' } {'qq' } {'qq' } {'rrr'} {'rrr'} {'rrr'} {'rrr'} {'ss' } {'ss' } {'ss' } {'ss' } {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'tuv'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'xyz'} {'1' } {'1' } {'1' } {'1' } {'1' } {'1' } {'1' } {'1' } {'1' } {'1' } {'1' } {'1' } {'1' } {'1' } {'1' } {'1' } {'1' } {'1' } {'1' } {'1' } {'1' } {'1' } {'1' } {'1' } {'2' } {'2' } {'2' } {'2' } {'2' } {'2' } {'2' } {'2' } {'2' } {'2' } {'2' } {'2' } {'2' } {'2' } {'2' } {'2' } {'2' } {'2' } {'2' } {'2' } {'2' } {'2' } {'2' } {'2' } {'3' } {'3' } {'3' } {'3' } {'3' } {'3' } {'3' } {'3' } {'3' } {'3' } {'3' } {'3' } {'3' } {'3' } {'3' } {'3' } {'3' } {'3' } {'3' } {'3' } {'3' } {'3' } {'3' } {'3' } {'4' } {'4' } {'4' } {'4' } {'4' } {'4' } {'4' } {'4' } {'4' } {'4' } {'4' } {'4' } {'4' } {'4' } {'4' } {'4' } {'4' } {'4' } {'4' } {'4' } {'4' } {'4' } {'4' } {'4' } {'5' } {'5' } {'5' } {'5' } {'5' } {'5' } {'5' } {'5' } {'5' } {'5' } {'5' } {'5' } {'5' } {'5' } {'5' } {'5' } {'5' } {'5' } {'5' } {'5' } {'5' } {'5' } {'5' } {'5' }
Adam Danz on 9 Dec 2021

David Hill on 7 Dec 2021
Edited: David Hill on 7 Dec 2021
You could get all possible combinations and then index into your struct.
[idxa,idxb,idxc]=ndgrid(1:5,1:3,1:7);
Christos Traianos on 9 Dec 2021
Thanks David,
How can the ndgrid function be used for multiple inputs vector and consequently multiple outputs?