How to get all possible combinations of data in a cell?

I have a cell with 4 rows that contains a number of data in this format:

A, B, C, D
E, F,
1, 2, 3, 4
5, 6, 7

How can i get all possible combinations (one from each row)? For example AE15, AF15, and so on..

[José-Luis]

What have you tried so far? This looks like a homework question.

Hints: The ugly solution would involve nested loops. A bit better would be to look into ndgrid(). bsxfun() could probably be used. Etc...

[Jethro G]

Hah I wish I was still at the age where I had homework to do. I don't have an issue with looping everything for each row manually i can do that. The problem is that I'm trying to find a method that executes the required number of loops irregardless of the size of cell that the user provides.

IE whether the user gives a cell with 10 rows or 3 rows

Answer 1

[José-Luis]

data = {{'A', 'B', 'C', 'D'}; ...
{'E','F',};...
{1, 2, 3, 4};...
{5, 6, 7}};

cell_size = cellfun(@(x) size(x,2) ,data);
tot_elements = cell_size' * cell_size;
[I,J,K,L] = ind2sub(cell_size',1:tot_elements);

result = [cell2mat(data{1}(I)'), cell2mat(data{2}(J)'), char([data{3}{K}]+48)', char([data{4}{L}]+48)'];

EDIT Going out of my way to avoid loops and having it work for variable-size input:

data = {{'A', 'B', 'C', 'D'}; ...
{'E','F',};...
{1, 2, 3, 4};...
{5, 6, 7}};

cell_size = cellfun(@(x) size(x,2) ,data);
tot_elements = prod(cell_size); 

 %Turning data into a cell array of character array
 is_a_number = cellfun(@(x) isnumeric(cell2mat(x)),data);
 data(is_a_number) = cellfun(@(x) {char(cell2mat(x) + 48)},data(is_a_number));
 data(~is_a_number) = cellfun(@(x) {cell2mat(x)},data(~is_a_number));

%Avoiding ind2sub, convoluted way of obtaining the indexes
idx = (1:numel(data));
idx_array = bsxfun(@(x,y) ceil( (mod(x-1,prod(cell_size(1:y)))+1) ./ ...
    (prod(cell_size(1:y)) / cell_size(y) ) ),...
    (1:tot_elements)', idx);

 %Finally getting the results based on idx_array
 result = cell2mat(cellfun(@(x) {data{x}(idx_array(:,x))}, num2cell(idx))')';

Not an (explicit) loop in sight but not pretty. Not very maintainable either. I won't directly understand this if I look at it down the line. Loops in this case would be clearer, IMO.

[Jethro G]

This definitely seems to be an approach that could work. The only thing i've noticed is that the total elements is not right since it gives 45 where it should be 96 (4*2*3*4) but i can fix that no problem.

My question is, what does the +48 do in the last command?

[José-Luis]

My bad.

 tot_elements = prod(cell_size);

The +48 helps transform numbers into ascii characters. 0 has an ascii value of 48.

[Jethro G]

Thank you very much. I guess the only thing that's left for me now is instead of defining IJKL (which only works for 4-row cells), to generete those depending on the number of rows in the cell that the user provides, but i'm sure i can figure that out! Thanks a lot!

[José-Luis]

My pleasure. Updated for variable input size.