1D array combinations

Hi all,

I have a 1D array containing numbers from 1 to 5.

A = [1
     2
     3
     4
     5]

How can I find all possible combinations (without doubles), so that...

B = [1
     1 2
     1 2 3
     1 2 3 4
     1 2 3 4 5
     2
     2 3
     etc.]

I tried a number of combinators from the FEX but they don't give me the result I'm after.

Thanks!

[KSSV]

are you looking for something like the function perms?

doc perms

Answer 1

[Stephen23]

This will generate a cell array of all combinations of all possible lengths:

C = cell(size(A));
for k = 1:numel(C)
    C{k} = nchoosek(A,k);
end

contained inside this cell array:

>> C{:}
ans =
   1
   2
   3
   4
   5
ans =
   1   2
   1   3
   1   4
   1   5
   2   3
   2   4
   2   5
   3   4
   3   5
   4   5
ans =
   1   2   3
   1   2   4
   1   2   5
   1   3   4
   1   3   5
   1   4   5
   2   3   4
   2   3   5
   2   4   5
   3   4   5
ans =
   1   2   3   4
   1   2   3   5
   1   2   4   5
   1   3   4   5
   2   3   4   5
ans =
   1   2   3   4   5

Without padding they will not fit into one numeric array, as they have different number of columns. To pad them try this:

C = cell(size(A));
for k = 1:numel(C)
    tmp = nchoosek(A,k);
    C{k} = [tmp,NaN(size(tmp,1),numel(A)-k)];
end
N = cell2mat(C);

which creates this numeric array:

>> N
N =
     1   NaN   NaN   NaN   NaN
     2   NaN   NaN   NaN   NaN
     3   NaN   NaN   NaN   NaN
     4   NaN   NaN   NaN   NaN
     5   NaN   NaN   NaN   NaN
     1     2   NaN   NaN   NaN
     1     3   NaN   NaN   NaN
     1     4   NaN   NaN   NaN
     1     5   NaN   NaN   NaN
     2     3   NaN   NaN   NaN
     2     4   NaN   NaN   NaN
     2     5   NaN   NaN   NaN
     3     4   NaN   NaN   NaN
     3     5   NaN   NaN   NaN
     4     5   NaN   NaN   NaN
     1     2     3   NaN   NaN
     1     2     4   NaN   NaN
     1     2     5   NaN   NaN
     1     3     4   NaN   NaN
     1     3     5   NaN   NaN
     1     4     5   NaN   NaN
     2     3     4   NaN   NaN
     2     3     5   NaN   NaN
     2     4     5   NaN   NaN
     3     4     5   NaN   NaN
     1     2     3     4   NaN
     1     2     3     5   NaN
     1     2     4     5   NaN
     1     3     4     5   NaN
     2     3     4     5   NaN
     1     2     3     4     5

[Barry]

Thank you very much, this is a great solution!

Answer 2

[Jos (10584)]

My function NCHOOSE will create those combinations without (slowly) looping over nchoosek. Each combination is stored in a cell. The cell array can be easily transformed into a 2D array by padding the entries with NaNs using PADCAT.

C = nchoose(1:5)
A = padcat(C{:})

NCHOOSE and PADCAT can be downloaded here:

http://www.mathworks.com/matlabcentral/fileexchange/20011-nchoose--v2-1-mar-2010-

http://www.mathworks.com/matlabcentral/fileexchange/22909-padcat

[Stephen23]

+1 nice solution.

[Barry]

+1 Thank you!

[Barry]

I'm having trouble understanding what exactly the function "bitget" is doing, is there a way to see how this function is working using a for-loop? Thanks!