MATLAB: Is there an alternative to nchoosek which is too slow

#nchoosekMATLAB

Try cnk = nchoosek(1:40, 10) and you'll see how slow it is. Is there an alternative?
Thanks

Best Answer

Well, you're asking for 40!/(10! 30!) elements -->
>> N=prod(31:40)/factorial(10)
N =
 847660528
>>
elements so it's not terribly surprising it might just take a while for the scribes to write 'em all down...
It boils down in the end to
function P = combs(v,m)
    n=length(v);
    P = [];
    if m < n && m > 1
        for k = 1:n-m+1
            Q = combs(v(k+1:n),m-1);
            P = [P; [v(ones(size(Q,1),1),k) Q]]; %#ok
        end
    end
end
which has a big problem in time in that P isn't preallocated.
ADDENDUM
Unfortunately, combnk has the same flaw using almost identically the same code.
Whether somebody has supplied mex file or other solution on FEX I didn't research.
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