COMBINATOR -combinations AND permutations

Two words: excellent job!

If I put a value greater than 170 I get an error.

Efficient, compact, clear, comprehensive help and comments in the source, comparisons with other functions from the FEX.

Small improvement: In perms_loop the term "[i*ones(m,1) t]" is slower then assigning [i] and [t] separately. I simplified the computation of indices (just some % faster). Then the loop becomes:
for n = 2:M
    q = P;
    m = G(n-1);
    P = zeros(n*m, n, CN);
    P(1:m, 1) = n;
    P(1:m, 2:n) = q;
    
    a = m + 1;
    for i = n-1:-1:1,
        t = q;
        t(t == i) = n;
        b = a + m - 1;
        P(a:b, 1) = i;
        P(a:b, 2:n) = t;
        a = b + 1;
    end
end
For Matlab 7.8, this is about 30% faster than the original subroutine perms_loop. To my surprise a method with pre-allocating the complete output at once and avoiding a growing is some percent slower.

Thanks, Jan

Another idea: COMBINATOR(200, 2, 'p') fails due to an overflow - without need. You could replace this:
  prod(1:M) / (prod(1:(M-K))) => prod(M-k+1:M)
in the calculation of BC and BC1 in perms_no_rep.
Similar in combs_rep: prod(M:(M+K-1)) / prod(1:K) is more susceptible for overflows than: prod((M:(M+K-1)) ./ (1:K)). Then COMBINATOR can handle large N as long as K is small enough.
I've implemented a lot of algorithms for permutations and combinations, e.g. Knuth's. My impression: COMBINATOR is very fast and memory efficient and I do not expect, that a Matlab implementation can be faster! Even a C-MEX for COMBINATOR(N,K,'p') with comparable speed is a hard work. Unfortunately I've rated this file already - so just: thanks again.

Nice one Matt.

There might be a small problem though. With matlab 2009 in windows and matlab 2008 in linux I can reproduce the following problem.

combinator(24,23,'c')

leaves the last row of the return matrix to zeros. It does not update it because the parameter

BC=prod(M-K+1:M) / (prod(1:K));

inside the function function CN = combs_no_rep(N,K), at the line 343 of combinator.m

results in BC=23.999999999999996 (instead of the correct value, 24)

I guess a round in that line will take care of it.
A few other combinations of numbers give no problem.

Oops, that was an error of omission on my part. I will post an update. Thanks Jan.

Thanks a lot, Matt.
It does help.

Great code, very fast and just what I needed... but I'm getting an error on the output data when I run the following case:

COMBINATOR(50,n,'c')

the last line has only zeros when n is 46 or 47, but not when it is 44, 45 or 48.

Can you check what's wrong?