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#!/usr/bin/env python

__version__ = "0.8"

This recipe shows a way to solve the K-combinations problem without replacement with a sequence of items using the dynamic programming technique.

Keywords: combination, binomial coefficient

See also: http://code.activestate.com/recipes/190465-generator-for-permutations-combinations-selections/ 
See also: http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/105962
See also: http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/66463
See also: http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/66465

def combinations(s, K):
    On entry: s sequence of items; K size of the combinations       
    Returns: list of all possible K-combinations without replacement of
    N = len(s)
    assert K<=N, 'Error K must be less or igual than N'
    S = [[] for i in range(K+1) ]
    for n in range(1,N+1):
        newS = [[] for i in range(K+1) ]
        for k in range(max(1, n-(N-K)), min(K+1, n+1)):
            if len(S[k-1])==0:
                newS[k].extend( [el+[s[n-1]] for el in S[k-1]] )
        S = newS

    return S[K]

if __name__ == '__main__':

    s = ['a', 'b', 'c', 'd', 'e', 'f', 'g']
    print combinations(s, 5)