Generates every possible combination from a set of discrete variables

combinations.py

#!/usr/bin/python


def combinations(S):
    """
    Generates every possible combination from a set of discrete variables

    Arguments
    ---------
    S: Cardinality of variable space. When S = [2, 3, 4] variables 1, 2 and
    3 have 2, 3 and 4 possible events respectively.

    Returns
    ---------
    Generator object yields every possible combination.
    """
    return combinationsAux(S, [])


def combinationsAux(S, P):
    if not S:
        yield P  # We have found a new combination
    else:
        for i in xrange(1, S[0] + 1):
            for perm in combinationsAux(S[1:], P + [i]):  # Lets explore more combinations
                yield perm


# Unit tests
if __name__ == '__main__':
    states = [2, 3, 2]

    # Is the number of combinations correct?
    assert reduce(lambda a, b: a * b, states) == len(list(combinations(states)))