Fast powerset function

Mark Dickinson dickinsm at
Sat Jul 14 08:07:17 CEST 2007

If you don't care about the order of the results, you can use a Gray
code ( this has the advantage
of only adding or removing a single element to get from one subset to
the next.

def powerset(s):
    d = dict(zip(
            (1<<i for i in range(len(s))),
            (set([e]) for e in s)

    subset = set()
    yield subset
    for i in range(1, 1<<len(s)):
        subset = subset ^ d[i & -i]
        yield subset

>>> list(powerset('abc'))
[set([]), set(['a']), set(['a', 'b']), set(['b']), set(['c', 'b']),
set(['a', 'c', 'b']), set(['a', 'c']), set(['c'])]

If you're using the subsets as they appear and don't need to store
them all at once, then it's significantly faster (on my machine) if
you replace the line subset = subset ^ d[i & -i] with an in-place
update:  subset ^= d[i & -i].


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