我如何从python中的任意集制作功率集？

Question

I had a lab today about making a power set from a set of arbitrary size, but I couldn't seem to think of the best way to do it. No one in the class has done Python before either. Only done java

Answer 1

There's a recipe in itertools for that:

def powerset(iterable):
    "powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)"
    s = list(iterable)
    return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))

Answer 2

The insight is that for each set S in the powerset, a given member of the original set is either in S or it isn't. Since this is a binary decision, the powerset doubles for each additional element in the original set.

powerset({a}) = {{}, {a}}

powerset({a,b}) = {{}, {a}, {b}, {a,b}}

powerset({a,b,c}) = union(
                       powerset({a,b}),
                       union({c}, X) where X in powerset({a,b})
                    )

This leads to a nice recursive algorithm that works for sets of "arbitrary size" as long as arbitrary is not too large.