Getting the subsets of a set in Python

Question

Suppose we need to write a function that gives the list of all the subsets of a set. The function and the doctest is given below. And we need to complete the whole definition of the function

def subsets(s):
   """Return a list of the subsets of s.

   >>> subsets({True, False})
   [{False, True}, {False}, {True}, set()]
   >>> counts = {x for x in range(10)} # A set comprehension
   >>> subs = subsets(counts)
   >>> len(subs)
   1024
   >>> counts in subs
   True
   >>> len(counts)
   10
   """
   assert type(s) == set, str(s) + ' is not a set.'
   if not s:
       return [set()]
   element = s.pop() 
   rest = subsets(s)
   s.add(element)    

---

It has to not use any built-in function

My approach is to add "element" into rest and return them all, but I am not really familiar how to use set, list in Python.

Answer 1

Look at the powerset() recipe in the itertools docs.

from itertools import chain, combinations

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))

def subsets(s):
    return map(set, powerset(s))

Answer 2

>>> s=set(range(10))
>>> L=list(s)
>>> subs = [{L[j] for j in range(len(L)) if 1<<j&i} for i in range(1,1<<len(L))]
>>> s in subs
True
>>> set() in subs
False