How can I find all the subsets of a set, with exactly n elements?

Question

I am writing a program in Python, and I realized that a problem I need to solve requires me, given a set S with n elements (|S|=n), to test a function on all possible subsets of a certain order m (i.e. with m number of elements). To use the answer to produce a partial solution, and then try again with the next order m=m+1, until m=n.

I am on my way to write a solution of the form:

def findsubsets(S,m):
    subsets=set([])
    ...
    return subsets

But knowing Python I expected a solution to be already there.

What is the best way to accomplish this?

Answer 1

itertools.combinations is your friend if you have Python 2.6 or greater. Otherwise, check the link for an implementation of an equivalent function.

import itertools
def findsubsets(S,m):
    return set(itertools.combinations(S, m))

Answer 2

It seems like this recipe does the trick: http://code.activestate.com/recipes/500268/

Answer 3

and, if you want each element of the list to be used only once, use 'permutations' also found in itertools.