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)) 

S: The set for which you want to find subsets
m: The number of elements in the subset