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This recipe yields each subset of size k from a super set of size n. I thought I had seen a recipe that did this before, but when I needed it I couldn't find it. There are two methods. The first operates on sets of integers of the form range(n). The seconds operates on arbitrary sets or lists.

Python, 75 lines
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75``` ```def k_subsets_i(n, k): ''' Yield each subset of size k from the set of intergers 0 .. n - 1 n -- an integer > 0 k -- an integer > 0 ''' # Validate args if n < 0: raise ValueError('n must be > 0, got n=%d' % n) if k < 0: raise ValueError('k must be > 0, got k=%d' % k) # check base cases if k == 0 or n < k: yield set() elif n == k: yield set(range(n)) else: # Use recursive formula based on binomial coeffecients: # choose(n, k) = choose(n - 1, k - 1) + choose(n - 1, k) for s in k_subsets_i(n - 1, k - 1): s.add(n - 1) yield s for s in k_subsets_i(n - 1, k): yield s def k_subsets(s, k): ''' Yield all subsets of size k from set (or list) s s -- a set or list (any iterable will suffice) k -- an integer > 0 ''' s = list(s) n = len(s) for k_set in k_subsets_i(n, k): yield set([s[i] for i in k_set]) def __test__(): two_sets = list(k_subsets_i(10, 2)) assert len(two_sets) == 45 two_set = two_sets assert len(two_set) == 2 class Tester: def __init__(self, i): self.i = i def __repr__(self): return 'Tester(%d)' % self.i super_set = [Tester(i) for i in range(100, 200, 10)] two_sets = list(k_subsets(super_set, 2)) assert len(two_sets) == 45 two_set = two_sets assert len(two_set) == 2 assert isinstance(two_set.pop(), Tester) __test__() for two in k_subsets(range(20, 26), 2): print two # prints: set([24, 25]) set([25, 23]) set([25, 22]) set([25, 21]) set([25, 20]) set([24, 23]) set([24, 22]) set([24, 21]) set([24, 20]) set([22, 23]) set([21, 23]) set([20, 23]) set([21, 22]) set([20, 22]) set([20, 21]) ```

I choose to yield sets since this is really a set type of problem. However, I’m not entirely convinced that using sets is the best way to implement this recipe as this precludes multiples of set elements. For instance, you might want to get all pairs of integers from a list with at least one repeated value, such as [1, 1, 2, 3]. One “pair” would be set([1, 1]) = set(), which turns out not to be a pair at all. Yielding lists would avoid this problem. Created by Justin Shaw on Sat, 20 Jan 2007 (PSF)

### Required Modules

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