for loop - Making Combinations (Python)

Question

In Python, is there a better way to get the set of combinations of n elements from a k-element set than nested for loops or list comprehensions?

For example, say from the set [1,2,3,4,5,6] I want to get [(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)]. Is there a better of of making it than

nums=[1,2,3,4,5,6]
doubles=[]
for a in nums:
    for b in nums[a+1:]
        doubles.append((a,b))

? It's okay if the elements of the list we end up with are sets, tuples, or lists; I just feel there should be an easier way to do this.

Answer 1

You can use itertools.combinations:

>>> from itertools import combinations
>>> nums = [1,2,3,4,5,6]
>>> list(combinations(nums, 2))
[(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 5), (4, 6), (5, 6)]

Answer 2

The itertools module has a lot of really powerful tools that can be used in situations like this. In this case, you want itertools.combinations. Some other ones that you might find useful are itertools.combinations_with_replacement and itertools.permutations.

Example:

>>> import itertools
>>> list(itertools.combinations(range(1,7),2))
[(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 5), (4, 6), (5, 6)]
>>> list(itertools.combinations_with_replacement(range(1,7),2))
[(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 5), (5, 6), (6, 6)]
>>> list(itertools.permutations(range(1,7),2))
[(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5)]

Answer 3

You could use the itertools module

import itertools
alphabet = ['1','2','3','4','5','6']
combos = list(itertools.combinations(alphabet, 2))
print combos