Permutations with repetition in Python

Question

I want to iterate over all the vertices of an n dimensional cube of size 1. I know I could do that with itertools.product as follows:

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Answer 1

For your use-case of 3d cubes, Eevee's solution is the correct one.

However for fun and to demonstrate the power of itertools, here's a linear-time solution that generalizes to higher dimensions:

from itertools import combinations

# n is the number of dimensions of the cube (3 for a 3d cube)
def generate_vertices(n):
    for number_of_ones in xrange(0, n + 1):
        for location_of_ones in combinations(xrange(0, n), number_of_ones):
            result = [0] * n
            for location in location_of_ones:
                result[location] = 1
            yield result

for vertex in generate_vertices(3):
    print vertex


# result:
# [0, 0, 0]
# [1, 0, 0]
# [0, 1, 0]
# [0, 0, 1]
# [1, 1, 0]
# [1, 0, 1]
# [0, 1, 1]
# [1, 1, 1]