How can I get "permutations with repetitions/replacement" from a list (Cartesian product of a list with itself)?
cartesian-product, combinatorics, python
Solution
You are looking for the Cartesian Product.
In mathematics, a Cartesian product (or product set) is the direct product of two sets.
In your case, this would be `{1, 2, 3, 4, 5, 6}` x `{1, 2, 3, 4, 5, 6}`. `itertools` can help you there:
import itertools
x = [1, 2, 3, 4, 5, 6]
[p for p in itertools.product(x, repeat=2)]
[(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3),
(2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3),
(5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)]
To get a random dice roll (in a totally inefficient way):
import random
random.choice([p for p in itertools.product(x, repeat=2)])
(6, 3)
Problem
Suppose I have a list `die_faces = [1, 2, 3, 4, 5, 6]`. I want to generate all 36 possible results for rolling two dice: `(1, 1)`, `(1, 2)`, `(2, 1)` etc. If I try using `permutations` from the `itertools` standard library: ``` >>> import itertools >>> die_faces = [1, 2, 3, 4, 5, 6] >>> list(itertools.permutations(die_faces, 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)] ``` there are only 30 results, missing the ones where the same number comes up on both dice. It seems that it only generates permutations without repetitions. How can I fix this?