Permutations of a list with constraints python

Question

I am desperately trying to get all the permutations of a list while enforcing position assignment constraints. I have a list [1,2,3,4,5,6] (6 is just an example, I would like to find something that could work with every lenght) and I want to find all the lists of lenght 3 (also an example) with the following constraints :

• position 1 can be occupied by numbers 1 and 2
• position 2 can be occupied by numbers 1,2 and 3
• position 3 can be occupied by numbers 2,3 and 4
• repetions of a same number are not allowed

That would give these lists : [1,2,3],[1,2,4],[1,3,2],[1,3,4],[2,1,3],[2,3,4],[2,1,4]

For those interested, what I am trying to implement is what is explained pages 5 and 6 of this paper

Answer 1

Filter the product() of those subsets:

from itertools import product

for combo in product([1, 2], [1, 2, 3], [2, 3, 4]):
    if len(set(combo)) == 3:
        print(combo)

or as a list comprehension:

[combo for combo in product([1, 2], [1, 2, 3], [2, 3, 4]) if len(set(combo)) == 3]

Output:

>>> from itertools import product
>>> [combo for combo in product([1, 2], [1, 2, 3], [2, 3, 4]) if len(set(combo)) == 3]
[(1, 2, 3), (1, 2, 4), (1, 3, 2), (1, 3, 4), (2, 1, 3), (2, 1, 4), (2, 3, 4)]