如何返回n个不同列表的所有可能组合的交集

Question

I was wondering if there is an algorithm that can return the intersection of all possible combinations of n different lists. My example is the following with n = 3 different lists:

list1 = [1,2,3,4,5]
list2 = [1,3,5]
list3 = [1,2,5]

the outcome should look like this:

list1_2_intersection = [1,3,5]
list1_3_intersection = [1,2,5]
list2_3_intersection = [1,5]
list1_2_3_intersection = [1,5]

I was thinking to first use combination to get all possible combinations of n sets and use that to create intersections using intersection manually. However, since I have 6 different sets this seems very time consuming, which is why I was wondering if there is a more efficient way to compute this. Thanks in advance: :)

Answer 1

If you have all sets in a list, you can use the more-itertools -package ( pip install more-itertools ), which is based on itertools , to get all combinations of those elements using more_itertools.powerset , as is done in this post .

Then getting the intersection is a matter of using set.intersection as you point out yourself. So a solution can look like this

from more_itertools import powerset

sets = [{1,2,3,4,5},{1,3,5},{1,2,5}]
pwset = powerset(sets)
res = [c[0].intersection(*c[1:]) if len(c)>1 else c for c in pwset]

Answer 2

If you just load or define the sets in an iterable like a list:

my_sets = [
    {1, 2, 3, 4, 5},
    {1, 3, 5},
    {1, 2, 5}
]

my_set_intersection = set.intersection(*my_sets)
print(my_set_intersection)

Of course, the print is just there to show the result, which is in my_set_intersection

If you just have a couple of sets:

set1 = {1, 2, 3, 4, 5},
set2 = {1, 3, 5},
set3 = {1, 2, 5}

intersection_123 = set1 & set2 & set3
# or:
intersection_123 = set.intersection(set1, set2, set3)