Vincent Li - 3 years ago 92
Python Question

# python combinations of multiple list

Is there any pythonic method to generate combinations between multiple list? (similar to Cartesian product but more complicated)

Example:

``````a = [1, 2, 3]
b = [4, 5, 6]
c = [7, 8, 9]
# ...
# there are more than 3 lists
``````

Expected output:

``````1. [(1, 4, 7), (2, 5, 8), (3, 6, 9)]
2. [(1, 4, 8), (2, 5, 7), (3, 6, 9)]
3. [(1, 4, 9), (2, 5, 7), (3, 6, 8)]
4. [(1, 5, 7), (2, 4, 8), (3, 6, 9)]
5. ...
``````

Update:

To clarify the question:

The result are all non-repeated combinations of Cartesian product of list a, b, c.

It can be done by another ugly method:

1) Generate the whole list of Cartesian product

``````from itertools import product, combinations, chain
t = list(product(a, b, c))
``````

2) Using combinations to generate all possible results

``````p = list(combinations(t, 3))
``````

3) Filter the repeated conditions

``````cnt = len(list(chain(a, b, c)))
f = [x for x in p if len(set(chain(*x))) == cnt]
``````

Update2:

Expected result generated by ugly method:

``````((1, 4, 7), (2, 5, 8), (3, 6, 9))
((1, 4, 7), (2, 5, 9), (3, 6, 8))
((1, 4, 7), (2, 6, 8), (3, 5, 9))
((1, 4, 7), (2, 6, 9), (3, 5, 8))
((1, 4, 8), (2, 5, 7), (3, 6, 9))
((1, 4, 8), (2, 5, 9), (3, 6, 7))
((1, 4, 8), (2, 6, 7), (3, 5, 9))
((1, 4, 8), (2, 6, 9), (3, 5, 7))
((1, 4, 9), (2, 5, 7), (3, 6, 8))
((1, 4, 9), (2, 5, 8), (3, 6, 7))
((1, 4, 9), (2, 6, 7), (3, 5, 8))
((1, 4, 9), (2, 6, 8), (3, 5, 7))
((1, 5, 7), (2, 4, 8), (3, 6, 9))
((1, 5, 7), (2, 4, 9), (3, 6, 8))
((1, 5, 7), (2, 6, 8), (3, 4, 9))
((1, 5, 7), (2, 6, 9), (3, 4, 8))
((1, 5, 8), (2, 4, 7), (3, 6, 9))
((1, 5, 8), (2, 4, 9), (3, 6, 7))
((1, 5, 8), (2, 6, 7), (3, 4, 9))
((1, 5, 8), (2, 6, 9), (3, 4, 7))
((1, 5, 9), (2, 4, 7), (3, 6, 8))
((1, 5, 9), (2, 4, 8), (3, 6, 7))
((1, 5, 9), (2, 6, 7), (3, 4, 8))
((1, 5, 9), (2, 6, 8), (3, 4, 7))
((1, 6, 7), (2, 4, 8), (3, 5, 9))
((1, 6, 7), (2, 4, 9), (3, 5, 8))
((1, 6, 7), (2, 5, 8), (3, 4, 9))
((1, 6, 7), (2, 5, 9), (3, 4, 8))
((1, 6, 8), (2, 4, 7), (3, 5, 9))
((1, 6, 8), (2, 4, 9), (3, 5, 7))
((1, 6, 8), (2, 5, 7), (3, 4, 9))
((1, 6, 8), (2, 5, 9), (3, 4, 7))
((1, 6, 9), (2, 4, 7), (3, 5, 8))
((1, 6, 9), (2, 4, 8), (3, 5, 7))
((1, 6, 9), (2, 5, 7), (3, 4, 8))
((1, 6, 9), (2, 5, 8), (3, 4, 7))
``````

What you want are not combinations but indeed permutations. 3 elements have 6 permutations, a Cartesian product of 2 sets of permutations has 36. PM 2Ring originally suspected that you want all 3 of these permuted since your question didn't tell otherwise. If the code in your question produces the desired output, it means you want `b` and `c` permuted but not `a`. Initially I wrote code that calculated the permutations for all of `a`, `b` and `c`. However, since `a` doesn't need to be permuted, we'll just wrap it in a list. This gets us very close to the desired output:

``````import itertools as it

a = [1, 2, 3]
b = [4, 5, 6]
c = [7, 8, 9]

for i in it.product([tuple(a)], it.permutations(b), it.permutations(c)):
print(i)
``````

``````((1, 2, 3), (4, 5, 6), (7, 8, 9))
((1, 2, 3), (4, 5, 6), (7, 9, 8))
((1, 2, 3), (4, 5, 6), (8, 7, 9))
``````

It is already almost the same format that you want but with indexes transposed so `o[x][y]` would match `o[y][x]` of your desired output. We use some `zip` magic to transpose them. As a plus, this function now works for any number of arguments:

``````import itertools as it

a = [1, 2, 3]
b = [4, 5, 6]
c = [7, 8, 9]

def funnyperms(first, *rest):
for i in it.product([first], *(it.permutations(j) for j in rest)):
yield tuple(zip(*i))

for i in funnyperms(a, b, c):
print(i)
``````

The output is

``````((1, 4, 7), (2, 5, 8), (3, 6, 9))
((1, 4, 7), (2, 5, 9), (3, 6, 8))
((1, 4, 8), (2, 5, 7), (3, 6, 9))
((1, 4, 8), (2, 5, 9), (3, 6, 7))
((1, 4, 9), (2, 5, 7), (3, 6, 8))
((1, 4, 9), (2, 5, 8), (3, 6, 7))
((1, 4, 7), (2, 6, 8), (3, 5, 9))
((1, 4, 7), (2, 6, 9), (3, 5, 8))
((1, 4, 8), (2, 6, 7), (3, 5, 9))
((1, 4, 8), (2, 6, 9), (3, 5, 7))
((1, 4, 9), (2, 6, 7), (3, 5, 8))
((1, 4, 9), (2, 6, 8), (3, 5, 7))
((1, 5, 7), (2, 4, 8), (3, 6, 9))
((1, 5, 7), (2, 4, 9), (3, 6, 8))
((1, 5, 8), (2, 4, 7), (3, 6, 9))
((1, 5, 8), (2, 4, 9), (3, 6, 7))
((1, 5, 9), (2, 4, 7), (3, 6, 8))
((1, 5, 9), (2, 4, 8), (3, 6, 7))
((1, 5, 7), (2, 6, 8), (3, 4, 9))
((1, 5, 7), (2, 6, 9), (3, 4, 8))
((1, 5, 8), (2, 6, 7), (3, 4, 9))
((1, 5, 8), (2, 6, 9), (3, 4, 7))
((1, 5, 9), (2, 6, 7), (3, 4, 8))
((1, 5, 9), (2, 6, 8), (3, 4, 7))
((1, 6, 7), (2, 4, 8), (3, 5, 9))
((1, 6, 7), (2, 4, 9), (3, 5, 8))
((1, 6, 8), (2, 4, 7), (3, 5, 9))
((1, 6, 8), (2, 4, 9), (3, 5, 7))
((1, 6, 9), (2, 4, 7), (3, 5, 8))
((1, 6, 9), (2, 4, 8), (3, 5, 7))
((1, 6, 7), (2, 5, 8), (3, 4, 9))
((1, 6, 7), (2, 5, 9), (3, 4, 8))
((1, 6, 8), (2, 5, 7), (3, 4, 9))
((1, 6, 8), (2, 5, 9), (3, 4, 7))
((1, 6, 9), (2, 5, 7), (3, 4, 8))
((1, 6, 9), (2, 5, 8), (3, 4, 7))
``````

Storing these into a set and comparing with the values produced by your method proves that they have identical output:

``````print(set(funnyperms(a, b, c)) == set(f))
``````

prints `True`, Q.E.D.

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