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# All combinations of a list of lists

Questions:

I’m basically looking for a python version of Combination of `List<List<int>>`

Given a list of lists, I need a new list that gives all the possible combinations of items between the lists.

``````[[1,2,3],[4,5,6],[7,8,9,10]] -> [[1,4,7],[1,4,8],...,[3,6,10]]
``````

The number of lists is unknown, so I need something that works for all cases. Bonus points for elegance!

you need `itertools.product`:

``````>>> import itertools
>>> a = [[1,2,3],[4,5,6],[7,8,9,10]]
>>> list(itertools.product(*a))
[(1, 4, 7), (1, 4, 8), (1, 4, 9), (1, 4, 10), (1, 5, 7), (1, 5, 8), (1, 5, 9), (1, 5, 10), (1, 6, 7), (1, 6, 8), (1, 6, 9), (1, 6, 10), (2, 4, 7), (2, 4, 8), (2, 4, 9), (2, 4, 10), (2, 5, 7), (2, 5, 8), (2, 5, 9), (2, 5, 10), (2, 6, 7), (2, 6, 8), (2, 6, 9), (2, 6, 10), (3, 4, 7), (3, 4, 8), (3, 4, 9), (3, 4, 10), (3, 5, 7), (3, 5, 8), (3, 5, 9), (3, 5, 10), (3, 6, 7), (3, 6, 8), (3, 6, 9), (3, 6, 10)]
``````

Questions:

The most elegant solution is to use itertools.product in python 2.6.

If you aren’t using Python 2.6, the docs for itertools.product actually show an equivalent function to do the product the “manual” way:

``````def product(*args, **kwds):
# product('ABCD', 'xy') --> Ax Ay Bx By Cx Cy Dx Dy
# product(range(2), repeat=3) --> 000 001 010 011 100 101 110 111
pools = map(tuple, args) * kwds.get('repeat', 1)
result = [[]]
for pool in pools:
result = [x+[y] for x in result for y in pool]
for prod in result:
yield tuple(prod)
``````

Questions:
``````listOLists = [[1,2,3],[4,5,6],[7,8,9,10]]
for list in itertools.product(*listOLists):
print list;
``````

I hope you find that as elegant as I did when I first encountered it.

Questions:

Numpy can do it:

`````` >>> import numpy
>>> a = [[1,2,3],[4,5,6],[7,8,9,10]]
>>> [list(x) for x in numpy.array(numpy.meshgrid(*a)).T.reshape(-1,len(a))]
[[ 1, 4, 7], [1, 5, 7], [1, 6, 7], ....]
``````

Questions:

Nothing wrong with straight up recursion for this task, and if you need a version that works with strings, this might fit your needs:

``````combinations = []

def combine(terms, accum):
last = (len(terms) == 1)
n = len(terms[0])
for i in range(n):
item = accum + terms[0][i]
if last:
combinations.append(item)
else:
combine(terms[1:], item)

>>> a = [['ab','cd','ef'],['12','34','56']]
>>> combine(a, '')
>>> print(combinations)
['ab12', 'ab34', 'ab56', 'cd12', 'cd34', 'cd56', 'ef12', 'ef34', 'ef56']
``````