Cartesian product in Python

A cartesian product is basically all combinations of given values, so for example I could have the following values:

a b c
1 1 1
  2 2
    3

I would then expect the cartesian product to be something like a1b1c1, a1b1c2, a1b1c3, a1b2c1 and so on…

Many, many times have had to solve this problem over and over in Python… it’s time to jot down some notes.

I’m taking the table above and making it into a dictionary:

d = {'a': [1], 'b': [1, 2], 'c': [1, 2, 3]}

This can be fed into the following cprod function:

import sys
import itertools

def cprod(dictionary):
    """Generate cartesian product"""

    if sys.version_info.major > 2:
        return (dict(zip(dictionary, x)) for x in itertools.product(*dictionary.values()))
    
    return (dict(itertools.izip(dictionary, x))
            for x in itertools.product(*dictionary.itervalues()))

…which will return a generator object, which can be looped over (once, before it gets destroyed):

>>> for _dict in cprod(d):
>>>     print(_dict)
{'a': 1, 'b': 1, 'c': 1}
{'a': 1, 'b': 1, 'c': 2}
{'a': 1, 'b': 1, 'c': 3}
{'a': 1, 'b': 2, 'c': 1}
{'a': 1, 'b': 2, 'c': 2}
{'a': 1, 'b': 2, 'c': 3}

Number of combinations are len(list(cprod(d))) (in this case 6).

If we wish to get the list of combinations directly, we can use the cprod_combos function:

def cprod_combos(dictionary):
    """Generate a list of cartesian product combinations"""
    combos = []
    for _dict in cprod(d):
        combo = ''
        for key, value in _dict.items():
            combo += '%s%s' % (key, value)
        combos.append(combo)
    return combos

…which will return a list of combinations:

>>> [i for i in cprod_combos(d)]
['a1b1c1', 'a1b1c2', 'a1b1c3', 'a1b2c1', 'a1b2c2', 'a1b2c3']