Carthesian product in Python

I recently worked on some side project that was using pandas dataframe with 2-level multiindexed columns. They could be represented as list of tuples, for example:

[("calendar", "year"), ("calendar", "month"), ("calendar", "day")]

Dataframe with such index would look like this - calendar being the upper level and year, month, day on the lower level.

      year month day
0     2019     2   1
1     2019     3  10

In order to create such multiindex, I needed to generate carthesian product of calendar and year, month, day.

Pandas MultiIndex object provides constructor methods for doing that, for example pd.MultiIndex.from_product:

import pandas as pd

multi_index = pd.MultiIndex.from_product([("calendar",), ("year", "month", "day")])

But I was also wondering if the same can be achieved with just the Python's standard library (and without using nested for loops).

zip & itertools.zip_longest

My initial hunch was to check if there's any parameter to built-in zip function to make it behave to fit my use-case. Zip stops at the shortest iterable so in my case

list(zip(("calendar",), ("year", "month", "day")))

would return:

[('calendar', 'year')]

Google advised to take a look itertools.zip_longest. Citing official documentation's definition:

Make an iterator that aggregates elements from each of the iterables. If the iterables are of uneven length, missing values are filled-in with fillvalue. Iteration continues until the longest iterable is exhausted

Let's compare the results using default & custom fillvalue.

Without providing fillvalue argument:

from itertools import zip_longest

zip_longest(("calendar",), ("year", "month", "day"))


[('calendar', 'year'), (None, 'month'), (None, 'day')]

With fillvalue = "calendar":

from itertools import zip_longest

list(zip_longest(("calendar",), ("year", "month", "day"), fillvalue="calendar"))


[('calendar', 'year'), ('calendar', 'month'), ('calendar', 'day')]

As you can see, zip_longest with fillvalue gives us desired result. But is there a better way?


There is! And it's called itertools.product.

itertools.product -> Cartesian product of input iterables.

from itertools import product

list(product(("calendar",), ("year", "month", "day")))


[('calendar', 'year'), ('calendar', 'month'), ('calendar', 'day')]

Exactly what we needed!

Sidenote: itertools.product does not discard duplicates. If you care about not having them, use set to remove them.

That's it for this post. Hope you learnt something new today.

Best Regards,

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