A combinatoric iterator will perform a set of statistical or mathematical operations on an input iterable.

A useful itertool that is a combinatoric iterator is the combinations() itertool. This itertool will produce an iterator of tuples that contain combinations of all elements in the input.

combinations(iterable, r)

The combinations() itertool takes in two inputs, the first is an iterable, and the second is a value r that represents the length of each combination tuple.

The return type of combinations() is an iterator that can be used in a for loop or can be converted into an iterable type using list() or a set().

To show how it’s used, suppose we have a list of even numbers and we want all possible combinations of 2 even numbers:

import itertools
even = [2, 4, 6]
even_combinations = list(itertools.combinations(even, 2))
print(even_combinations)

Here we:

• Import the module itertools.
• Create an iterator using combinations() with the list of even numbers as the first argument and 2 as the second argument.
• Set even_combinations equal to a list of the elements in the iterator returned from combinations().
• Print even_combinations. The resulting list of 2 member tuples are the combinations of all 3 members of even:

  [(2, 4), (2, 6), (4, 6)]

Now, let’s try using a combinations itertool within our pet store!