Caching combinations

The module itertools has an iterable called combinations that accepts two arguments, an iterable it and an integer r, and then “return[s] successive r-length combinations of elements in the iterable [it]”.

For example, you can use combinations to answer this question: if I have a class of 30 students and I need to pick 6 students for a volleyball team, how many different teams could I possibly create? The correct answer is a staggering 593,775 teams!

The way you compute this with combinations is through the following code:

print(
    len(list(combinations(range(30), 6)))
)

This was a random hypothetical question that shows how, in some mathematical contexts, you want to know the length of this result produced by combinations without caring about the “r-length combinations” that can be produced. Thus, you can write a function for this:

from itertools import combinations

def combinations_len(n, r):
    return len(list(combinations(range(n), r)))

Now, you can get the same result by computing

print(combinations_len(30, 6))

Now, you might think “hey, let’s add a cache to this function! You go back to your trusted cached_factory and apply it to combinations_len:

from itertools import combinations

def cached_factory(f):
    cache = {}
    def cached_f(n):
        if n not in cache:
            cache[n] = f(n)
        return cache[n]

    return cached_f

@cached_factory
def combinations_len(n, r):
    return len(list(combinations(range(n), r)))

This looks great… But the cached function doesn’t work:

print(combinations_len(10, 4))
"""
Traceback (most recent call last):
  File "<python-input-77>", line 1, in <module>
    print(combinations_len(10, 4))
          ~~~~~~~~~~~~~~~~^^^^^^^
TypeError: cached_function_factory.<locals>.cached_f() takes 1 positional argument but 2 were given
"""

What the heck is wrong here? Can you see it? And how do you fix it?