Statistics: combinations in Python

Question

I need to compute combinatorials (nCr) in Python but cannot find the function to do that in math, numpy or stat libraries. Something

Answer 1

If your program has an upper bound to n (say n <= N) and needs to repeatedly compute nCr (preferably for >>N times), using lru_cache can give you a huge performance boost:

from functools import lru_cache

@lru_cache(maxsize=None)
def nCr(n, r):
    return 1 if r == 0 or r == n else nCr(n - 1, r - 1) + nCr(n - 1, r)

Constructing the cache (which is done implicitly) takes up to O(N^2) time. Any subsequent calls to nCr will return in O(1).