counting combinations and permutations efficiently

Question

I have some code to count permutations and combinations, and I\'m trying to make it work better for large numbers.

I\'ve found a better algorithm for permutations th

Answer 1

There's a function for this in scipy which hasn't been mentioned yet: scipy.special.comb. It seems efficient based on some quick timing results for your doctest (~0.004 seconds for comb(100000, 1000, 1) == comb(100000, 99000, 1)).

[While this specific question seems to be about algorithms the question is there a math ncr function in python is marked as a duplicate of this...]