combinatorics

Combinatorics Library

boring_math.combinatorics.comb(n: int, m: int, /, target_top: int = 700, target_bot: int = 5) → int

C(n,m) - choose m from n.

  • number of ways m items can be taken from n items.

  • geared to works efficiently for Python’s arbitrary length integers

    • slower but comparable to math.comb

  • default parameters geared to large values of n and m

  • the defaults work reasonably well for smaller (human size) values

  • for inner loops with smaller values,

    • use target_top = target_bot = 1

    • or just use math.comb(n, m) instead

Parameters:

  • n – total number of distinct items to choose from

  • m – number of items to choose

Returns:

number of ways to choose m items from n items

Raises:

ValueError – if either n < 0 or m < 0

boring_math.combinatorics.perm(n: int, m: int, /) → int

Permutations P(n,m) - number of m orderings taken from n items.

  • about 5 times slower than the math.perm C code

    • keeping around for PyPy 3.12+ or Python going JIT

    • currently the PyPy team is working on 3.11

Raises:

ValueError – if n < 0 or m < 0