Fast ackermann

ackermann.py

from functools import lru_cache


@lru_cache(maxsize=1024)
def kn(a, b, order):
    assert order >= 1
    if order == 1:
        return a ** b
    sub_order = order - 1
    res = a
    for i in range(order):
        res = kn(res, b, sub_order)
    return res


def conway(p, q, r):
    return kn(p, q, r)


def ackermann(m, n):
    return conway(2, n + 3, m - 2) - 3