The game of getting balls.

get_ball.py

import sys


def have_wining_strategy(*bags: int) -> bool:
    if 0 == sum(bags):
        return False
    for i in range(len(bags)):
        for n in range(bags[i]):
            if not have_wining_strategy(*bags[:i], n, *bags[i + 1:]):
                return True
    return False


def have_failing_strategy(*bags: int) -> bool:
    if 0 == sum(bags):
        return True
    for i in range(len(bags)):
        for n in range(bags[i]):
            if not have_failing_strategy(*bags[:i], n, *bags[i + 1:]):
                return True
    return False


print(have_wining_strategy(*[int(x) for x in sys.argv[1:]]))
print(have_failing_strategy(*[int(x) for x in sys.argv[1:]]))

get_ball_with_cache.py

import sys

cache = {}


def key(*args: int) -> str:
    args = list(args)
    args.sort()
    return str(args)


def have_wining_strategy(*bags: int) -> bool:
    if key(*bags) in cache:
        return cache[key(*bags)]
    if 0 == sum(bags):
        cache[key(*bags)] = False
        return False
    for i in range(len(bags)):
        for n in range(bags[i]):
            if not have_wining_strategy(*bags[:i], n, *bags[i + 1:]):
                cache[key(*bags)] = True
                return True
    cache[key(*bags)] = False
    return False


def have_failing_strategy(*bags: int) -> bool:
    if key(*bags) in cache:
        return cache[key(*bags)]
    if 0 == sum(bags):
        cache[key(*bags)] = False
        return False
    for i in range(len(bags)):
        for n in range(bags[i]):
            if not have_failing_strategy(*bags[:i], n, *bags[i + 1:]):
                cache[key(*bags)] = True
                return True
    cache[key(*bags)] = False
    return False


print(have_wining_strategy(*[int(x) for x in sys.argv[1:]]))
print(have_failing_strategy(*[int(x) for x in sys.argv[1:]]))