rope_problem.py

from typing import List
#lengths
def test_max_prod(total: int, acc = None) -> List[int]:
	if acc is None:
		acc = []
	if total == 0:
		return acc
	else:
		max_list = []
		for i in range(1, total + 1):
			current_list = test_max_prod(total - i, acc + [i])
			max_list = max(max_list, current_list, key = lambda x: (product(x), -len(x)))
		return max_list
#product
def test_max_prod(total: int) -> int:
	return 1 if total == 0 else max([i * test_max_prod(total - i) for i in range(1, total + 1)])

#number of cuts
def test_max_prod3(total: int) -> int:
	return 0 if total == 0 else max([1 + test_max_prod(total - i) for i in range(1, total + 1)])

def product(x: List[int]) -> int:
	if len(x) == 0:
		return 1
	else:
		return x[0] * product(x[1:])