P

```
"""A naive recursive implementation of 0-1 Knapsack Problem
https://en.wikipedia.org/wiki/Knapsack_problem
"""
from __future__ import annotations
def knapsack(capacity: int, weights: list[int], values: list[int], counter: int) -> int:
"""
Returns the maximum value that can be put in a knapsack of a capacity cap,
whereby each weight w has a specific value val.
>>> cap = 50
>>> val = [60, 100, 120]
>>> w = [10, 20, 30]
>>> c = len(val)
>>> knapsack(cap, w, val, c)
220
The result is 220 cause the values of 100 and 120 got the weight of 50
which is the limit of the capacity.
"""
# Base Case
if counter == 0 or capacity == 0:
return 0
# If weight of the nth item is more than Knapsack of capacity,
# then this item cannot be included in the optimal solution,
# else return the maximum of two cases:
# (1) nth item included
# (2) not included
if weights[counter - 1] > capacity:
return knapsack(capacity, weights, values, counter - 1)
else:
left_capacity = capacity - weights[counter - 1]
new_value_included = values[counter - 1] + knapsack(
left_capacity, weights, values, counter - 1
)
without_new_value = knapsack(capacity, weights, values, counter - 1)
return max(new_value_included, without_new_value)
if __name__ == "__main__":
import doctest
doctest.testmod()
```