mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-30 16:31:08 +00:00
802ac83c3d
* Add naive recursive implementation of 0-1 Knapsack problem * Fix shadowing * Add doctest * Fix type hints * Add link to wiki * Blacked the file * Fix isort * Move knapsack / add readme and more tests * Add missed main in tests
48 lines
1.4 KiB
Python
48 lines
1.4 KiB
Python
from typing import List
|
|
|
|
""" A naive recursive implementation of 0-1 Knapsack Problem
|
|
https://en.wikipedia.org/wiki/Knapsack_problem
|
|
"""
|
|
|
|
|
|
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()
|