## Python, dynamic_programming, fractional_knapsack_2.py

``````# https://en.wikipedia.org/wiki/Continuous_knapsack_problem
# https://www.guru99.com/fractional-knapsack-problem-greedy.html
# https://medium.com/walkinthecode/greedy-algorithm-fractional-knapsack-problem-9aba1daecc93

from __future__ import annotations

def fractional_knapsack(
value: list[int], weight: list[int], capacity: int
) -> tuple[float, list[float]]:
"""
>>> value = [1, 3, 5, 7, 9]
>>> weight = [0.9, 0.7, 0.5, 0.3, 0.1]
>>> fractional_knapsack(value, weight, 5)
(25, [1, 1, 1, 1, 1])
>>> fractional_knapsack(value, weight, 15)
(25, [1, 1, 1, 1, 1])
>>> fractional_knapsack(value, weight, 25)
(25, [1, 1, 1, 1, 1])
>>> fractional_knapsack(value, weight, 26)
(25, [1, 1, 1, 1, 1])
>>> fractional_knapsack(value, weight, -1)
(-90.0, [0, 0, 0, 0, -10.0])
>>> fractional_knapsack([1, 3, 5, 7], weight, 30)
(16, [1, 1, 1, 1])
>>> fractional_knapsack(value, [0.9, 0.7, 0.5, 0.3, 0.1], 30)
(25, [1, 1, 1, 1, 1])
>>> fractional_knapsack([], [], 30)
(0, [])
"""
index = list(range(len(value)))
ratio = [v / w for v, w in zip(value, weight)]
index.sort(key=lambda i: ratio[i], reverse=True)

max_value: float = 0
fractions: list[float] = [0] * len(value)
for i in index:
if weight[i] <= capacity:
fractions[i] = 1
max_value += value[i]
capacity -= weight[i]
else:
fractions[i] = capacity / weight[i]
max_value += value[i] * capacity / weight[i]
break

return max_value, fractions

if __name__ == "__main__":
import doctest

doctest.testmod()
``````