Fractional Knapsack 2

# 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()
Algerlogo

Β© Alger 2022

About us

We are a group of programmers helping each other build new things, whether it be writing complex encryption programs, or simple ciphers. Our goal is to work together to document and model beautiful, helpful and interesting algorithms using code. We are an open-source community - anyone can contribute. We check each other's work, communicate and collaborate to solve problems. We strive to be welcoming, respectful, yet make sure that our code follows the latest programming guidelines.