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* Moved fractional knapsack from 'dynamic_programming' to 'greedy_methods' * Updated DIRECTORY.md
54 lines
1.6 KiB
Python
54 lines
1.6 KiB
Python
# https://en.wikipedia.org/wiki/Continuous_knapsack_problem
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# https://www.guru99.com/fractional-knapsack-problem-greedy.html
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# https://medium.com/walkinthecode/greedy-algorithm-fractional-knapsack-problem-9aba1daecc93
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from __future__ import annotations
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def fractional_knapsack(
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value: list[int], weight: list[int], capacity: int
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) -> tuple[float, list[float]]:
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"""
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>>> value = [1, 3, 5, 7, 9]
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>>> weight = [0.9, 0.7, 0.5, 0.3, 0.1]
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>>> fractional_knapsack(value, weight, 5)
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(25, [1, 1, 1, 1, 1])
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>>> fractional_knapsack(value, weight, 15)
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(25, [1, 1, 1, 1, 1])
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>>> fractional_knapsack(value, weight, 25)
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(25, [1, 1, 1, 1, 1])
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>>> fractional_knapsack(value, weight, 26)
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(25, [1, 1, 1, 1, 1])
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>>> fractional_knapsack(value, weight, -1)
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(-90.0, [0, 0, 0, 0, -10.0])
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>>> fractional_knapsack([1, 3, 5, 7], weight, 30)
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(16, [1, 1, 1, 1])
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>>> fractional_knapsack(value, [0.9, 0.7, 0.5, 0.3, 0.1], 30)
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(25, [1, 1, 1, 1, 1])
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>>> fractional_knapsack([], [], 30)
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(0, [])
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"""
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index = list(range(len(value)))
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ratio = [v / w for v, w in zip(value, weight)]
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index.sort(key=lambda i: ratio[i], reverse=True)
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max_value: float = 0
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fractions: list[float] = [0] * len(value)
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for i in index:
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if weight[i] <= capacity:
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fractions[i] = 1
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max_value += value[i]
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capacity -= weight[i]
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else:
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fractions[i] = capacity / weight[i]
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max_value += value[i] * capacity / weight[i]
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break
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return max_value, fractions
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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