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61 lines
2.1 KiB
Python
61 lines
2.1 KiB
Python
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# 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 typing import List, Tuple
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def fractional_knapsack(
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value: List[int], weight: List[int], capacity: int
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) -> Tuple[int, List[int]]:
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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 = 0
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fractions = [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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n = int(input("Enter number of items: "))
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value = input(f"Enter the values of the {n} item(s) in order: ").split()
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value = [int(v) for v in value]
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weight = input(f"Enter the positive weights of the {n} item(s) in order: ".split())
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weight = [int(w) for w in weight]
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capacity = int(input("Enter maximum weight: "))
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max_value, fractions = fractional_knapsack(value, weight, capacity)
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print("The maximum value of items that can be carried:", max_value)
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print("The fractions in which the items should be taken:", fractions)
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