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47 lines
1.3 KiB
47 lines
1.3 KiB
"""
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File: fractional_knapsack.py
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Created Time: 2023-07-19
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Author: krahets (krahets@163.com)
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"""
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class Item:
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"""物品"""
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def __init__(self, w: int, v: int):
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self.w = w # 物品重量
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self.v = v # 物品價值
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def fractional_knapsack(wgt: list[int], val: list[int], cap: int) -> int:
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"""分數背包：貪婪"""
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# 建立物品串列，包含兩個屬性：重量、價值
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items = [Item(w, v) for w, v in zip(wgt, val)]
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# 按照單位價值 item.v / item.w 從高到低進行排序
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items.sort(key=lambda item: item.v / item.w, reverse=True)
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# 迴圈貪婪選擇
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res = 0
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for item in items:
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if item.w <= cap:
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# 若剩餘容量充足，則將當前物品整個裝進背包
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res += item.v
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cap -= item.w
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else:
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# 若剩餘容量不足，則將當前物品的一部分裝進背包
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res += (item.v / item.w) * cap
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# 已無剩餘容量，因此跳出迴圈
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break
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return res
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"""Driver Code"""
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if __name__ == "__main__":
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wgt = [10, 20, 30, 40, 50]
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val = [50, 120, 150, 210, 240]
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cap = 50
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n = len(wgt)
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# 貪婪演算法
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res = fractional_knapsack(wgt, val, cap)
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print(f"不超過背包容量的最大物品價值為 {res}")
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