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56 lines
1.7 KiB
56 lines
1.7 KiB
"""
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File: unbounded_knapsack.py
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Created Time: 2023-07-10
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Author: Krahets (krahets@163.com)
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"""
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def unbounded_knapsack_dp(wgt: list[int], val: list[int], cap: int) -> int:
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"""完全背包：动态规划"""
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n = len(wgt)
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# 初始化 dp 表
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dp = [[0] * (cap + 1) for _ in range(n + 1)]
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# 状态转移
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for i in range(1, n + 1):
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for c in range(1, cap + 1):
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if wgt[i - 1] > c:
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# 若超过背包容量，则不选物品 i
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dp[i][c] = dp[i - 1][c]
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else:
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# 不选和选物品 i 这两种方案的较大值
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dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1])
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return dp[n][cap]
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def unbounded_knapsack_dp_comp(wgt: list[int], val: list[int], cap: int) -> int:
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"""完全背包：空间优化后的动态规划"""
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n = len(wgt)
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# 初始化 dp 表
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dp = [0] * (cap + 1)
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# 状态转移
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for i in range(1, n + 1):
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# 正序遍历
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for c in range(1, cap + 1):
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if wgt[i - 1] > c:
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# 若超过背包容量，则不选物品 i
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dp[c] = dp[c]
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else:
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# 不选和选物品 i 这两种方案的较大值
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dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])
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return dp[cap]
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"""Driver Code"""
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if __name__ == "__main__":
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wgt = [1, 2, 3]
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val = [5, 11, 15]
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cap = 4
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# 动态规划
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res = unbounded_knapsack_dp(wgt, val, cap)
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print(f"不超过背包容量的最大物品价值为 {res}")
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# 空间优化后的动态规划
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res = unbounded_knapsack_dp_comp(wgt, val, cap)
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print(f"不超过背包容量的最大物品价值为 {res}")
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