31 lines
1.0 KiB
Python
31 lines
1.0 KiB
Python
"""
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Author: Wenru Dong
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"""
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from typing import List
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def knapsack01(weights: List[int], values: List[int], capacity: int) -> int:
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# Denote the state as (i, c), where i is the stage number,
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# and c is the capacity available. Denote f(i, c) to be the
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# maximum value when the capacity available is c, and Item 0
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# to Item i-1 are to be packed.
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# The goal is to find f(n-1, W), where W is the total capacity.
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# Then the DP functional equation is:
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# f(i, c) = max(xᵢvᵢ + f(i-1, c-xᵢwᵢ)), xᵢ ∈ D, i ≥ 0,
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# f(-1, c) = 0, 0 ≤ c ≤ W,
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# where
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# / {0}, if wᵢ > c
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# D = D(i, c) =
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# \ {0, 1}, if wᵢ ≤ c
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prev = [0] * (capacity + 1)
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for w, v in zip(weights, values):
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prev = [c >= w and max(prev[c], prev[c-w] + v) for c in range(capacity + 1)]
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return prev[-1]
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if __name__ == "__main__":
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# To find the maximum weight that can be packed,
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# set values equal to the weights
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print(knapsack01([2, 2, 4, 6, 3], [2, 2, 4, 6, 3], 9))
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