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Contents/10.Dynamic-Programming/04.Knapsack-Problem/05.Knapsack-Problem-05.md

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> **0-1 背包问题求具体方案**:有 $n$ 种物品和一个最多能装重量为 $W$ 的背包,第 $i$ 种物品的重量为 $weight[i]$,价值为 $value[i]$,每件物品有且只有 $1$ 件。请问将哪些物品装入背包,可使这些物品的总重量不超过背包载重上限,且价值总和最大?
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#### 4:动态规划 + 路径记录
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#### 思路 4:动态规划 + 路径记录
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0-1 背包问题的状态转移方程为:$dp[i][w] = max \lbrace dp[i - 1][w], \quad dp[i - 1][w - weight[i - 1]] + value[i - 1] \rbrace$
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