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51 lines
1.2 KiB
51 lines
1.2 KiB
// File: unbounded_knapsack.go
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// Created Time: 2023-07-23
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// Author: Reanon (793584285@qq.com)
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package chapter_dynamic_programming
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import "math"
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/* 完全背包：动态规划 */
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func unboundedKnapsackDP(wgt, val []int, cap int) int {
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n := len(wgt)
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// 初始化 dp 表
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dp := make([][]int, n+1)
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for i := 0; i <= n; i++ {
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dp[i] = make([]int, cap+1)
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}
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// 状态转移
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for i := 1; i <= n; i++ {
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for c := 1; c <= cap; c++ {
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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] = int(math.Max(float64(dp[i-1][c]), float64(dp[i][c-wgt[i-1]]+val[i-1])))
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}
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}
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}
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return dp[n][cap]
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}
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/* 完全背包：空间优化后的动态规划 */
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func unboundedKnapsackDPComp(wgt, val []int, cap int) int {
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n := len(wgt)
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// 初始化 dp 表
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dp := make([]int, cap+1)
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// 状态转移
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for i := 1; i <= n; i++ {
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for c := 1; c <= cap; c++ {
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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] = int(math.Max(float64(dp[c]), float64(dp[c-wgt[i-1]]+val[i-1])))
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}
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}
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}
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return dp[cap]
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}
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