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https://github.com/krahets/hello-algo.git
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e720aa2d24
* Sync recent changes to the revised Word. * Revised the preface chapter * Revised the introduction chapter * Revised the computation complexity chapter * Revised the chapter data structure * Revised the chapter array and linked list * Revised the chapter stack and queue * Revised the chapter hashing * Revised the chapter tree * Revised the chapter heap * Revised the chapter graph * Revised the chapter searching * Reivised the sorting chapter * Revised the divide and conquer chapter * Revised the chapter backtacking * Revised the DP chapter * Revised the greedy chapter * Revised the appendix chapter * Revised the preface chapter doubly * Revised the figures
88 lines
2.4 KiB
Go
88 lines
2.4 KiB
Go
// File: 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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/* 0-1 背包：暴力搜索 */
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func knapsackDFS(wgt, val []int, i, c int) int {
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// 若已选完所有物品或背包无剩余容量，则返回价值 0
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if i == 0 || c == 0 {
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return 0
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}
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// 若超过背包容量，则只能选择不放入背包
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if wgt[i-1] > c {
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return knapsackDFS(wgt, val, i-1, c)
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}
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// 计算不放入和放入物品 i 的最大价值
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no := knapsackDFS(wgt, val, i-1, c)
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yes := knapsackDFS(wgt, val, i-1, c-wgt[i-1]) + val[i-1]
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// 返回两种方案中价值更大的那一个
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return int(math.Max(float64(no), float64(yes)))
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}
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/* 0-1 背包：记忆化搜索 */
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func knapsackDFSMem(wgt, val []int, mem [][]int, i, c int) int {
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// 若已选完所有物品或背包无剩余容量，则返回价值 0
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if i == 0 || c == 0 {
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return 0
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}
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// 若已有记录，则直接返回
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if mem[i][c] != -1 {
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return mem[i][c]
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}
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// 若超过背包容量，则只能选择不放入背包
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if wgt[i-1] > c {
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return knapsackDFSMem(wgt, val, mem, i-1, c)
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}
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// 计算不放入和放入物品 i 的最大价值
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no := knapsackDFSMem(wgt, val, mem, i-1, c)
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yes := knapsackDFSMem(wgt, val, mem, i-1, c-wgt[i-1]) + val[i-1]
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// 返回两种方案中价值更大的那一个
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mem[i][c] = int(math.Max(float64(no), float64(yes)))
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return mem[i][c]
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}
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/* 0-1 背包：动态规划 */
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func knapsackDP(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-1][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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/* 0-1 背包：空间优化后的动态规划 */
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func knapsackDPComp(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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// 倒序遍历
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for c := cap; c >= 1; c-- {
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if wgt[i-1] <= c {
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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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