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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
54 lines
1.2 KiB
Go
54 lines
1.2 KiB
Go
// File: coin_change_ii.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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/* 零钱兑换 II：动态规划 */
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func coinChangeIIDP(coins []int, amt int) int {
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n := len(coins)
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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, amt+1)
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}
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// 初始化首列
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for i := 0; i <= n; i++ {
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dp[i][0] = 1
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}
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// 状态转移：其余行和列
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for i := 1; i <= n; i++ {
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for a := 1; a <= amt; a++ {
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if coins[i-1] > a {
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// 若超过目标金额，则不选硬币 i
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dp[i][a] = dp[i-1][a]
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} else {
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// 不选和选硬币 i 这两种方案之和
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dp[i][a] = dp[i-1][a] + dp[i][a-coins[i-1]]
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}
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}
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}
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return dp[n][amt]
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}
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/* 零钱兑换 II：空间优化后的动态规划 */
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func coinChangeIIDPComp(coins []int, amt int) int {
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n := len(coins)
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// 初始化 dp 表
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dp := make([]int, amt+1)
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dp[0] = 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 a := 1; a <= amt; a++ {
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if coins[i-1] > a {
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// 若超过目标金额，则不选硬币 i
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dp[a] = dp[a]
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} else {
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// 不选和选硬币 i 这两种方案之和
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dp[a] = dp[a] + dp[a-coins[i-1]]
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}
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}
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}
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return dp[amt]
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}
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