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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
70 lines
2.1 KiB
Swift
70 lines
2.1 KiB
Swift
/**
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* File: coin_change.swift
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* Created Time: 2023-07-15
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* Author: nuomi1 (nuomi1@qq.com)
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*/
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/* 零钱兑换：动态规划 */
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func coinChangeDP(coins: [Int], amt: Int) -> Int {
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let n = coins.count
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let MAX = amt + 1
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// 初始化 dp 表
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var dp = Array(repeating: Array(repeating: 0, count: amt + 1), count: n + 1)
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// 状态转移：首行首列
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for a in stride(from: 1, through: amt, by: 1) {
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dp[0][a] = MAX
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}
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// 状态转移：其余行和列
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for i in stride(from: 1, through: n, by: 1) {
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for a in stride(from: 1, through: amt, by: 1) {
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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 这两种方案的较小值
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dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1)
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}
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}
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}
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return dp[n][amt] != MAX ? dp[n][amt] : -1
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}
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/* 零钱兑换：空间优化后的动态规划 */
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func coinChangeDPComp(coins: [Int], amt: Int) -> Int {
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let n = coins.count
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let MAX = amt + 1
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// 初始化 dp 表
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var dp = Array(repeating: MAX, count: amt + 1)
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dp[0] = 0
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// 状态转移
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for i in stride(from: 1, through: n, by: 1) {
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for a in stride(from: 1, through: amt, by: 1) {
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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 这两种方案的较小值
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dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1)
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}
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}
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}
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return dp[amt] != MAX ? dp[amt] : -1
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}
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@main
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enum CoinChange {
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/* Driver Code */
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static func main() {
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let coins = [1, 2, 5]
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let amt = 4
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// 动态规划
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var res = coinChangeDP(coins: coins, amt: amt)
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print("凑到目标金额所需的最少硬币数量为 \(res)")
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// 空间优化后的动态规划
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res = coinChangeDPComp(coins: coins, amt: amt)
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print("凑到目标金额所需的最少硬币数量为 \(res)")
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}
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}
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