70 lines
2.0 KiB
Swift
70 lines
2.0 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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/* 零錢兌換：動態規劃 */
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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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// 狀態轉移：首行首列
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for a in 1 ... amt {
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dp[0][a] = MAX
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}
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// 狀態轉移：其餘行和列
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for i in 1 ... n {
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for a in 1 ... amt {
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if coins[i - 1] > a {
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// 若超過目標金額，則不選硬幣 i
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dp[i][a] = dp[i - 1][a]
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} else {
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// 不選和選硬幣 i 這兩種方案的較小值
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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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/* 零錢兌換：空間最佳化後的動態規劃 */
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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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// 狀態轉移
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for i in 1 ... n {
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for a in 1 ... amt {
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if coins[i - 1] > a {
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// 若超過目標金額，則不選硬幣 i
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dp[a] = dp[a]
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} else {
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// 不選和選硬幣 i 這兩種方案的較小值
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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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// 動態規劃
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var res = coinChangeDP(coins: coins, amt: amt)
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print("湊到目標金額所需的最少硬幣數量為 \(res)")
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// 空間最佳化後的動態規劃
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res = coinChangeDPComp(coins: coins, amt: amt)
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print("湊到目標金額所需的最少硬幣數量為 \(res)")
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}
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}
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