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71 lines
1.9 KiB
71 lines
1.9 KiB
/**
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* File: coin_change.kt
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* Created Time: 2024-01-25
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* Author: curtishd (1023632660@qq.com)
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*/
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package chapter_dynamic_programming
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import kotlin.math.min
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/* 零錢兌換：動態規劃 */
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fun coinChangeDP(coins: IntArray, amt: Int): Int {
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val n = coins.size
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val MAX = amt + 1
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// 初始化 dp 表
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val dp = Array(n + 1) { IntArray(amt + 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 if (dp[n][amt] != MAX) dp[n][amt] else -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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fun coinChangeDPComp(coins: IntArray, amt: Int): Int {
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val n = coins.size
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val MAX = amt + 1
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// 初始化 dp 表
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val dp = IntArray(amt + 1)
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dp.fill(MAX)
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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 if (dp[amt] != MAX) dp[amt] else -1
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}
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/* Driver Code */
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fun main() {
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val coins = intArrayOf(1, 2, 5)
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val amt = 4
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// 動態規劃
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var res = coinChangeDP(coins, amt)
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println("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, amt)
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println("湊到目標金額所需的最少硬幣數量為 $res")
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} |