68 lines
2.1 KiB
Java
68 lines
2.1 KiB
Java
/**
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* File: coin_change_ii.java
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* Created Time: 2023-07-11
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* Author: krahets (krahets@163.com)
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*/
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package chapter_dynamic_programming;
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public class coin_change_ii {
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/* 零錢兌換 II：動態規劃 */
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static int coinChangeIIDP(int[] coins, int amt) {
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int n = coins.length;
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// 初始化 dp 表
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int[][] dp = new int[n + 1][amt + 1];
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// 初始化首列
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for (int i = 0; i <= n; i++) {
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dp[i][0] = 1;
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}
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// 狀態轉移
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for (int i = 1; i <= n; i++) {
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for (int a = 1; a <= amt; a++) {
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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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/* 零錢兌換 II：空間最佳化後的動態規劃 */
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static int coinChangeIIDPComp(int[] coins, int amt) {
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int n = coins.length;
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// 初始化 dp 表
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int[] dp = new int[amt + 1];
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dp[0] = 1;
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// 狀態轉移
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for (int i = 1; i <= n; i++) {
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for (int a = 1; a <= amt; a++) {
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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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public static void main(String[] args) {
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int[] coins = { 1, 2, 5 };
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int amt = 5;
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// 動態規劃
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int res = coinChangeIIDP(coins, amt);
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System.out.println("湊出目標金額的硬幣組合數量為 " + res);
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// 空間最佳化後的動態規劃
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res = coinChangeIIDPComp(coins, amt);
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System.out.println("湊出目標金額的硬幣組合數量為 " + res);
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}
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}
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