hello-algo/codes/java/chapter_dynamic_programming/coin_change_ii.java

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/**
* File: coin_change_ii.java
* Created Time: 2023-07-11
* Author: Krahets (krahets@163.com)
*/
package chapter_dynamic_programming;
public class coin_change_ii {
/* 零钱兑换 II动态规划 */
static int coinChangeIIDP(int[] coins, int amt) {
int n = coins.length;
// 初始化 dp 表
int[][] dp = new int[n + 1][amt + 1];
// 初始化首列
for (int i = 0; i <= n; i++) {
dp[i][0] = 1;
}
// 状态转移
for (int i = 1; i <= n; i++) {
for (int a = 1; a <= amt; a++) {
if (coins[i - 1] > a) {
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// 若超过目标金额,则不选硬币 i
dp[i][a] = dp[i - 1][a];
} else {
// 不选和选硬币 i 这两种方案之和
dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];
}
}
}
return dp[n][amt];
}
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/* 零钱兑换 II空间优化后的动态规划 */
static int coinChangeIIDPComp(int[] coins, int amt) {
int n = coins.length;
// 初始化 dp 表
int[] dp = new int[amt + 1];
dp[0] = 1;
// 状态转移
for (int i = 1; i <= n; i++) {
for (int a = 1; a <= amt; a++) {
if (coins[i - 1] > a) {
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// 若超过目标金额,则不选硬币 i
dp[a] = dp[a];
} else {
// 不选和选硬币 i 这两种方案之和
dp[a] = dp[a] + dp[a - coins[i - 1]];
}
}
}
return dp[amt];
}
public static void main(String[] args) {
int[] coins = { 1, 2, 5 };
int amt = 5;
// 动态规划
int res = coinChangeIIDP(coins, amt);
System.out.println("凑出目标金额的硬币组合数量为 " + res);
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// 空间优化后的动态规划
res = coinChangeIIDPComp(coins, amt);
System.out.println("凑出目标金额的硬币组合数量为 " + res);
}
}