You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
73 lines
2.3 KiB
73 lines
2.3 KiB
/**
|
|
* File: coin_change.java
|
|
* Created Time: 2023-07-11
|
|
* Author: Krahets (krahets@163.com)
|
|
*/
|
|
|
|
package chapter_dynamic_programming;
|
|
|
|
import java.util.Arrays;
|
|
|
|
public class coin_change {
|
|
/* 零钱兑换：动态规划 */
|
|
static int coinChangeDP(int[] coins, int amt) {
|
|
int n = coins.length;
|
|
int MAX = amt + 1;
|
|
// 初始化 dp 表
|
|
int[][] dp = new int[n + 1][amt + 1];
|
|
// 状态转移：首行首列
|
|
for (int a = 1; a <= amt; a++) {
|
|
dp[0][a] = MAX;
|
|
}
|
|
// 状态转移：其余行和列
|
|
for (int i = 1; i <= n; i++) {
|
|
for (int a = 1; a <= amt; a++) {
|
|
if (coins[i - 1] > a) {
|
|
// 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 这两种方案的较小值
|
|
dp[i][a] = Math.min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);
|
|
}
|
|
}
|
|
}
|
|
return dp[n][amt] != MAX ? dp[n][amt] : -1;
|
|
}
|
|
|
|
/* 零钱兑换：空间优化后的动态规划 */
|
|
static int coinChangeDPComp(int[] coins, int amt) {
|
|
int n = coins.length;
|
|
int MAX = amt + 1;
|
|
// 初始化 dp 表
|
|
int[] dp = new int[amt + 1];
|
|
Arrays.fill(dp, MAX);
|
|
dp[0] = 0;
|
|
// 状态转移
|
|
for (int i = 1; i <= n; i++) {
|
|
for (int a = 1; a <= amt; a++) {
|
|
if (coins[i - 1] > a) {
|
|
// 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 这两种方案的较小值
|
|
dp[a] = Math.min(dp[a], dp[a - coins[i - 1]] + 1);
|
|
}
|
|
}
|
|
}
|
|
return dp[amt] != MAX ? dp[amt] : -1;
|
|
}
|
|
|
|
public static void main(String[] args) {
|
|
int[] coins = { 1, 2, 5 };
|
|
int amt = 4;
|
|
|
|
// 动态规划
|
|
int res = coinChangeDP(coins, amt);
|
|
System.out.println("凑到目标金额所需的最少硬币数量为 " + res);
|
|
|
|
// 空间优化后的动态规划
|
|
res = coinChangeDPComp(coins, amt);
|
|
System.out.println("凑到目标金额所需的最少硬币数量为 " + res);
|
|
}
|
|
}
|