mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-27 17:06:29 +08:00
e720aa2d24
* Sync recent changes to the revised Word. * Revised the preface chapter * Revised the introduction chapter * Revised the computation complexity chapter * Revised the chapter data structure * Revised the chapter array and linked list * Revised the chapter stack and queue * Revised the chapter hashing * Revised the chapter tree * Revised the chapter heap * Revised the chapter graph * Revised the chapter searching * Reivised the sorting chapter * Revised the divide and conquer chapter * Revised the chapter backtacking * Revised the DP chapter * Revised the greedy chapter * Revised the appendix chapter * Revised the preface chapter doubly * Revised the figures
71 lines
2.2 KiB
C#
71 lines
2.2 KiB
C#
/**
|
|
* File: coin_change.cs
|
|
* Created Time: 2023-07-12
|
|
* Author: hpstory (hpstory1024@163.com)
|
|
*/
|
|
|
|
namespace hello_algo.chapter_dynamic_programming;
|
|
|
|
public class coin_change {
|
|
/* 零钱兑换：动态规划 */
|
|
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 */
|
|
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];
|
|
Array.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;
|
|
}
|
|
|
|
[Test]
|
|
public void Test() {
|
|
int[] coins = [1, 2, 5];
|
|
int amt = 4;
|
|
|
|
// 动态规划
|
|
int res = CoinChangeDP(coins, amt);
|
|
Console.WriteLine("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);
|
|
Console.WriteLine("凑到目标金额所需的最少硬币数量为 " + res);
|
|
}
|
|
}
|