hello-algo/codes/csharp/chapter_dynamic_programming/climbing_stairs_dp.cs
2023-08-27 00:50:18 +08:00

49 lines
1.3 KiB
C#

/**
* File: climbing_stairs_dp.cs
* Created Time: 2023-06-30
* Author: hpstory (hpstory1024@163.com)
*/
namespace hello_algo.chapter_dynamic_programming;
public class climbing_stairs_dp {
/* 爬楼梯:动态规划 */
public int climbingStairsDP(int n) {
if (n == 1 || n == 2)
return n;
// 初始化 dp 表,用于存储子问题的解
int[] dp = new int[n + 1];
// 初始状态:预设最小子问题的解
dp[1] = 1;
dp[2] = 2;
// 状态转移:从较小子问题逐步求解较大子问题
for (int i = 3; i <= n; i++) {
dp[i] = dp[i - 1] + dp[i - 2];
}
return dp[n];
}
/* 爬楼梯:空间优化后的动态规划 */
public int climbingStairsDPComp(int n) {
if (n == 1 || n == 2)
return n;
int a = 1, b = 2;
for (int i = 3; i <= n; i++) {
int tmp = b;
b = a + b;
a = tmp;
}
return b;
}
[Test]
public void Test() {
int n = 9;
int res = climbingStairsDP(n);
Console.WriteLine($"爬 {n} 阶楼梯共有 {res} 种方案");
res = climbingStairsDPComp(n);
Console.WriteLine($"爬 {n} 阶楼梯共有 {res} 种方案");
}
}