/**
* 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");
    }
}