/**
 * File: climbing_stairs_constraint_dp.cpp
 * Created Time: 2023-07-01
 * Author: krahets (krahets@163.com)
 */

#include "../utils/common.hpp"

/* 带约束爬楼梯：动态规划 */
int climbingStairsConstraintDP(int n) {
    if (n == 1 || n == 2) {
        return 1;
    }
    // 初始化 dp 表，用于存储子问题的解
    vector<vector<int>> dp(n + 1, vector<int>(3, 0));
    // 初始状态：预设最小子问题的解
    dp[1][1] = 1;
    dp[1][2] = 0;
    dp[2][1] = 0;
    dp[2][2] = 1;
    // 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][1] = dp[i - 1][2];
        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];
    }
    return dp[n][1] + dp[n][2];
}

/* Driver Code */
int main() {
    int n = 9;

    int res = climbingStairsConstraintDP(n);
    cout << "爬 " << n << " 阶楼梯共有 " << res << " 种方案" << endl;

    return 0;
}