/**
 * File: climbing_stairs_constraint_dp.js
 * Created Time: 2023-08-23
 * Author: Gaofer Chou (gaofer-chou@qq.com)
 */

/* 带约束爬楼梯：动态规划 */
function climbingStairsConstraintDP(n) {
    if (n === 1 || n === 2) {
        return 1;
    }
    // 初始化 dp 表，用于存储子问题的解
    const dp = Array.from(new Array(n + 1), () => new Array(3));
    // 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 (let 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 */
const n = 9;
const res = climbingStairsConstraintDP(n);
console.log(`爬 ${n} 阶楼梯共有 ${res} 种方案`);