/**
 * File: climbing_stairs_backtrack.js
 * Created Time: 2023-07-26
 * Author: yuan0221 (yl1452491917@gmail.com)
 */

/* 回溯 */
function backtrack(choices, state, n, res) {
    // 当爬到第 n 阶时，方案数量加 1
    if (state === n) res.set(0, res.get(0) + 1);
    // 遍历所有选择
    for (const choice of choices) {
        // 剪枝：不允许越过第 n 阶
        if (state + choice > n) continue;
        // 尝试：做出选择，更新状态
        backtrack(choices, state + choice, n, res);
        // 回退
    }
}

/* 爬楼梯：回溯 */
function climbingStairsBacktrack(n) {
    const choices = [1, 2]; // 可选择向上爬 1 或 2 阶
    const state = 0; // 从第 0 阶开始爬
    const res = new Map();
    res.set(0, 0); // 使用 res[0] 记录方案数量
    backtrack(choices, state, n, res);
    return res.get(0);
}

/* Driver Code */
const n = 9;
const res = climbingStairsBacktrack(n);
console.log(`爬 ${n} 阶楼梯共有 ${res} 种方案`);