"""
File: climbing_stairs_backtrack.py
Created Time: 2023-06-30
Author: krahets (krahets@163.com)
"""


def backtrack(choices: list[int], state: int, n: int, res: list[int]) -> int:
    """回溯"""
    # 当爬到第 n 阶时，方案数量加 1
    if state == n:
        res[0] += 1
    # 遍历所有选择
    for choice in 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


def climbing_stairs_backtrack(n: int) -> int:
    """爬楼梯：回溯"""
    choices = [1, 2]  # 可选择向上爬 1 阶或 2 阶
    state = 0  # 从第 0 阶开始爬
    res = [0]  # 使用 res[0] 记录方案数量
    backtrack(choices, state, n, res)
    return res[0]


"""Driver Code"""
if __name__ == "__main__":
    n = 9

    res = climbing_stairs_backtrack(n)
    print(f"爬 {n} 阶楼梯共有 {res} 种方案")