mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-25 23:46:29 +08:00
37 lines
974 B
Python
37 lines
974 B
Python
"""
|
|
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:
|
|
break
|
|
# 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 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")
|