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38 lines
974 B
Python
38 lines
974 B
Python
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"""
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File: climbing_stairs_backtrack.py
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Created Time: 2023-06-30
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Author: Krahets (krahets@163.com)
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"""
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def backtrack(choices: list[int], state: int, n: int, res: list[int]) -> int:
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"""回溯"""
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# 当爬到第 n 阶时，方案数量加 1
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if state == n:
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res[0] += 1
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# 遍历所有选择
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for choice in choices:
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# 剪枝：不允许越过第 n 阶
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if state + choice > n:
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break
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# 尝试：做出选择，更新状态
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backtrack(choices, state + choice, n, res)
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# 回退
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def climbing_stairs_backtrack(n: int) -> int:
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"""爬楼梯：回溯"""
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choices = [1, 2] # 可选择向上爬 1 或 2 阶
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state = 0 # 从第 0 阶开始爬
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res = [0] # 使用 res[0] 记录方案数量
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backtrack(choices, state, n, res)
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return res[0]
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"""Driver Code"""
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if __name__ == "__main__":
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n = 9
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res = climbing_stairs_backtrack(n)
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print(f"爬 {n} 阶楼梯共有 {res} 种方案")
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