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38 lines
980 B
38 lines
980 B
8 months ago
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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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# 當爬到第 n 階時，方案數量加 1
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if state == n:
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res[0] += 1
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# 走訪所有選擇
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for choice in choices:
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# 剪枝：不允許越過第 n 階
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if state + choice > n:
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continue
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# 嘗試：做出選擇，更新狀態
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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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"""爬樓梯：回溯"""
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choices = [1, 2] # 可選擇向上爬 1 階或 2 階
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state = 0 # 從第 0 階開始爬
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res = [0] # 使用 res[0] 記錄方案數量
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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} 階樓梯共有 {res} 種方案")
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