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35 lines
830 B
Python
35 lines
830 B
Python
"""
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File: climbing_stairs_dfs_mem.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 dfs(i: int, mem: list[int]) -> int:
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"""记忆化搜索"""
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# 已知 dp[1] 和 dp[2] ，返回之
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if i == 1 or i == 2:
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return i
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# 若存在记录 dp[i] ，则直接返回之
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if mem[i] != -1:
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return mem[i]
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# dp[i] = dp[i-1] + dp[i-2]
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count = dfs(i - 1, mem) + dfs(i - 2, mem)
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# 记录 dp[i]
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mem[i] = count
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return count
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def climbing_stairs_dfs_mem(n: int) -> int:
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"""爬楼梯：记忆化搜索"""
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# mem[i] 记录爬到第 i 阶的方案总数，-1 代表无记录
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mem = [-1] * (n + 1)
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return dfs(n, mem)
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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_dfs_mem(n)
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print(f"爬 {n} 阶楼梯共有 {res} 种方案")
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