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"""
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File: climbing_stairs_dp.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 climbing_stairs_dp(n: int) -> int:
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"""爬楼梯：动态规划"""
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if n == 1 or n == 2:
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return n
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# 初始化 dp 表，用于存储子问题的解
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dp = [0] * (n + 1)
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# 初始状态：预设最小子问题的解
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dp[1], dp[2] = 1, 2
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# 状态转移：从较小子问题逐步求解较大子问题
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for i in range(3, n + 1):
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dp[i] = dp[i - 1] + dp[i - 2]
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return dp[n]
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def climbing_stairs_dp_comp(n: int) -> int:
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"""爬楼梯：状态压缩后的动态规划"""
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if n == 1 or n == 2:
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return n
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a, b = 1, 2
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for _ in range(3, n + 1):
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a, b = b, a + b
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return b
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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_dp(n)
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print(f"爬 {n} 阶楼梯共有 {res} 种方案")
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res = climbing_stairs_dp_comp(n)
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print(f"爬 {n} 阶楼梯共有 {res} 种方案")
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