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"""
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File: climbing_stairs_constraint_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_constraint_dp(n: int) -> int:
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"""带约束爬楼梯：动态规划"""
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if n == 1 or n == 2:
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return 1
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# 初始化 dp 表，用于存储子问题的解
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dp = [[0] * 3 for _ in range(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][1], dp[1][2] = 1, 0
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dp[2][1], dp[2][2] = 0, 1
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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][1] = dp[i - 1][2]
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dp[i][2] = dp[i - 2][1] + dp[i - 2][2]
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return dp[n][1] + dp[n][2]
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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_constraint_dp(n)
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print(f"爬 {n} 阶楼梯共有 {res} 种方案")
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