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41 lines
1 KiB
Python
41 lines
1 KiB
Python
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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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"""Climbing stairs: Dynamic programming"""
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if n == 1 or n == 2:
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return n
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# Initialize dp table, used to store subproblem solutions
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dp = [0] * (n + 1)
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# Initial state: preset the smallest subproblem solution
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dp[1], dp[2] = 1, 2
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# State transition: gradually solve larger subproblems from smaller ones
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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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"""Climbing stairs: Space-optimized dynamic programming"""
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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"Climb {n} steps, there are {res} solutions in total")
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res = climbing_stairs_dp_comp(n)
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print(f"Climb {n} steps, there are {res} solutions in total")
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