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54 lines
1.3 KiB
Python
54 lines
1.3 KiB
Python
"""
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File: hanota.py
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Created Time: 2023-07-16
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Author: krahets (krahets@163.com)
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"""
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def move(src: list[int], tar: list[int]):
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"""移动一个圆盘"""
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# 从 src 顶部拿出一个圆盘
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pan = src.pop()
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# 将圆盘放入 tar 顶部
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tar.append(pan)
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def dfs(i: int, src: list[int], buf: list[int], tar: list[int]):
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"""求解汉诺塔问题 f(i)"""
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# 若 src 只剩下一个圆盘，则直接将其移到 tar
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if i == 1:
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move(src, tar)
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return
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# 子问题 f(i-1) ：将 src 顶部 i-1 个圆盘借助 tar 移到 buf
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dfs(i - 1, src, tar, buf)
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# 子问题 f(1) ：将 src 剩余一个圆盘移到 tar
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move(src, tar)
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# 子问题 f(i-1) ：将 buf 顶部 i-1 个圆盘借助 src 移到 tar
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dfs(i - 1, buf, src, tar)
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def solve_hanota(A: list[int], B: list[int], C: list[int]):
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"""求解汉诺塔问题"""
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n = len(A)
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# 将 A 顶部 n 个圆盘借助 B 移到 C
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dfs(n, A, B, C)
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"""Driver Code"""
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if __name__ == "__main__":
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# 列表尾部是柱子顶部
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A = [5, 4, 3, 2, 1]
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B = []
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C = []
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print("初始状态下：")
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print(f"A = {A}")
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print(f"B = {B}")
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print(f"C = {C}")
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solve_hanota(A, B, C)
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print("圆盘移动完成后：")
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print(f"A = {A}")
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print(f"B = {B}")
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print(f"C = {C}")
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