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hello-algo/codes/python/chapter_divide_and_conquer/hanota.py

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1.3 KiB

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