UVA254 Towers of HanoiDFS

Posted 2021-06-30 海岛Blog

In 1883, Edouard Lucas invented, or perhaps reinvented, one of the most popular puzzles of all times – the Tower of Hanoi, as he called it – which is still used today in many computer science textbooks to demonstrate how to write a recursive algorithm or program. First of all, we will make a list of the rules of the puzzle:
• There are three pegs: A, B and C.
• There are n disks. The number n is constant while working the puzzle.
• All disks are different in size.
• The disks are initially stacked on peg A so that they increase in size from the top to the bottom.
• The goal of the puzzle is to transfer the entire tower from the A peg to one of the others pegs.
• One disk at a time can be moved from the top of a stack either to an empty peg or to a peg with a larger disk than itself on the top of its stack.
    A good way to get a feeling for the puzzle is to write a program which will show a copy of the puzzle on the screen and let you simulate moving the disks around. The next step could be to write a program for solving the puzzle in a efficient way. You don’t have to do neither, but only know the actual situation after a given number of moves by using a determinate algorithm.
The Algorithm
    It is well known and rather easy to prove that the minimum number of moves needed to complete the puzzle with n disks is 2^{n − 1}. A simple algorithm which allows us to reach this optimum is as follows: for odd moves, take the smallest disk (number 1) from the peg where it lies to the next one in the circular sequence ABCABC . . . ; for even moves, make the only possible move not involving disk 1.
Input
The input file will consist of a series of lines. Each line will contain two integers n, m: n, lying within
the range [0, 100], will denote the number of disks and m, belonging to [0, 2^{n − 1}], will be the number
of the last move. The file will end at a line formed by two zeros.
Output
The output will consist again of a series of lines, one for each line of the input. Each of them will be formed by three integers indicating the number of disks in the pegs A, B and C respectively, when using the algorithm described above.
Sample Input
3 5
64 2
8 45
0 0
Sample Output
1 1 1
62 1 1
4 2 2

问题链接：UVA254 Towers of Hanoi
问题简述：河内塔问题，给定盘子数量和移动的步数，问盘子的状态。
问题分析：移动步数比较大，用Python语言来解决。
程序说明：（略）
参考链接：（略）
题记：（略）

AC的Python语言程序如下：

# UVA254 Towers of Hanoi

peg = []
n, m = 0, 0

def hanoi(k, u, v):
  if (k == 0): return
  t = u ^ v
  if m & 1 << (k - 1):
    peg[u] -= k - 1
    peg[t] += k - 1
    peg[u] -= 1
    peg[v] += 1
    hanoi(k - 1, t, v)
  else:
    hanoi(k - 1, u, t)

while True:
  n, m = map(int, input().split())
  if n + m == 0: break
  peg = [0, n, 0, 0]
  if n & 1: hanoi(n, 1, 2)
  else: hanoi(n, 1, 3)
  print(peg[1], peg[2], peg[3])