Hanoi Hanoi Tower

An ancient Hindu legend: in the center of the world, in the heart of Sheng Miao, a yellow copper plate was inserted with three stone needles. In the creation of the world, The Hindu god Brahma, on one of the needles, dressed from the bottom to the top 64 pieces of gold, which is called the Hanoi (Hanoi Tower). No matter the day or night, there is always a monk in accordance with the following rules to move these gold pieces: one at a time, no matter where the needle, the small pieces must be on top of the large.

The monks predicted that the end of the world would come when all the gold pieces were moved from the golden sheet of Brahma to another, and that the Vatican, the temples and the sentient beings would perish ...

The story does not say much, Hanoi is a typical application of recursive thinking, on the code:

1#include <stdio.h>2 3 //move n pieces of gold, with Y, from X to Z4 voidMoveintNCharXCharYCharz)5 {6     if(1==N)7printf"%c\n,%c", x,z);8     Else9     {TenMove (n1, X, z, y);//n-1 a gold sheet from X, with Z, move to y Oneprintf"%c\n,%c", x,z);//move the nth gold sheet from X to Z AMove (n1, y, x, z);//move n-1 a gold sheet from Y, x, to Z -     } - } the  - intMain () - { -     intN; +printf"Please enter the number of layers for Hanoi:"); -scanf"%d",&n); +Move (N,'X','Y','Z'); A  at     return 0; -}

Finally, consider the relationship between the number of steps and the number of gold slices moved:

Each additional piece of gold, it moves the number of steps is equal to the original step twice times plus 1. The recursive formula is: f (n+1) = 2*f (n) + 1, it is not difficult to get f (n) = 2^n-1.

For example, 3 pieces of gold steps for 7, then 4 pieces of gold steps for 2*7+1=15 step, 5 pieces of gold steps for 2*15+1=31 step.

At this point, you can calculate the number of pieces of gold is 64 o'clock, moving the number of steps: 18446744073709551615 steps. Suppose 1 seconds to move, the time required is: 1.,844,674,407,370,96e,+19 seconds, about 584.5 billion years, to the time the universe is not ...

Hanoi Hanoi Tower