Monday, 24 October 2016
The Tower of Hanoi (also called the Tower of Brahma or Lucas' Tower,[1] and sometimes pluralized) is a mathematical game or puzzle. It consists of three rods, and a number of disks of different sizes which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conicalshape.
The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules:
- Only one disk can be moved at a time.
- Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack i.e. a disk can only be moved if it is the uppermost disk on a stack.
- No disk may be placed on top of a smaller disk.
With three disks, the puzzle can be solved in seven moves. The minimum number of moves required to solve a Tower of Hanoi puzzle is 2n - 1, where n is the number of disks.
Simpler statement of iterative solution
For an even number of disks:
- make the legal move between pegs A and B
- make the legal move between pegs A and C
- make the legal move between pegs B and C
- repeat until complete
For an odd number of disks:
- make the legal move between pegs A and C
- make the legal move between pegs A and B
- make the legal move between pegs C and B
- repeat until complete
In each case, a total of 2n-1 moves are made .
SEE ANimate hanoi:
the pole:
c++ code:
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| /* ************************************* | |
| Tower of Hanoi | |
| Author:Md.Mostafa kamal | |
| Author URI: https://mostafa.itnishi.com/ | |
| ***************************************/ | |
| #include<iostream> | |
| using namespace std; | |
| void hanoi(int m, char a, char b,char c){ | |
| if(m==1){ | |
| cout<<"Move the disk from "<<a<<" to"<<b<<"\n"; | |
| } | |
| else{ | |
| hanoi(m-1,a,c,b); | |
| cout<<"Move disk from"<<a<<"to"<<b<<"\n"; | |
| hanoi(m-1,c,b,a); | |
| } | |
| } | |
| int main(){ | |
| int n; | |
| cout<<"how many discs: "; | |
| cin>>n; | |
| hanoi(n,'A','B','C'); | |
| return 0; | |
| } |
A switch statement in action switch example
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