# Tower of Hanoi using recursion (C++ program)

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Implementation of Tower of HANOI in using C++ program, Learn: What is Tower of Hanoi? How to implement using recursion in C++?
Submitted by Abhishek Jain, on July 23, 2017

The Tower of Hanoi is a mathematical puzzle invented by the French mathematician Edouard Lucas in 1883.

There are three pegs, source(A), Auxiliary (B) and Destination(C). Peg A contains a set of disks stacked to resemble a tower, with the largest disk at the bottom and the smallest disk at the top. figure 1 Illustrate the initial configuration of the pegs for 3 disks. The objective is to transfer the entire tower of disks in peg A to peg C maintaining the same order of the disks.

Obeying the following rules:

1. Only one disk can be transfer at a time.
2. Each move consists of taking the upper disk from one of the peg and placing it on the top of another peg i.e. a disk can only be moved if it is the uppermost disk of the peg.
3. Never a larger disk is placed on a smaller disk during the transfer.

(figure 1)

The solution to the puzzle calls for an application of recursive functions and recurrence relations.

A skeletal recursive procedure (Outline) for the solution of the problem for N number of disks is as follows:

1. Move the top N-1 disks from peg A to peg B (using C as an auxiliarypeg)
2. Move the bottom disk from peg A to peg C
3. Move N-1 disks from Peg B to Peg C (using Peg A as an auxiliary peg)

The pictorial representation of the skeletal recursive procedure for N=4 disks is shown in Figure 2.

(figure 2)

### Algorithm

```TOH( n,  Sour, Aux , Des)
If(n=1)
Write ("Move Disk “, n ," from ", Sour ," to ",Des)
Else
TOH(n-1,Sour,Des,Aux);
Write ("Move Disk “, n ," from ", Sour ," to ",Des)
TOH(n-1,Aux,Sour,Des);
END
```

Let’s take an example to better understand the algorithm (For n=3).

(figure 3)

## Implementation of Tower of HANOI in using C++ program

```#include<iostream>
using namespace std;

//tower of HANOI function implementation
void TOH(int n,char Sour, char Aux,char Des)
{
if(n==1)
{
cout<<"Move Disk "<<n<<" from "<<Sour<<" to "<<Des<<endl;
return;
}

TOH(n-1,Sour,Des,Aux);
cout<<"Move Disk "<<n<<" from "<<Sour<<" to "<<Des<<endl;
TOH(n-1,Aux,Sour,Des);
}

//main program
int main()
{
int n;

cout<<"Enter no. of disks:";
cin>>n;
//calling the TOH
TOH(n,'A','B','C');

return 0;
}
```

Output

```Enter no. of disks:3
Move Disk 1 from A to C
Move Disk 2 from A to B
Move Disk 1 from C to B
Move Disk 3 from A to C
Move Disk 1 from B to A
Move Disk 2 from B to C
Move Disk 1 from A to C
```

Image Reference:

1. http://www.peterloos.de/index.php/m-wpf/m-wpf-userdefined-controls/59-a-wpf-towersofhanoi
2. http://algorithms.tutorialhorizon.com/towers-of-hanoi/
3. https://www.researchgate.net/publication/278658550_An_Evolutionary_Approach_to_Tower_of_Hanoi_Problem
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