# Program for Tower of Hanoi

Tower of Hanoi is a mathematical puzzle where we have three rods and n disks. The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules:
1) Only one disk can be moved at a time.
2) 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.
3) No disk may be placed on top of a smaller disk.

Approach :

```Take an example for 2 disks :
Let rod 1 = 'A', rod 2 = 'B', rod 3 = 'C'.

Step 1 : Shift first disk from 'A' to 'B'.
Step 2 : Shift second disk from 'A' to 'C'.
Step 3 : Shift first disk from 'B' to 'C'.

The pattern here is :
Shift 'n-1' disks from 'A' to 'B'.
Shift last disk from 'A' to 'C'.
Shift 'n-1' disks from 'B' to 'C'.

Image illustration for 3 disks :

Image Source : http://mathforum.org/dr.math/faq/faq.disk3.gif
```

Examples:

```Input : 2
Output : Disk 1 moved from A to B
Disk 2 moved from A to C
Disk 1 moved from B to C

Input : 3
Output : Disk 1 moved from A to C
Disk 2 moved from A to B
Disk 1 moved from C to B
Disk 3 moved from A to C
Disk 1 moved from B to A
Disk 2 moved from B to C
Disk 1 moved from A to C
```

## C/C++

```#include <stdio.h>

// C recursive function to solve tower of hanoi puzzle
void towerOfHanoi(int n, char from_rod, char to_rod, char aux_rod)
{
if (n == 1)
{
printf("n Move disk 1 from rod %c to rod %c", from_rod, to_rod);
return;
}
towerOfHanoi(n-1, from_rod, aux_rod, to_rod);
printf("n Move disk %d from rod %c to rod %c", n, from_rod, to_rod);
towerOfHanoi(n-1, aux_rod, to_rod, from_rod);
}

int main()
{
int n = 4; // Number of disks
towerOfHanoi(n, 'A', 'C', 'B');  // A, B and C are names of rods
return 0;
}
```

## Java

```// Java recursive program to solve tower of hanoi puzzle

class GFG
{
// Java recursive function to solve tower of hanoi puzzle
static void towerOfHanoi(int n, char from_rod, char to_rod, char aux_rod)
{
if (n == 1)
{
System.out.println("Move disk 1 from rod " +  from_rod + " to rod " + to_rod);
return;
}
towerOfHanoi(n-1, from_rod, aux_rod, to_rod);
System.out.println("Move disk " + n + " from rod " +  from_rod + " to rod " + to_rod);
towerOfHanoi(n-1, aux_rod, to_rod, from_rod);
}

//  Driver method
public static void main(String args[])
{
int n = 4; // Number of disks
towerOfHanoi(n, 'A', 'C', 'B');  // A, B and C are names of rods
}
}
```

## Python

```# Recursive Python function to solve tower of hanoi

def TowerOfHanoi(n , from_rod, to_rod, aux_rod):
if n == 1:
print "Move disk 1 from rod",from_rod,"to rod",to_rod
return
TowerOfHanoi(n-1, from_rod, aux_rod, to_rod)
print "Move disk",n,"from rod",from_rod,"to rod",to_rod
TowerOfHanoi(n-1, aux_rod, to_rod, from_rod)

# Driver code
n = 4
TowerOfHanoi(n, 'A', 'C', 'B')
# A, C, B are the name of rods

# Contributed By Harshit Agrawal
```

Output:

``` Move disk 1 from rod A to rod B
Move disk 2 from rod A to rod C
Move disk 1 from rod B to rod C
Move disk 3 from rod A to rod B
Move disk 1 from rod C to rod A
Move disk 2 from rod C to rod B
Move disk 1 from rod A to rod B
Move disk 4 from rod A to rod C
Move disk 1 from rod B to rod C
Move disk 2 from rod B to rod A
Move disk 1 from rod C to rod A
Move disk 3 from rod B to rod C
Move disk 1 from rod A to rod B
Move disk 2 from rod A to rod C
Move disk 1 from rod B to rod C
```

For n disks, total 2n – 1 moves are required.
Related Articles

References:
http://en.wikipedia.org/wiki/Tower_of_Hanoi

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