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 :
faq.disk3

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

PHP

<?php
//PHP code to solve Tower of Hanoi problem.

// Recursive Function to solve Tower of Hanoi
function towerOfHanoi($n, $from_rod, $to_rod, $aux_rod) {
    
    if ($n === 1) {
    echo ("Move disk 1 from rod $from_rod to rod $to_rod \n");
    return;
    } 
    
    towerOfHanoi($n-1, $from_rod, $aux_rod, $to_rod);
    echo ("Move disk $n from rod $from_rod to rod $to_rod \n");
    towerOfHanoi($n-1, $aux_rod, $to_rod, $from_rod);

}

// Driver code

// number of disks
$n = 4;

// A, B and C are names of rods
towerOfHanoi($n, 'A', 'C', 'B');

// This code is contributed by akash7981 
?>

C#


// C# recursive program to solve 
// tower of hanoi puzzle
using System;

class geek
{

    // C# 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)
        {
            Console.WriteLine("Move disk 1 from rod " + from_rod 
                                           + " to rod " + to_rod);
            return;
        }
        towerOfHanoi(n-1, from_rod, aux_rod, to_rod);
        Console.WriteLine("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()
    {
        // Number of disks
        int n = 4; 
        
        // A, B and C are names of rods
        towerOfHanoi(n, 'A', 'C', 'B'); 
    }
}

// This code is contributed by Sam007

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.

eg: For 4 disks 24 – 1 = 15 moves are required.

For n disks, total 2n+1 – 1 function calls are made.

eg: For 4 disks 24+1 – 1 = 31 function calls are made.
Related Articles

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

This article is contributed by Rohit Thapliyal. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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Improved By : vaibhav29498, Rustam Ali




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