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 :

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

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

C++

// C++ recursive function to  
// solve tower of hanoi puzzle  
#include <bits/stdc++.h> 
using namespace std; 
  
void towerOfHanoi(int n, char from_rod, 
                    char to_rod, char aux_rod)  
{  
    if (n == 1)  
    {  
        cout << "Move disk 1 from rod " << from_rod <<  
                            " to rod " << to_rod<<endl;  
        return;  
    }  
    towerOfHanoi(n - 1, from_rod, aux_rod, to_rod);  
    cout << "Move disk " << n << " from rod " << from_rod << 
                                " to rod " << to_rod << endl;  
    towerOfHanoi(n - 1, aux_rod, to_rod, from_rod);  
}  
  
// Driver code 
int main()  
{  
    int n = 4; // Number of disks  
    towerOfHanoi(n, 'A', 'C', 'B'); // A, B and C are names of rods  
    return 0;  
}  
  
// This is code is contributed by rathbhupendra 

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 

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 

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  
?> 

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 2^n-1 function calls are made.

eg: For 4 disks 2^4-1 = 8 function calls are made.

Additionally, we can display contents of all 3 rods at each step to improve visualization

The following code uses stack-like data structure using PHP array along with push() and pop() operations
to actually modify contents at each step

<?php 
  
// Tower of Hanoi (n-disk) algorithm in PHP with Display of Pole/rod  
// Contents the 3 poles representation 
$poles = array(array(), array(), array()); 
  
function TOH($n, $A="A", $B="B", $C="C"){ 
      
    if ($n > 0){ 
        TOH($n-1, $A, $C, $B); 
        echo "Move disk from rod $A to rod $C \n"; 
        move($A, $C); 
        dispPoles(); 
        TOH($n-1, $B, $A, $C); 
    } 
    else { 
        return; 
    } 
} 
  
function initPoles($n){ 
    global $poles; 
  
    for ($i=$n; $i>=1; --$i){ 
        $poles[0][] = $i; 
    } 
} 
  
  
function move($source, $destination){ 
    global $poles; 
      
    // get source and destination pointers 
    if ($source=="A") $ptr1=0; 
    elseif ($source=="B") $ptr1 = 1; 
    else $ptr1 = 2; 
      
    if ($destination=="A") $ptr2 = 0; 
    elseif ($destination=="B") $ptr2 = 1; 
    else $ptr2 = 2; 
      
    $top = array_pop($poles[$ptr1]); 
    array_push($poles[$ptr2], $top); 
} 
  
function dispPoles(){   
    global $poles; 
    echo "A: [".implode(", ", $poles[0])."] "; 
    echo "B: [".implode(", ", $poles[1])."] "; 
    echo "C: [".implode(", ", $poles[2])."] "; 
    echo "\n\n"; 
} 
  
$numdisks = 4; 
initPoles($numdisks); 
echo "Tower of Hanoi Solution for $numdisks disks: \n\n"; 
dispPoles(); 
TOH($numdisks); 
  
// This code is contributed by ShreyakChakraborty 
?> 

Output:

Tower of Hanoi Solution for 4 disks:

A: [4, 3, 2, 1] B: [] C: []

Move disk from rod A to rod B
A: [4, 3, 2] B: [1] C: []

Move disk from rod A to rod C
A: [4, 3] B: [1] C: [2]

Move disk from rod B to rod C
A: [4, 3] B: [] C: [2, 1]

Move disk from rod A to rod B
A: [4] B: [3] C: [2, 1]

Move disk from rod C to rod A
A: [4, 1] B: [3] C: [2]

Move disk from rod C to rod B
A: [4, 1] B: [3, 2] C: []

Move disk from rod A to rod B
A: [4] B: [3, 2, 1] C: []

Move disk from rod A to rod C
A: [] B: [3, 2, 1] C: [4]

Move disk from rod B to rod C
A: [] B: [3, 2] C: [4, 1]

Move disk from rod B to rod A
A: [2] B: [3] C: [4, 1]

Move disk from rod C to rod A
A: [2, 1] B: [3] C: [4]

Move disk from rod B to rod C
A: [2, 1] B: [] C: [4, 3]

Move disk from rod A to rod B
A: [2] B: [1] C: [4, 3]

Move disk from rod A to rod C
A: [] B: [1] C: [4, 3, 2]

Move disk from rod B to rod C
A: [] B: [] C: [4, 3, 2, 1]

Related Articles

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

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My Personal Notes

Nov	DEC	Jan
	03
2019	2020	2021

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

C++

C

Java

Python

C#

PHP

Additionally, we can display contents of all 3 rods at each step to improve visualization

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