The Tower of Hanoi: Solving the Puzzle with Elegance in C

Explore the captivating puzzle of the Tower of Hanoi and witness its elegant solution through a C program.

Dive into the implementation of the recursive algorithm, unravel the logic behind the moves, and witness the step-by-step transformation of the tower.

Discover the power of C programming in efficiently solving complex problems like the Tower of Hanoi.

Table of Contents

Introduction:

The Tower of Hanoi is a classic mathematical puzzle that challenges our problem-solving skills and showcases the elegance of recursive algorithms.

In this article, we explore the Tower of Hanoi problem and present a C program that solves it.

Witness the mesmerizing transformation of the tower, understand the logic behind each move, and delve into the intricacies of the recursive solution.

Prepare to be captivated by the beauty of the Tower of Hanoi in C.

#include <stdio.h>

void towerOfHanoi(int n, char source, char auxiliary, char destination) {
    if (n == 1) {
        printf("Move disk 1 from %c to %c\n", source, destination);
        return;
    }
    
    towerOfHanoi(n - 1, source, destination, auxiliary);
    printf("Move disk %d from %c to %c\n", n, source, destination);
    towerOfHanoi(n - 1, auxiliary, source, destination);
}

int main() {
    int numDisks = 3; // Change this value to the desired number of disks
    
    printf("Tower of Hanoi solution for %d disks:\n", numDisks);
    towerOfHanoi(numDisks, 'A', 'B', 'C');
    
    return 0;
}


:

Output

The provided code is an implementation of the Tower of Hanoi problem in C. Let’s go through the code and explain how it works:

The towerOfHanoi function:
- This function takes four parameters: n (the number of disks), source (the peg from which the disks are moved), auxiliary (the auxiliary peg), and destination (the peg to which the disks are moved).
- The function first checks if there is only one disk (n == 1). In this case, it directly prints the move from the source peg to the destination peg and returns.
- If there is more than one disk, it recursively calls itself with n - 1 disks, moving them from the source peg to the auxiliary peg.
- It then prints the move of the remaining disk (the largest one) from the source peg to the destination peg.
- Finally, it recursively calls itself again to move the n - 1 disks from the auxiliary peg to the destination peg.
The main function:
- This function initializes the number of disks (numDisks) to 3. You can modify this value to change the number of disks for the Tower of Hanoi problem.
- It then prints a message indicating the number of disks in the Tower of Hanoi problem.
- It calls the towerOfHanoi function, passing the number of disks, and the names of the three pegs: ‘A’ as the source, ‘B’ as the auxiliary, and ‘C’ as the destination.
- Finally, it returns 0 to indicate successful program execution.

When you run this program, it will display the step-by-step moves required to solve the Tower of Hanoi problem for the specified number of disks.

The program follows the recursive algorithm described in the previous explanation, moving the disks from the source peg to the destination peg while adhering to the rules of the puzzle.

Output:

Tower of Hanoi solution for 3 disks:
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

Understanding the Tower of Hanoi Puzzle:

The Tower of Hanoi puzzle consists of three pegs and a number of disks of different sizes.

The objective is to transfer the entire stack of disks from one peg to another while following specific rules:

only one disk can be moved at a time, larger disks cannot be placed on top of smaller ones, and the stack must be recreated on a different peg.

Implementing the Tower of Hanoi Program in C:

The Tower of Hanoi problem can be solved using a recursive approach.

In C programming, we can create a function that takes the number of disks and the names of the source, auxiliary, and destination pegs as parameters. This function will then recursively move the disks, following the rules of the puzzle.

Solving the Puzzle: The Recursive Algorithm:

The recursive algorithm for the Tower of Hanoi problem involves three steps:

Move n-1 disks from the source peg to the auxiliary peg.
Move the remaining largest disk from the source peg to the destination peg.
Move the n-1 disks from the auxiliary peg to the destination peg.

Exploring the Logic behind the Tower’s Transformation:

The key to solving the Tower of Hanoi lies in understanding the logic behind the disk movements.

Each recursive call reduces the problem to a smaller subproblem, until we reach the base case of a single disk.

The moves are strategically orchestrated to ensure the correct placement of disks, adhering to the puzzle’s rules.

Efficiency and Complexity of the Tower of Hanoi Algorithm:

The Tower of Hanoi algorithm has a time complexity of O(2^n), making it exponential. This complexity arises due to the recursive nature of the algorithm, where each disk requires two recursive calls. However, the algorithm’s efficiency can be improved by optimizing the implementation and reducing redundant calculations.