Understanding The Tower Of Hanoi, With Examples

Are you an aspiring programmer looking to sharpen your skills? One of the best tools for new developers is the Tower of Hanoi, a classic algorithmic game. Can you use the right code to move a series of disks from one peg to another?

While you might not think much about this as a practice method, mastering the Tower of Hanoi is no easy task. So how do you get started?

In this article, we break down the basics of the game and how it works in standard programming languages. We even give you the syntax as a cheat code! So let’s get into it so you can solve the Tower of Hanoi.

What Is the Tower of Hanoi?

Since the late 1800s, the Tower of Hanoi has puzzled mathematicians with its elegant simplicity and algorithmic properties. Since then, beginner programmers use it to develop skills such as recursion, critical thinking, creativity, and problem-solving.

The puzzle at its core has only a few parameters. You start the game with three pegs and multiple, different-sized disks. In the Tower of Hanoi, you need to move each disk from its pegs until they’re stacked from largest to smallest. The puzzle has three simple rules:

1. You can only move one disk at a time.
2. You can only move the top disk from any stack.
3. You cannot place a larger disk on top of a smaller one.

The puzzle finds its benefit in that it requires developers to break up the whole of the problem into subproblems. This is highly useful for programmers when taking on large projects.

How Does It Work?

You’ll want to define a recursive function (“tower_of_hanoi”) to get started. This has four parameters:

• “N”: The number of disks in the puzzle.
• “Source”: The peg from where we’ll move a disk.
• “Destination”: The peg where we’ll move that disk to.
• “Auxiliary”: The peg that can be used as a temporary disk position.

After defining our function, our program uses recursion to call respective pegs, depending on their number. We use recursive functions until there are no more disks to move.

In the Tower of Hanoi, three subproblems exist:

• Moving disks from the source peg to the auxiliary peg
• Moving disks from the source peg to the destination peg
• Moving disks from the auxiliary peg to the destination peg

These subproblems work themselves out while following the three rules until ‘n’ = 0. Then, the recursion unwinds and the Tower of Hanoi comes to completion.

How Do You Write the Tower of Hanoi?

This classic puzzle has simple parameters but might prove challenging for novice developers. To get you started, we’ve provided the syntax to solve a Tower of Hanoi problem with six disks:

def tower_of_hanoi(n, source, destination, auxiliary):
    if n > 0:
        # Move n-1 disks from source to auxiliary peg
        tower_of_hanoi(n-1, source, auxiliary, destination)
        
        # Move the nth disk from source to destination peg
        print("Move disk", n, "from", source, "to", destination)
        
        # Move the n-1 disks from auxiliary to destination peg
        tower_of_hanoi(n-1, auxiliary, destination, source)

# Example usage
tower_of_hanoi(6, "A", "C", "B")

Final Thoughts

We hope this guide helps you understand the mechanics of the Tower of Hanoi. From basic problem-solving to advanced recursion, this classic game can help you develop the skills you need to master programming.