The Tower of Hanoi is a classic puzzle that involves three pegs and a set of different-sized discs. The goal is to move all the discs from one peg to another, while following three simple rules:

You can only move one disc at a time. A disc can only be placed on top of a larger disc or an empty peg. Only the top disc of a peg can be moved. Now, let’s relate this puzzle to the stack data structure.

Imagine each peg represents a stack, and the discs represent elements that can be pushed onto or popped from the stack. The largest disc corresponds to the bottom of the stack, and the smallest disc corresponds to the top of the stack. The rules of the Tower of Hanoi puzzle closely resemble the behavior of a stack:

Moving one disc at a time:

In a stack, you can only manipulate the top element. Similarly, in the Tower of Hanoi, you can only move the top disc from one peg to another.

Placing smaller discs on larger ones:

Just like in a stack, where you can only push elements on top of the stack, you can only place a smaller disc on top of a larger disc in the Tower of Hanoi.

Only the top disc can be moved:

Just as you can only interact with the top element of a stack, you can only move the top disc of a peg in the Tower of Hanoi.

When solving the Tower of Hanoi puzzle, you use the properties of the stack data structure to strategize your moves. You often need to temporarily store discs on other pegs, simulating the process of pushing and popping elements on and off the stack. As you work through the puzzle, you’ll see how the behavior of stacks is central to understanding and solving the Tower of Hanoi challenge.

In essence, the Tower of Hanoi puzzle provides a real-world context for grasping the concepts of stacks and their operations in programming. It’s a great way to solidify your understanding of how a stack works and how elements are managed within it.