What Is Tower of Hanoi Problem in Data Structure?

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Larry Thompson

The Tower of Hanoi problem is a classic puzzle that is often used to introduce the concept of recursion in computer programming. It involves three pegs and a number of disks of different sizes, which can slide onto any peg. The objective is to move the entire stack of disks from one peg to another, following a few simple rules.

Rules of the Tower of Hanoi Problem

Before we dive into the implementation details, let’s go over the rules:

  • Only one disk can be moved at a time.
  • Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty peg.
  • No disk may be placed on top of a smaller disk.

These rules make the problem interesting and challenging to solve. Now let’s look at how we can implement a solution using recursion.

Solving Tower of Hanoi Using Recursion

To solve the Tower of Hanoi problem, we need to define a recursive function that takes in three parameters:

  • n: The number of disks to be moved.
  • source: The peg from which we want to move the disks.
  • destination: The peg where we want to move the disks.

The base case for our recursive function occurs when there is only one disk left to be moved. In this case, we simply move that disk from the source peg to the destination peg:


if n == 1:
    print("Move disk from", source, "to", destination)

For the recursive case, we need to break down the problem into smaller subproblems. We can do this by following these steps:

  1. Move n-1 disks from the source peg to an auxiliary peg (using the destination peg as a temporary peg).
  2. Move the remaining disk (the largest one) from the source peg to the destination peg.
  3. Move the n-1 disks from the auxiliary peg to the destination peg (using the source peg as a temporary peg).

The recursive function for solving the Tower of Hanoi problem can be implemented as follows:


def tower_of_hanoi(n, source, destination, auxiliary):
    if n == 1:
        print("Move disk from", source, "to", destination)
    else:
        tower_of_hanoi(n-1, source, auxiliary, destination)
        print("Move disk from", source, "to", destination)
        tower_of_hanoi(n-1, auxiliary, destination, source)

# Example usage
tower_of_hanoi(3, 'A', 'C', 'B')

The above code will output:


Move disk from A to C
Move disk from A to B
Move disk from C to B
Move disk from A to C
Move disk from B to A
Move disk from B to C
Move disk from A to C

Conclusion

In this tutorial, we explored the Tower of Hanoi problem and learned how it can be solved using recursion. The rules of this puzzle make it an interesting challenge for programmers and serve as a great introduction to recursive thinking.

By breaking down the problem into smaller subproblems, we can solve it effectively. Remember to consider the base case and follow the steps of the recursive solution.

Now that you understand the basics of the Tower of Hanoi problem, try implementing it yourself and see how well you can solve this classic puzzle!

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