tower of hanoi

The Tower of Hanoi is a classic mathematical puzzle that involves moving a stack of disks from one peg to another, with the constraint that a larger disk cannot be placed on top of a smaller disk. The puzzle consists of three pegs, labeled A, B, and C, and a number of disks of different sizes.

Here is a step-by-step explanation of the Tower of Hanoi algorithm:

1. Start with the initial configuration of disks on the first peg (A) and the other two pegs (B and C) empty.

2. Determine the number of disks to be moved. Let's assume this number is 'n'.

3. Move 'n-1' disks from the initial peg (A) to the auxiliary peg (B), using the destination peg (C) as a temporary peg. This is done recursively.

4. Move the largest disk from the initial peg (A) to the destination peg (C).

5. Move the 'n-1' disks from the auxiliary peg (B) to the destination peg (C), using the initial peg (A) as a temporary peg. This is also done recursively.

6. The Tower of Hanoi puzzle is solved when all the disks have been moved to the destination peg (C).

The algorithm follows the principle of recursion, breaking down the problem into smaller subproblems until a base case is reached. In this case, the base case is when there is only one disk to be moved, which can be done directly.

By following these steps, the Tower of Hanoi puzzle can be solved. It is worth noting that the number of moves required to solve the puzzle is 2^n - 1, where 'n' is the number of disks. This puzzle is often used to illustrate recursion and problem-solving strategies in computer science.