Class Lecture: Towers of Hanoi Algorithm Implementation

Overview

In this lecture, we focus on implementing the recursive algorithm for solving the Towers of Hanoi problem, using a concrete example to illustrate the steps involved.

Key Points

• Objective: Implement the recursive algorithm for Towers of Hanoi to transfer disks from a source peg to a destination peg using an intermediate peg.
• Example: Transfer 3 disks from peg A to peg B via peg C.

Algorithm Explanation

1. Base Case:

   • If n = 1, simply move the disk from the source peg to the destination peg.

2. Recursive Case:

   • If n > 1, break down the problem into smaller subproblems:
     • Move n-1 disks from the source peg to the intermediate peg.
     • Move the nth disk directly from the source peg to the destination peg.
     • Move the n-1 disks from the intermediate peg to the destination peg.

3. Understanding the Process:

   • Initial call: T(A, B, C, 3) aims to move disks from A to B via C.
   • Use recursive calls to manage the sequence of moves:
     • Transition sequences: T(A, C, B, 2), T(B, C, A, 1), T(C, A, B, 1), etc.

Move Sequence for 3 Disks

1. Move 1: A to B
2. Move 2: A to C
3. Move 3: B to C
4. Move 4: A to B
5. Move 5: C to A
6. Move 6: C to B
7. Move 7: A to B

• Total Moves: 7 moves are required to complete the task for 3 disks, verifying the algorithm's correctness.

Verification

• The correct execution of moves is visually verified by simulating the transfer of disks, ensuring they all end in the correct order on peg B.

Conclusion

• Successfully implemented and verified the recursive algorithm for solving Towers of Hanoi.
• Confirmed that the algorithm produces the correct move sequence.

Next Steps

• Explore more complex cases or larger n values in future presentations.

Thank you for attending this lecture. We will continue to expand on these concepts in future discussions.