Tower of Hanoi, which is a classic problem in computer science and mathematics. The Tower of Hanoi involves three rods and a number of disks of different sizes. The goal is to move all the disks from one rod to another, but there are a few rules we need to follow Tower of Hanoi The Tower of Hanoi is a classic puzzle that involves three rods and a set of disks of different sizes. The puzzle is designed to test problem-solving skills and often demonstrates the concept of recursion in algorithms. The rules are simple but require logical thinking to solve: 1. Rules of the Puzzle: ○ Only one disk can be moved at a time. ○ Only the top disk of any rod can be moved. ○ A larger disk cannot be placed on top of a smaller disk. 2. Objective: The goal is to move all the disks from the starting rod (Rod A) to the destination rod (Rod C), using the third rod (Rod B) as auxiliary space. The challenge is to move all the disks while respecting the above rules. 3. Example with 3 Disks: Consider a scenario where we have 3 disks (labeled 1, 2, and 3, with 1 being the smallest and 3 being the largest). Initially, all disks are on Rod A, arranged in increasing size from bottom to top. The goal is to move all the disks to Rod C. Here’s how you would solve the problem step by step: ○ Step 1: Move disk 1 to Rod C. ○ Step 2: Move disk 2 to Rod B. ○ Step 3: Move disk 1 from Rod C to Rod B (on top of disk 2). ○ Step 4: Move disk 3 to Rod C. ○ Step 5: Move disk 1 from Rod B to Rod A. ○ Step 6: Move disk 2 from Rod B to Rod C. ○ Step 7: Move disk 1 from Rod A to Rod C. 4. After these steps, all disks will be successfully moved to Rod C, and they are now in the correct order (from largest to smallest). 5. Key Concept – Recursion: The Tower of Hanoi problem is often solved using recursion, where the problem is broken down into smaller sub-problems. For example, if you can solve the problem with 2 disks, you can build up a solution for 3 disks by using the solution for 2 disks as part of it. This recursive approach allows us to break down a complex problem into smaller, more manageable parts. 6. Number of Moves: The minimum number of moves required to solve the Tower of Hanoi puzzle for n disks is given by the formula: M(n)=2n−1M(n) = 2^n - 1 This means that for 3 disks, the minimum number of moves is: M(3)=23−1=7M(3) = 2^3 - 1 = 7