Concept of Tower of Hanoi
Tower of Hanoi: The Tower of Hanoi is a mathematical puzzle that consists of three rods and a number of disks of different sizes. The objective is to move the entire stack of disks from one rod to another, following these 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 an empty rod.
- No larger disk may be placed on top of a smaller disk.
How does it work?
- Start with all disks stacked in ascending order of size on the source rod.
- Move the smallest disk to the target rod.
- Use the auxiliary rod to temporarily hold disks as needed.
- Repeat the process recursively for the remaining disks.
Key Observations:
- The minimum number of moves required to solve the puzzle is 2n - 1, where n is the number of disks.
- The problem can be solved recursively by breaking it into smaller subproblems.
Applications:
- Understanding recursion and algorithm design.
- Problem-solving in computer science and mathematics.
- Teaching logical thinking and planning.
Time Complexity:
- The time complexity of the Tower of Hanoi problem is O(2n), where n is the number of disks.