Tower_of_Hanoi

Introduction:

The Tower of Hanoi (also called the Tower of Brahma or Lucas' Tower and sometimes pluralized as Towers) is a mathematical game or puzzle. It consists of three rods and a number of disks of different sizes, which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape.

Rules:

The objective of the puzzle is to move the entire stack to another rod, obeying the following simple 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 rod.

- No larger disk may be placed on top of a smaller disk.

With 3 disks, the puzzle can be solved in 7 moves. The minimal number of moves required to solve a Tower of Hanoi puzzle is 2n − 1, where n is the number of disks.

Example of TOH problem for 3 disks:

When we run a following code of TOH problem, we get following result:

Steps

Step-1

Move disk 1 from A to C

Step-2

Move disk 2 from A to B

Step-3

Move disk 1 from C to B

Step-4

Move disk 3 from A to C

Step-5

Move disk 1 from B to A

Step-6

Move disk 2 from B to C

Step-7

Move disk 1 from A to C