- Towers of Hanoi is a famous game.
- In this game there are three poles and N number of disks placed one over another in increasing in size from top to bottom.
- Objective of this game is to move disks from first pole to last pole.
- And the condition is we can not place bigger disk on top of smaller disk.
- Initially all disks placed in first pole smaller disk will be on top and bigger disk will be on bottom.
- We need to move all the disks from from first pole to last pole.

**Rules of tower of Hanoi:**

- We can move only one disk at a time.
- At any poi of time larger disk can not be placed on smaller disk.

- In order to solve this problem we have given a second pole so we can use second pole and move disks from first pole to third pole.
- We can solve this using rec recursive procedure.

**Tower of Hanoi with**

**Single disk: N=1**

- Three poles are A , B ,C
- And a disk is present at A we need to move from A to C
- As it its single disk we can directly move disk A - > C

**Tower of Hanoi with**Two disks : N=2- Three poles are A , B ,C
- And two disks are placed in pole A, Disk 1 and Disk2 top to bottom.( assume Disk 2 is smaller and Disk 1 bigger)
- Move Disk2 from A to B
- Move Disk1 From A to C.
- Move Disk2 from B to C.

**Tower of Hanoi with**Three disks : N=3- Three poles are A , B ,C
- And three disks are placed in pole A, Disk 1 top to bot, Disk2 and Disk 2 top bottom to .( assume Disk 3 is smaller and Disk 1 bigger)
- In this firs we need to move two disk from A to B which we already done in above procedure
- So we need to repeat that here.
- Move Disk1 from A to C.
- Now Moving two disks from B to C we have already seen in above procedure so its recursive.

**Tower of Hanoi Recursive Algorithm:**

N = number of disks

If N == 1

- Move Single disk from A to C

- 1.Move n-1 disks from start A to B TowersofHanoi(n-1,start, end , aux)
- Move last Disk from A to C
- Move n-1 disks from B to C. TowersofHanoi(n-1,start, aux, end )

- Step 1 and 3 are recursive procedures.
- Lets see hoe to write java recursive program for this towers of Hanoi problem
- Here B as auxiliary pole.

**Program #1: Java Example program on towers of Hanoi:**

- package towersofhanoi;
- import java.util.Scanner;
- public class TowersofHanoi {
- public void TOH(int n, String start, String aux, String end) {
- if (n == 1) {
- System.out.println(start + " -> " + end);
- } else {
- TOH(n - 1, start, end, aux);
- System.out.println(start + " -> " + end);
- TOH(n - 1, aux, start, end);
- }
- }
- public static void main(String[] args) {
- TowersofHanoi towersOfHanoi = new TowersofHanoi();
- System.out.print("Enter number of discs: ");
- Scanner scanner = new Scanner(System.in);
- int discs = scanner.nextInt();
- towersOfHanoi.TOH(discs, "A", "B", "C");
- }
- }

**Output:**

- Enter number of discs:
- 3
- A -> C
- A -> B
- C -> B
- A -> C
- B -> A
- B -> C
- A -> C

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