• 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 recursive solution

 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 in data structure program

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
If   N >1

  1. 1.Move n-1 disks from start A to B  TowersofHanoi(n-1,start, end , aux)
  2. Move last Disk from A to C
  3. 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:

  1. package towersofhanoi;
  2. import java.util.Scanner;
  4. public class TowersofHanoi {
  6. public void TOH(int n, String start, String aux, String end) {
  8.            if (n == 1) {
  9.                System.out.println(start + " -> " + end);
  10.            } else {
  11.                TOH(n - 1, start, end, aux);
  12.                System.out.println(start + " -> " + end);
  13.                TOH(n - 1, aux, start, end);
  14.            }
  15. }
  17. public static void main(String[] args) {
  19.            TowersofHanoi towersOfHanoi = new TowersofHanoi();
  21.            System.out.print("Enter number of discs: ");
  22.            Scanner scanner = new Scanner(System.in);
  23.            int discs = scanner.nextInt();
  24.            towersOfHanoi.TOH(discs, "A", "B", "C");
  25. }
  27. }


  1. Enter number of discs: 
  2. 3
  3. A -> C
  4. A -> B
  5. C -> B
  6. A -> C
  7. B -> A
  8. B -> C
  9. A -> C

Instance Of Java

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