How to solve Tower of Hanoi using Recursion ?

What is Tower of Hanoi ?

A mathematical game or puzzle which 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 an eat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape.

The objective of the puzzle is to move the entire stack to another rod, obeying the following rules :

  1. Only one disk may be moved at a time.

  2. Each move consists of taking the upper disk from one of the rods and sliding it onto another rod, on top of the other disks that may already be present on that rod.

  3. No disk may be placed on top of a smaller disk.

Solution

public class HanoiTower {

  static int nDisks = 3;

  public static void main(String[] args) {

     hanoiTower(nDisks, 'A', 'B', 'C');

  }

  public static void hanoiTower(

            int topN, char src, char inter, char dest) {

    if (topN == 1) {

      System.out.println("Disk 1 from " + src + " to " + dest);

    } else {

      // src to inter

      hanoiTower(topN - 1, src, dest, inter);

      // move bottom

      System.out.println("Disk " + topN + " from " + src + " to " + dest);

      // inter to dest

      hanoiTower(topN - 1, inter, src, dest);

    }

  }

}

Output

Disc 1 from A to C

Disc 2 from A to B

Disc 1 from C to B

Disc 3 from A to C

Disc 1 from B to A

Disc 2 from B to C

Disc 1 from A to C