Question

Java Program for Tower of Hanoi along with required theory

Answer 1

Tower of Hanoi

The Tower of Hanoi is also called the Tower of Brahma or Lucas' Tower and sometimes pluralized as Towers . Tower of Hanoi 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.

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

1. Only one disk can be moved at a time.
2. 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.
3. 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.

Steps : 

1. Move n-1 disks from start to auxillary
2. Move nth disk from start to end 
3. Move n-1 disks from auxillary  to end .

Algorithm : 

TowerOfHanoi(n , start, end, aux) TowerOfHanoi(n-1, start, aux, end)  TowerOfHanoi(n-1, aux, end, start)

Example : 

Program Code

class Tower{    public static void TowerOfHanoi(int n, char start, char end, char aux)    {       if(n==1)       {       System.out.println("Move disk 1 from rod "+start+" to rod "+end);       return;       }       TowerOfHanoi(n-1, start, aux, end) ;       System.out.println("Move disk "+n+" from rod "+start+" to rod "+end );       TowerOfHanoi(n-1, aux, end, start);    }    public static void main(String args[])    {      int n = 4;      TowerOfHanoi(n,'A', 'C', 'B');    } }

Output

Move disk 1 from rod A to rod B Move disk 2 from rod A to rod C Move disk 1 from rod B to rod C Move disk 3 from rod A to rod B Move disk 1 from rod C to rod A Move disk 2 from rod C to rod B Move disk 1 from rod A to rod B Move disk 4 from rod A to rod C Move disk 1 from rod B to rod C Move disk 2 from rod B to rod A Move disk 1 from rod C to rod A Move disk 3 from rod B to rod C Move disk 1 from rod A to rod B Move disk 2 from rod A to rod C Move disk 1 from rod B to rod C

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