Please follow the directions/specs exactly and include detailed comments so that I may understand.

This program creates three classes: Tower, Disk and TowerOfHanoi. You simulate a Tower with an array and the Disks have a numeric size. The Tower is an ArrayList of Disks that is, Tower inherits from ArrayList. You will be playing the game with different disk numbers ranging from 3 to 32 and recording the number of moves for each game.

When playing the game with 5 disks, please display the towers to see the movement between them. Do this only when playing with 5 disks.

The Disk objects are very simple. They hold an integer stating its size. They have a 1-parameter constructor, Disk(int) that initializes the size and a toString() method for displaying the Disk. Disk is an immutable class.

For instance: If the game has 6 disks, then there will be 6 Disk objects and their sizes will be 1, 2, 3, 4, 5, and 6.

The Disk objects are added to the three Tower objects, which are implemented as an ArrayList of Disks. The Tower class must inherit (extends) from ArrayList. It has two instance variables: int numDisks and char name. The Tower class has four methods: 2-parameter constructor: Tower (char, int), init(), move (Tower), and toString().

The Tower only adds Disks to the end and takes them off the end. So, to initialize the beginning Tower, you need to add them in order from largest to smallest. The Disk sizes are numbered 1, 2, 3, ., numDisks.

for (int size = numDisks; size >= 1; size--)

{

Disk disk = new Disk (size);

add (disk);

}

Table 1: Disk class

Data/Method Disk	Parameters	Description	Called From
int size
1-param constructor: Disk ()	int diskSize	Initializes the disk size	main
String toString()		Return the Disk size as a String	Tower toString()

Table 2: Tower class: Inherits from ArrayList

Data/Method Tower	Parameters	Description	Called From
char name int numDisks
2-param constructor: Tower ()	char tower, int numDisks	Initializes the tower name and # of disks and passes the # of disks to the ArrayList constructor that takes the initial array capacity as its only parameter. First stmt in this method should be super (numberDisks);	Main
void init()		Initializes the tower with the Disks. Only called for Tower A. Instantiate each of the needed disks with integers from 1 to # of disks and add them to the array starting from the highest number disk. Hint See code above	main
void move ()	Tower destinationTower	Get the Disk from this Tower (array element index: size()-1). Remove it and add it to the incoming destination Tower. Remember you can use all the methods of ArrayList, since you are an ArrayList by inheritance. This is 3 lines of code.	moveDisks
String toString()		Look at the Sample Ouput to see how to display the contents of a Tower. It uses the Disk toString method for the numbers	displayTowers

The TowerOfHanoi class has the main driver that plays the mathematical game.

It has three static data members:

Tower[] towers: an array of 3 Towers

int numDisks: the number of disks

long numMoves: a variable to hold the number of moves

It has three static methods:

main()

displayTowers()

moveDisks (numDisks, towerBeg, towerAux, towerEnd,).

Table 3: TowerOfHanoi class

Data/Method TowerOfHanoi	Parameters	Description	Called From
Tower[] towers long numMoves int numDisks		static data members
public static void displayTowers ()		Uses the Tower toString() method to display the towers. See the sample output below. This is only called when numDisks == 5 is true	main & moveDisks
public static void moveDisks()	int numberDisks, Tower beg, Tower aux, Tower end	This is the recursive method that plays the game. See the algorithm in the above text. Only call displayTowers when numDisks == 5 is true	main
public static void main ()	String[] args	See algorithm below	system

The TowerOfHanoi main method is just a for loop to play the game with different numbers of disks ranging from 3 to 32. The algorithm given below is for the code inside the loop:

Initialize the static variables to be used and updated in moveDisk method

Instantiate the three towers, calling them A, B, C

Initialize the first tower (towers[0]) with all the disks

When numberDisks == 5 is true, display the towers array

Call moveDisks recursive method to play the game

Display the number of moves for this number of disks

.....................................................................................................................................

Sample Output

Towers of Hanoi

===============

Moving 3 completed in 7 moves!

Moving 4 completed in 15 moves!

Towers:

Tower A: [5, 4, 3, 2, 1]

Tower B: []

Tower C: []

Towers:

Tower A: [5, 4, 3, 2]

Tower B: [1]

Tower C: []

Towers:

Tower A: [5, 4, 3]

Tower B: [1]

Tower C: [2]

Towers:

Tower A: [5, 4, 3]

Tower B: []

Tower C: [2, 1]

Towers:

Tower A: [5, 4]

Tower B: [3]

Tower C: [2, 1]

Towers:

Tower A: [5, 4, 1]

Tower B: [3]

Tower C: [2]

Towers:

Tower A: [5, 4, 1]

Tower B: [3, 2]

Tower C: []

Towers:

Tower A: [5, 4]

Tower B: [3, 2, 1]

Tower C: []

Towers:

Tower A: [5]

Tower B: [3, 2, 1]

Tower C: [4]

Towers:

Tower A: [5]

Tower B: [3, 2]

Tower C: [4, 1]

Towers:

Tower A: [5, 2]

Tower B: [3]

Tower C: [4, 1]

Towers:

Tower A: [5, 2, 1]

Tower B: [3]

Tower C: [4]

Towers:

Tower A: [5, 2, 1]

Tower B: []

Tower C: [4, 3]

Towers:

Tower A: [5, 2]

Tower B: [1]

Tower C: [4, 3]

Towers:

Tower A: [5]

Tower B: [1]

Tower C: [4, 3, 2]

Towers:

Tower A: [5]

Tower B: []

Tower C: [4, 3, 2, 1]

Towers:

Tower A: []

Tower B: [5]

Tower C: [4, 3, 2, 1]

Towers:

Tower A: [1]

Tower B: [5]

Tower C: [4, 3, 2]

Towers:

Tower A: [1]

Tower B: [5, 2]

Tower C: [4, 3]

Towers:

Tower A: []

Tower B: [5, 2, 1]

Tower C: [4, 3]

Towers:

Tower A: [3]

Tower B: [5, 2, 1]

Tower C: [4]

Towers:

Tower A: [3]

Tower B: [5, 2]

Tower C: [4, 1]

Towers:

Tower A: [3, 2]

Tower B: [5]

Tower C: [4, 1]

Towers:

Tower A: [3, 2, 1]

Tower B: [5]

Tower C: [4]

Towers:

Tower A: [3, 2, 1]

Tower B: [5, 4]

Tower C: []

Towers:

Tower A: [3, 2]

Tower B: [5, 4, 1]

Tower C: []

Towers:

Tower A: [3]

Tower B: [5, 4, 1]

Tower C: [2]

Towers:

Tower A: [3]

Tower B: [5, 4]

Tower C: [2, 1]

Towers:

Tower A: []

Tower B: [5, 4, 3]

Tower C: [2, 1]

Towers:

Tower A: [1]

Tower B: [5, 4, 3]

Tower C: [2]

Towers:

Tower A: [1]

Tower B: [5, 4, 3, 2]

Tower C: []

Towers:

Tower A: []

Tower B: [5, 4, 3, 2, 1]

Tower C: []

Moving 5 completed in 31 moves!

Moving 6 completed in 63 moves!

Moving 30 completed in 1073741823 moves!

Moving 31 completed in 2147483647 moves!

Moving 32 completed in 4294967295 moves!