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: 1. Initialize the static variables to be used and updated in moveDisk method 2. Instantiate the three towers, calling them A, B, C 3. Initialize the first tower (towers[0]) with all the disks 4. When numberDisks == 5 is true, display the towers array 5. Call moveDisks recursive method to play the game 6. Display the number of moves for this number of disks