Give an implementation of the size$()$ method for the following CircularlyLinkedList class assuming that we did not maintain size as an instance variable. The size $()$ method should return a count of the number of node in the list. Hint: see chapter on Linked List

Following is the code for the CircularlyLinkedList class:

public class CircularlyLinkedList $\{$

$//-------------------$nested Node class$------------------$

private static class Node $\{$

private E element; $//$reference to the element stored at this node

private Node next; $//$reference to the subsequent node in the list

public Node$($E$,$ e$,$ Node n$)\{$

element$=$e;

next$=$ n;

$\}$

public E getElement$()\{$return elements;$\}$

public Node getNext$()\{$return next;$\}$

public void setNext$($Node n$)\{$next$=$n;$\}$

$//$ instance variables of the CircularlyLinkedList

private Node tail$=$null; $//$we store tail $($but not head$)$

private int size$=0$; $//$number of nodes in the list

public CircularlyLinkedList$()\{\}//$constructs an initially empty list

$//$access methods

public int size$()\{$return size;$\}$

public Boolean isEmpty$()\{$return size$==0$;$\}$

public E first$()\{//$returns $($but does not remove$)$ the first element

If $($isEmpty$())$ return null;

return tail.getNext$().$getElement$()$; $//$the head is after the tail

$\}$

public E last$()\{//$returns $($but does not remove$)$ the last element

If $($isEmpty$())$ return null;

return tail.getElement$()$;

$\}$

public void rotate$()\{//$rotate the first element to the back of the list

If $($tail $!=$ null$)//$if empty, do nothing

tail$=$tail.getNext$()$; $//$the old head becomes the new tail

$\}$

public void addFirst $($E e$)\{//$adds element e to the front of the list

If $($size$==0)\{$

tail $=$ new Node$<>($e$,$ null$)$;

tail.setNext$($tail$)$; $//$link to itself circularly

$\}$ else $\{$

Node newest$=$new Node$<>($e$,$ tail.getNext$())$;

tail.setNext$($newest$)$;

$\}$

size$++$;

$\}$

public void addLast$($E e$)\{//$adds element e to the end of the list

addFirst$($e$)$; $//$insert new element at front of list

tail$=$tail.getNext$()$; $//$now new element becomes the tail

$\}$

public E removeFirst$()\{//$removes and returns the first element

If $($isEmpty$())$ return null; $//$nothing to remove

Node head $=$ tail.getNext$()$;

If $($head$==$tail$)$ tail $=$ null; $//$must be the only node left

else tail.setNext$($head$.$getNext$())$; $//$removes head from the list

size $--$;

return head.getElement$()$;

$\}$

$\}$