Insert element in a sorted Circular Linked List

Write a  function to insert a new value in a sorted Circular Linked List . See the following figure .



Implementation :

class Node 
{
    int data ;
    Node next;
    Node(int d)
    {
        data =d;
        next=null;
    }
}
class LinkedList
{
    Node root=null;
    Node newnode;
    Node temp;
    /*function to insert the element at the end */
    public void insert_at_end(int d)
    {
    newnode = new Node(d);
    if(root==null)
    {
        root=newnode;
        newnode.next=root;
    }
    else 
    {
        temp=root;
        while(temp.next!=root)
        {
            temp=temp.next;
        }
        temp.next=newnode;
        newnode.next=root;
    }
    }
   //function to insert the element in sorted list
   public void insert_in_sorted_list(int num)
    {     
     newnode=new Node(num);
     temp =root;
     // if root is null
     if(root==null)
     {
        root=newnode;
        newnode.next=root;
      
     }
     // if element to be added is less than root node
       /*  then we will reach till the last node and then 
         add newnode after last node nad make newnode as root node */
     if(temp.data >=newnode.data)
     {
         while(temp.next!=root )
         temp=temp.next;
        
        temp.next=newnode;
        newnode.next=root;
        root=newnode;
     }
     // if element to be added is greater than root node 
      /* then we will locate the node after which node is neede to added         
      */
      else{
         while(temp.next!=root && temp.next.data<newnode.data )
         temp=temp.next;
         
         newnode.next=temp.next;
         temp.next=newnode;
         }
    }
    
    /*function to display the list   */
    public void display()
    {
        Node start=root;
        
        if(start!=null)
        {
        do
        {
            System.out.print(start.data+"->");
            start=start.next;
        }
        while(start!=root);
        }
    }
}
 
public class Main {
    public static void main (String[] args)     {
    LinkedList list=new LinkedList();
    /* as we have to insert the element in a sorted list 
    we are inserting the element in sorted order  */
    list.insert_at_end(1);
    list.insert_at_end(3);
    list.insert_at_end(4);
    list.insert_at_end(5);
    System.out.println("\nTraversing the linked List");
    list.display();
    System.out.println("\nTraversing the linked List");
    list.insert_in_sorted_list(1);
    list.display();
  }
}

Time Complexity : O(n)

Test Case:
1. List may be empty hence we will make a newnode then we will then newnode as root node.
2. List may already contain the num to be added.
 
Please comment if you find any mistake.