Write a C function to insert a new value in a sorted Circular Linked List (CLL). For example, if the input CLL is following:

Sorted insert for circular linked list

After insertion of 7, the above CLL should be changed to following

Sorted insert for circular linked list

Algorithm:
Allocate memory for the newly inserted node and put data in the newly allocated node. Let the pointer to the new node be new_node. After memory allocation, following are the three cases that need to be handled.

1) Linked List is empty:  
    a)  since new_node is the only node in CLL, make a self loop.      
          new_node->next = new_node;  
    b) change the head pointer to point to new node.
          *head_ref = new_node;
2) New node is to be inserted just before the head node:    
  (a) Find out the last node using a loop.
         while(current->next != *head_ref)
            current = current->next;
  (b) Change the next of last node. 
         current->next = new_node;
  (c) Change next of new node to point to head.
         new_node->next = *head_ref;
  (d) change the head pointer to point to new node.
         *head_ref = new_node;
3) New node is to be  inserted somewhere after the head: 
   (a) Locate the node after which new node is to be inserted.
         while ( current->next!= *head_ref && 
             current->next->data < new_node->data)
         {   current = current->next;   }
   (b) Make next of new_node as next of the located pointer
         new_node->next = current->next;
   (c) Change the next of the located pointer
         current->next = new_node;
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Java Programming:

// Java program for sorted insert in circular linked list
 
class Node
{
    int data;
    Node next;
 
    Node(int d)
    {
        data = d;
        next = null;
    }
}
 
class LinkedList
{
    Node head;
 
    // Constructor
    LinkedList()   { head = null; }
 
    /* function to insert a new_node in a list in sorted way.
     Note that this function expects a pointer to head node
     as this can modify the head of the input linked list */
    void sortedInsert(Node new_node)
    {
        Node current = head;
 
        // Case 1 of the above algo
        if (current == null)
        {
            new_node.next = new_node;
            head = new_node;
 
        }
 
        // Case 2 of the above algo
        else if (current.data >= new_node.data)
        {
 
            /* If value is smaller than head's value then
             we need to change next of last node */
            while (current.next != head)
                current = current.next;
 
            current.next = new_node;
            new_node.next = head;
            head = new_node;
        }
 
        // Case 3 of the above algo
        else
        {
 
            /* Locate the node before the point of insertion */
            while (current.next != head &&
                   current.next.data < new_node.data)
                current = current.next;
 
            new_node.next = current.next;
            current.next = new_node;
        }
    }
 
    // Utility method to print a linked list
    void printList()
    {
        if (head != null)
        {
            Node temp = head;
            do
            {
                System.out.print(temp.data + " ");
                temp = temp.next;
            }  while (temp != head);
        }
    }
 
    // Driver code to test above
    public static void main(String[] args)
    {
        LinkedList list = new LinkedList();
 
        // Creating the linkedlist
        int arr[] = new int[] {12, 56, 2, 11, 1, 90};
 
        /* start with empty linked list */
        Node temp = null;
 
        /* Create linked list from the array arr[].
         Created linked list will be 1->2->11->12->56->90*/
        for (int i = 0; i < 6; i++)
        {
            temp = new Node(arr[i]);
            list.sortedInsert(temp);
        }
 
        list.printList();
    }
}

Output:

1 2 11 12 56 90

Time Complexity: O(n) where n is the number of nodes in the given linked list.

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Case 2 of the above algorithm/code can be optimized. Please see this comment from Pavan. To implement the suggested change we need to modify the case 2 to following.

// Case 2 of the above algo
else if (current->data >= new_node->data)
{
  // swap the data part of head node and new node
  // assuming that we have a function swap(int *, int *)
  swap(&(current->data), &(new_node->data)); 
 
  new_node->next = (*head_ref)->next;
  (*head_ref)->next = new_node;
}
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