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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C Programming:

#include<stdio.h>
#include<stdlib.h>
 
/* structure for a node */
struct node
{
  int data;
  struct node *next;
};
 
/* 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(struct node** head_ref, struct node* new_node)
{
  struct node* current = *head_ref;
 
  // Case 1 of the above algo
  if (current == NULL)
  {
     new_node->next = new_node;
     *head_ref = 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_ref)
        current = current->next;
    current->next = new_node;
    new_node->next = *head_ref;
    *head_ref = new_node;
  }
 
  // Case 3 of the above algo
  else
  {
    /* Locate the node before the point of insertion */
    while (current->next!= *head_ref && 
           current->next->data < new_node->data)
      current = current->next;
 
    new_node->next = current->next;
    current->next = new_node;
  }
}
 
/* Function to print nodes in a given linked list */
void printList(struct node *start)
{
  struct node *temp;
 
  if(start != NULL)
  {
    temp = start;
    printf("\n");
    do {
      printf("%d ", temp->data);
      temp = temp->next;
    } while(temp != start);
  }
}
 
/* Driver program to test above functions */
int main()
{
  int arr[] = {12, 56, 2, 11, 1, 90};
  int list_size, i;
 
  /* start with empty linked list */
  struct node *start = NULL;
  struct node *temp;
 
  /* Create linked list from the array arr[].
    Created linked list will be 1->2->11->12->56->90 */
  for (i = 0; i< 6; i++)
  {
    temp = (struct node *)malloc(sizeof(struct node));
    temp->data = arr[i];
    sortedInsert(&start, temp);
  }
 
  printList(start);
 
  return 0;
}

Output:

1 2 11 12 56 90

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

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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