Eliminar elemento en lista vinculada circular en C

Implementación

La implementación de este algoritmo se da a continuación:

#include <stdio.h>
#include <stdlib.h>

struct node {
   int data;
   struct node *next;
};

struct node *head = NULL;
struct node *current = NULL;
struct node *prev = NULL;

//insert link at the first location
void insert(int data) {
   // Allocate memory for new node;
   struct node *link = (struct node*) malloc(sizeof(struct node));

   link->data = data;
   link->next = NULL;

   // If head is empty, create new list
   if(head==NULL) {
      head = link;
      head->next = link;
      return;
   }

   current = head;

   // move to the end of the list
   while(current->next != head)
      current = current->next;

   // Insert link at the end of the list
   current->next = link;

   // Link the last node back to head
   link->next = head;

}

void remove_data(int data) {
   int pos = 0;

   if(head==NULL) {
      printf("Linked List not initialized");
      return;
   } 

   if(head->data == data) {
      if(head->next != head) {
         current = head;
         while(current->next!=head) {
            current = current->next;
         }
         
         current->next = head->next;
         head = head->next;
         return;
      } else {
         head = NULL;
         printf("List is empty\n");
         exit(0);
      }
   
   } else if(head->data != data && head->next == NULL) {
      printf("%d not found in the list\n", data);
      return;
   }

   current = head;

   while(current->next != head && current->data != data) {
      prev = current;
      current = current->next;
   }        

   if(current->data == data) {
      prev->next = prev->next->next;
      free(current);
   } else
      printf("%d not found in the list.", data);
}

//display the list
void printList() {
   struct node *ptr = head;

   printf("\n[head] =>");
   
   //start from the beginning
   while(ptr->next != head) {        
      printf(" %d =>",ptr->data);
      ptr = ptr->next;
   }
   
   printf(" %d =>",ptr->data);
   printf(" [head]\n");
}

int main() {
   insert(10);
   insert(20);
   insert(30);
   insert(1);
   insert(40);
   insert(56); 

   printf("Original List -");
   printList();
   remove_data(1);

   printf("List after removal -");
   printList();

   return 0;
}

Salida

La salida del programa debe ser:

Original List -
[head] => 10 => 20 => 30 => 1 => 40 => 56 => [head]
List after removal -
[head] => 10 => 20 => 30 => 40 => 56 => [head]