Introduction to Circular Linked List

What is Circular linked list?

The circular linked list is a linked list where all nodes are connected to form a circle. In a circular linked list, the first node and the last node are connected to each other which forms a circle. There is no NULL at the end.

There are generally two types of circular linked lists:

• Circular singly linked list: In a circular Singly linked list, the last node of the list contains a pointer to the first node of the list. We traverse the circular singly linked list until we reach the same node where we started. The circular singly linked list has no beginning or end. No null value is present in the next part of any of the nodes.

Representation of Circular singly linked list

• Circular Doubly linked list: Circular Doubly Linked List has properties of both doubly linked list and circular linked list in which two consecutive elements are linked or connected by the previous and next pointer and the last node points to the first node by the next pointer and also the first node points to the last node by the previous pointer.

Representation of circular doubly linked list

Note: We will be using the singly circular linked list to represent the working of the circular linked list.

Representation of circular linked list:

Circular linked lists are similar to single Linked Lists with the exception of connecting the last node to the first node.

Node representation of a Circular Linked List:

C

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

C++

// Class Node, similar to the linked list
class Node{
    int value;

// Points to the next node.
    Node next;
}

Python3

# Class Node, similar to the linked list
class Node:
    def __init__(self,data):
        self.data = data
        self.next = None

Java

public class Node {
    int data;
    Node next;

    public Node(int data) {
        this.data = data;
        this.next = null;
    }
}

C#

public class Node
{
    public int data;
    public Node next;

    public Node(int data)
    {
        this.data = data;
        this.next = null;
    }
}

Javascript

class Node {
  constructor(data) {
    this.data = data;
    this.next = null;
  }
}

PHP

class Node {
  public $data;
  public $next;

  function __construct($data) {
    $this->data = $data;
    $this->next = null;
  }
}

Example of Circular singly linked list:

Example of  circular linked list

The above  Circular singly linked list can be represented as:

C

Node* one = createNode(3);
Node* two = createNode(5);
Node* three = createNode(9);

// Connect nodes
one->next = two;
two->next = three;
three->next = one;

C++

// Initialize the Nodes.
Node one = new Node(3);
Node two = new Node(5);
Node three = new Node(9);

// Connect nodes
one.next = two;
two.next = three;
three.next = one;

Python3

# Initialize the Nodes.
one = Node(3)
two = Node(5)
three = Node(9)

# Connect nodes
one.next = two
two.next = three
three.next = one

Java

// Define the Node class
class Node {
    int value;
    Node next;

    public Node(int value) {
        this.value = value;
    }
}

// Initialize the Nodes.
Node one = new Node(3);
Node two = new Node(5);
Node three = new Node(9);

// Connect nodes
one.next = two;
two.next = three;
three.next = one;

C#

Node one = new Node(3);
Node two = new Node(5);
Node three = new Node(9);

// Connect nodes
one.next = two;
two.next = three;
three.next = one;

Javascript

let one = new Node(3);
let two = new Node(5);
let three = new Node(9);

// Connect nodes
one.next = two;
two.next = three;
three.next = one;

PHP

$one = new Node(3);
$two = new Node(5);
$three = new Node(9);

// Connect nodes
$one->next = $two;
$two->next = $three;
$three->next = $one;

Explanation: In the above program one, two, and three are the node with values 3, 5, and 9 respectively which are connected in a circular manner as:

• For Node One: The Next pointer stores the address of Node two.
• For Node Two: The Next stores the address of Node three
• For Node Three: The Next points to node one.

Operations on the circular linked list:

We can do some operations on the circular linked list similar to the singly linked list which are:

1. Insertion
2. Deletion

1. Insertion in the circular linked list:

A node can be added in three ways:

1. Insertion at the beginning of the list
2. Insertion at the end of the list
3. Insertion in between the nodes

1) Insertion at the beginning of the list: To insert a node at the beginning of the list, follow these steps: 

• Create a node, say T. 
• Make T -> next = last -> next. 
• last -> next = T. 

Circular linked list before insertion

And then, 

Circular linked list after insertion

2) Insertion at the end of the list: To insert a node at the end of the list, follow these steps: 

• Create a node, say T. 
• Make T -> next = last -> next; 
• last -> next = T. 
• last = T. 

Before insertion,

Circular linked list before insertion of node at the end

After insertion,

Circular linked list after insertion of node at the end

3) Insertion in between the nodes: To insert a node in between the two nodes, follow these steps: 

• Create a node, say T. 
• Search for the node after which T needs to be inserted, say that node is P. 
• Make T -> next = P -> next; 
• P -> next = T.

Suppose 12 needs to be inserted after the node has the value 10,

Circular linked list before insertion

After searching and insertion,

Circular linked list after  insertion

2. Deletion in a circular linked list:

1) Delete the node only if it is the only node in the circular linked list:

• Free the node’s memory
• The last value should be NULL A node always points to another node, so NULL assignment is not necessary.
  Any node can be set as the starting point.
  Nodes are traversed quickly from the first to the last.

2) Deletion of the last node:

• Locate the node before the last node (let it be temp)
• Keep the address of the node next to the last node in temp
• Delete the last memory
• Put temp at the end

3) Delete any node from the circular linked list: We will be given a node and our task is to delete that node from the circular linked list.

Algorithm:
Case 1: List is empty. 

• If the list is empty we will simply return.

Case 2:List is not empty  

• If the list is not empty then we define two pointers curr and prev and initialize the pointer curr with the head node.
• Traverse the list using curr to find the node to be deleted and before moving to curr to the next node, every time set prev = curr.
• If the node is found, check if it is the only node in the list. If yes, set head = NULL and free(curr).
• If the list has more than one node, check if it is the first node of the list. Condition to check this( curr == head). If yes, then move prev until it reaches the last node. After prev reaches the last node, set head = head -> next and prev -> next = head. Delete curr.
• If curr is not the first node, we check if it is the last node in the list. Condition to check this is (curr -> next == head).
• If curr is the last node. Set prev -> next = head and delete the node curr by free(curr).
• If the node to be deleted is neither the first node nor the last node, then set prev -> next = curr -> next and delete curr.
• If the node is not present in the list return head and don’t do anything.

Below is the implementation for the above approach:

C

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

// Structure for a node
struct Node {
    int data;
    struct Node* next;
};

// Function to insert a node at the
// beginning of a Circular linked list
void push(struct Node** head_ref, int data)
{

    // Create a new node and make head
    // as next of it.
    struct Node* ptr1 = (struct Node*)malloc(sizeof(struct Node));
    ptr1->data = data;
    ptr1->next = *head_ref;

    // If linked list is not NULL then
    // set the next of last node
    if (*head_ref != NULL) {

        // Find the node before head and
        // update next of it.
        struct Node* temp = *head_ref;
        while (temp->next != *head_ref)
            temp = temp->next;
        temp->next = ptr1;
    }
    else

        // For the first node
        ptr1->next = ptr1;

    *head_ref = ptr1;
}

// Function to print nodes in a given
// circular linked list
void printList(struct Node* head)
{
    struct Node* temp = head;
    if (head != NULL) {
        do {
            printf("%d ", temp->data);
            temp = temp->next;
        } while (temp != head);
    }

    printf("\n");
}

// Function to delete a given node
// from the list
void deleteNode(struct Node** head, int key)
{

    // If linked list is empty
    if (*head == NULL)
        return;

    // If the list contains only a
    // single node
    if ((*head)->data == key && (*head)->next == *head) {
        free(*head);
        *head = NULL;
        return;
    }

    struct Node *last = *head, *d;

    // If head is to be deleted
    if ((*head)->data == key) {

        // Find the last node of the list
        while (last->next != *head)
            last = last->next;

        // Point last node to the next of
        // head i.e. the second node
        // of the list
        last->next = (*head)->next;
        free(*head);
        *head = last->next;
        return;
    }

    // Either the node to be deleted is
    // not found or the end of list
    // is not reached
    while (last->next != *head && last->next->data != key) {
        last = last->next;
    }

    // If node to be deleted was found
    if (last->next->data == key) {
        d = last->next;
        last->next = d->next;
        free(d);
    }
    else
        printf("Given node is not found in the list!!!\n");
}

// Driver code
int main()
{
    // Initialize lists as empty
    struct Node* head = NULL;

    // Created linked list will be
    // 2->5->7->8->10
    push(&head, 2);
    push(&head, 5);
    push(&head, 7);
    push(&head, 8);
    push(&head, 10);

    printf("List Before Deletion: ");
    printList(head);

    deleteNode(&head, 7);

    printf("List After Deletion: ");
    printList(head);

    return 0;
}

C++

// C++ program to delete a given key from
// linked list.
#include <bits/stdc++.h>
using namespace std;

// Structure for a node
class Node {
public:
    int data;
    Node* next;
};

// Function to insert a node at the
// beginning of a Circular linked list
void push(Node** head_ref, int data)
{

    // Create a new node and make head
    // as next of it.
    Node* ptr1 = new Node();
    ptr1->data = data;
    ptr1->next = *head_ref;

    // If linked list is not NULL then
    // set the next of last node
    if (*head_ref != NULL) {

        // Find the node before head and
        // update next of it.
        Node* temp = *head_ref;
        while (temp->next != *head_ref)
            temp = temp->next;
        temp->next = ptr1;
    }
    else

        // For the first node
        ptr1->next = ptr1;

    *head_ref = ptr1;
}

// Function to print nodes in a given
// circular linked list
void printList(Node* head)
{
    Node* temp = head;
    if (head != NULL) {
        do {
            cout << temp->data << " ";
            temp = temp->next;
        } while (temp != head);
    }

    cout << endl;
}

// Function to delete a given node
// from the list
void deleteNode(Node** head, int key)
{

    // If linked list is empty
    if (*head == NULL)
        return;

    // If the list contains only a
    // single node
    if ((*head)->data == key && (*head)->next == *head) {
        free(*head);
        *head = NULL;
        return;
    }

    Node *last = *head, *d;

    // If head is to be deleted
    if ((*head)->data == key) {

        // Find the last node of the list
        while (last->next != *head)
            last = last->next;

        // Point last node to the next of
        // head i.e. the second node
        // of the list
        last->next = (*head)->next;
        free(*head);
        *head = last->next;
        return;
    }

    // Either the node to be deleted is
    // not found or the end of list
    // is not reached
    while (last->next != *head && last->next->data != key) {
        last = last->next;
    }

    // If node to be deleted was found
    if (last->next->data == key) {
        d = last->next;
        last->next = d->next;
        free(d);
    }
    else
        cout << "Given node is not found in the list!!!\n";
}

// Driver code
int main()
{
    // Initialize lists as empty
    Node* head = NULL;

    // Created linked list will be
    // 2->5->7->8->10
    push(&head, 2);
    push(&head, 5);
    push(&head, 7);
    push(&head, 8);
    push(&head, 10);

    cout << "List Before Deletion: ";
    printList(head);

    deleteNode(&head, 7);

    cout << "List After Deletion: ";
    printList(head);

    return 0;
}

Java

// Java program to delete a given key from
// linked list.
import java.io.*;
import java.util.*;

public class GFG {
    /* structure for a node */
    static class Node {
        int data;
        Node next;
    };

    /* Function to insert a node at the beginning of
a Circular linked list */
    static Node push(Node head_ref, int data)
    {
        // Create a new node and make head as next
        // of it.
        Node ptr1 = new Node();
        ptr1.data = data;
        ptr1.next = head_ref;

        /* If linked list is not null then set the
next of last node */
        if (head_ref != null) {
            // Find the node before head and update
            // next of it.
            Node temp = head_ref;
            while (temp.next != head_ref)
                temp = temp.next;
            temp.next = ptr1;
        }
        else
            ptr1.next = ptr1; /*For the first node */

        head_ref = ptr1;
        return head_ref;
    }

    /* Function to print nodes in a given
circular linked list */
    static void printList(Node head)
    {
        Node temp = head;
        if (head != null) {
            do {
                System.out.printf("%d ", temp.data);
                temp = temp.next;
            } while (temp != head);
        }

        System.out.printf("\n");
    }

    /* Function to delete a given node from the list */
    static Node deleteNode(Node head, int key)
    {
        if (head == null)
            return null;
        int flag = 0;
        // Find the required node
        Node curr = head, prev = new Node();
        while (curr.data != key) {
            if (curr.next == head) {
                System.out.printf(
                    "Given node is not found in the list!!!\n");
                flag = 1;
                break;
            }

            prev = curr;
            curr = curr.next;
        }

        // Check if the element is not present in the list
        if (flag == 1)
            return head;

        // Check if node is only node
        if (curr == head && curr.next == head) {
            head = null;
            return head;
        }

        // If more than one node, check if
        // it is first node
        if (curr == head) {
            prev = head;
            while (prev.next != head)
                prev = prev.next;
            head = curr.next;
            prev.next = head;
        }

        // check if node is last node
        else if (curr.next == head) {
            prev.next = head;
        }
        else {
            prev.next = curr.next;
        }
        return head;
    }

    /* Driver code */
    public static void main(String args[])
    {
        /* Initialize lists as empty */
        Node head = null;

        /* Created linked list will be 2.5.7.8.10 */
        head = push(head, 2);
        head = push(head, 5);
        head = push(head, 7);
        head = push(head, 8);
        head = push(head, 10);

        System.out.printf("List Before Deletion: ");
        printList(head);

        head = deleteNode(head, 7);

        System.out.printf("List After Deletion: ");
        printList(head);
    }
}

// This code is contributed by Susobhan Akhuli

Python3

# Python program to delete a given key from linked list
class Node:
    def __init__(self, data):
        self.data = data
        self.next = None

# Function to insert a node at the
# beginning of a Circular linked list


def push(head, data):
    # Create a new node and make head as next of it.
    newP = Node(data)
    newP.next = head

    # If linked list is not NULL then
    # set the next of last node
    if head != None:
        # Find the node before head and
        # update next of it.
        temp = head
        while (temp.next != head):
            temp = temp.next
        temp.next = newP
    else:
        newP.next = newP
    head = newP
    return head

# Function to print nodes in a given circular linked list


def printList(head):
    if head == None:
        print("List is Empty")
        return
    temp = head.next
    print(head.data, end=' ')
    if (head != None):
        while (temp != head):
            print(temp.data, end=" ")
            temp = temp.next
    print()

# Function to delete a given node
# from the list


def deleteNode(head, key):
    # If linked list is empty
    if (head == None):
        return

    # If the list contains only a
    # single node
    if (head.data == key and head.next == head):
        head = None
        return

    last = head

    # If head is to be deleted
    if (head.data == key):
        # Find the last node of the list
        while (last.next != head):
            last = last.next

        # Point last node to the next of
        # head i.e. the second node
        # of the list
        last.next = head.next
        head = last.next
        return

    # Either the node to be deleted is
    # not found or the end of list
    # is not reached
    while (last.next != head and last.next.data != key):
        last = last.next

    # If node to be deleted was found
    if (last.next.data == key):
        d = last.next
        last.next = d.next
        d = None
    else:
        print("Given node is not found in the list!!!")


# Driver code
# Initialize lists as empty
head = None

# Created linked list will be
# 2->5->7->8->10
head = push(head, 2)
head = push(head, 5)
head = push(head, 7)
head = push(head, 8)
head = push(head, 10)

print("List Before Deletion: ")
printList(head)

deleteNode(head, 7)
print("List After Deletion: ")
printList(head)

Javascript

// Javascript program to delete a given key from linked list.

// Structure for a node
class Node {
  constructor() {
    this.data;
    this.next;
  }
}

// Function to insert a node at the
// beginning of a Circular linked list
function push(head, data) {
  // Create a new node and make head
  // as next of it.
  var ptr1 = new Node();
  ptr1.data = data;
  ptr1.next = head;

  // If linked list is not NULL then
  // set the next of last node
  if (head != null) {
    // Find the node before head and
    // update next of it.
    let temp = head;
    while (temp.next != head) temp = temp.next;
    temp.next = ptr1;
  }

  // For the first node
  else ptr1.next = ptr1;

  head = ptr1;
  return head;
}

// Function to print nodes in a given
// circular linked list
function printList(head) {
  let tempp = head;
  if (head != null) {
    do {
      console.log(tempp.data);
      tempp = tempp.next;
    } while (tempp != head);
  }
}

// Function to delete a given node
// from the list
function deleteNode(head, key) {
  // If linked list is empty
  if (head == null) return;

  // If the list contains only a
  // single node
  if (head.data == key && head.next == head) {
    head = null;
    return;
  }

  let last = head;

  // If head is to be deleted
  if (head.data == key) {
    // Find the last node of the list
    while (last.next != head) last = last.next;

    // Point last node to the next of
    // head i.e. the second node
    // of the list
    last.next = head.next;
    head = last.next;
    return;
  }

  // Either the node to be deleted is
  // not found or the end of list
  // is not reached
  while (last.next != head && last.next.data != key) {
    last = last.next;
  }

  // If node to be deleted was found
  if (last.next.data == key) {
    d = last.next;
    last.next = d.next;
    d = null;
  } else console.log("Given node is not found in the list!!!");
}

// Driver code

// Initialize lists as empty
head = null;

// Created linked list will be
// 2->5->7->8->10
head = push(head, 2);
head = push(head, 5);
head = push(head, 7);
head = push(head, 8);
head = push(head, 10);

console.log("List Before Deletion: ");
printList(head);

deleteNode(head, 7);

console.log("List After Deletion: ");
printList(head);

C#

using System;

// Structure for a node
public class Node {
    public int data;
    public Node next;
}

// Class for Circular Linked List
public class CircularLinkedList {

    // Function to insert a node at the
    // beginning of a Circular linked list
    public static void Push(ref Node head_ref, int data)
    {

        // Create a new node and make head
        // as next of it.
        Node ptr1 = new Node();
        ptr1.data = data;
        ptr1.next = head_ref;

        // If linked list is not NULL then
        // set the next of last node
        if (head_ref != null) {

            // Find the node before head and
            // update next of it.
            Node temp = head_ref;
            while (temp.next != head_ref)
                temp = temp.next;
            temp.next = ptr1;
        }
        else

            // For the first node
            ptr1.next = ptr1;

        head_ref = ptr1;
    }

    // Function to print nodes in a given
    // circular linked list
    public static void PrintList(Node head)
    {
        Node temp = head;
        if (head != null) {
            do {
                Console.Write(temp.data + " ");
                temp = temp.next;
            } while (temp != head);
        }

        Console.WriteLine();
    }

    // Function to delete a given node
    // from the list
    public static void DeleteNode(ref Node head, int key)
    {

        // If linked list is empty
        if (head == null)
            return;

        // If the list contains only a
        // single node
        if (head.data == key && head.next == head) {
            head = null;
            return;
        }

        Node last = head, d;

        // If head is to be deleted
        if (head.data == key) {

            // Find the last node of the list
            while (last.next != head)
                last = last.next;

            // Point last node to the next of
            // head i.e. the second node
            // of the list
            last.next = head.next;
            head = last.next;
            return;
        }

        // Either the node to be deleted is
        // not found or the end of list
        // is not reached
        while (last.next != head && last.next.data != key) {
            last = last.next;
        }

        // If node to be deleted was found
        if (last.next.data == key) {
            d = last.next;
            last.next = d.next;
        }
        else
            Console.WriteLine(
                "Given node is not found in the list!!!");
    }

    // Driver code
    public static void Main()
    {

        // Initialize lists as empty
        Node head = null;

        // Created linked list will be
        // 2->5->7->8->10
        Push(ref head, 2);
        Push(ref head, 5);
        Push(ref head, 7);
        Push(ref head, 8);
        Push(ref head, 10);

        Console.Write("List Before Deletion: ");
        PrintList(head);

        DeleteNode(ref head, 7);

        Console.Write("List After Deletion: ");
        PrintList(head);
    }
}

Output

List Before Deletion: 10 8 7 5 2 
List After Deletion: 10 8 5 2 

Time Complexity: O(N), Worst case occurs when the element to be deleted is the last element and we need to move through the whole list.
Auxiliary Space: O(1), As constant extra space is used.

Advantages of Circular Linked Lists:

• Any node can be a starting point. We can traverse the whole list by starting from any point. We just need to stop when the first visited node is visited again. 
• Useful for implementation of a queue. Unlike this implementation, we don’t need to maintain two pointers for front and rear if we use a circular linked list. We can maintain a pointer to the last inserted node and the front can always be obtained as next of last.

• Circular lists are useful in applications to repeatedly go around the list. For example, when multiple applications are running on a PC, it is common for the operating system to put the running applications on a list and then cycle through them, giving each of them a slice of time to execute, and then making them wait while the CPU is given to another application. It is convenient for the operating system to use a circular list so that when it reaches the end of the list it can cycle around to the front of the list. 
• Circular Doubly Linked Lists are used for the implementation of advanced data structures like the Fibonacci Heap.
•  Implementing a circular linked list can be relatively easy compared to other more complex data structures like trees or graphs.

Disadvantages of circular linked list:

• Compared to singly linked lists, circular lists are more complex.
• Reversing a circular list is more complicated than singly or doubly reversing a circular list.
• It is possible for the code to go into an infinite loop if it is not handled carefully.
• It is harder to find the end of the list and control the loop.
• Although circular linked lists can be efficient in certain applications, their performance can be slower than other data structures in certain cases, such as when the list needs to be sorted or searched.
• Circular linked lists don’t provide direct access to individual nodes

Applications of circular linked lists:

• Multiplayer games use this to give each player a chance to play.
• A circular linked list can be used to organize multiple running applications on an operating system. These applications are iterated over by the OS.
• Circular linked lists can be used in resource allocation problems.
• Circular linked lists are commonly used to implement circular buffers,
• Circular linked lists can be used in simulation and gaming.

Why circular linked list?

• A node always points to another node, so NULL assignment is not necessary.
• Any node can be set as the starting point.
• Nodes are traversed quickly from the first to the last.

Next Posts: Circular Linked List | Set 2 (Traversal) Circular Singly Linked List | Insertion Please write comments if you find any bug in above code/algorithm, or find other ways to solve the same problem