A circular linked list is a type of linked list in which the first and the last nodes are also connected to each other to form a circle.

There are basically two types of circular linked list:

Here, the address of the last node consists of the address of the first node.

Here, in addition to the last node storing the address of the first node, the first node will also store the address of the last node.

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

## Representation of Circular Linked List

Let's see how we can represent a circular linked list on an algorithm/code. Suppose we have a linked list:

Here, the single node is represented as

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

Each struct node has a data item and a pointer to the next struct node.

Now we will create a simple circular linked list with three items to understand how this works.

``````/* Initialize nodes */
struct node *last;
struct node *one = NULL;
struct node *two = NULL;
struct node *three = NULL;

/* Allocate memory */
one = malloc(sizeof(struct node));
two = malloc(sizeof(struct node));
three = malloc(sizeof(struct node));

/* Assign data values */
one->data = 1;
two->data = 2;
three->data = 3;

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

/* Save address of third node in last */
last = three;``````

In the above code, one, two, and three are the nodes with data items 1, 2, and 3 respectively.

For node one

• next stores the address of two (there is no node before it)

For node two

• next stores the address of three

For node three

• next stores `NULL` (there is no node after it)
• next points to node one

## Insertion on a Circular Linked List

We can insert elements at 3 different positions of a circular linked list:

Suppose we have a circular linked list with elements 1, 2, and 3.

Let's add a node with value 6 at different positions of the circular linked list we made above. The first step is to create a new node.

• allocate memory for `newNode`
• assign the data to `newNode`

### 1. Insertion at the Beginning

• store the address of the current first node in the `newNode` (i.e. pointing the `newNode` to the current first node)
• point the last node to `newNode` (i.e making `newNode` as head)

### 2. Insertion in between two nodes

Let's insert newNode after the first node.

• travel to the node given (let this node be `p`)
• point the `next` of `newNode` to the node next to `p`
• store the address of `newNode` at `next` of `p`

### 3. Insertion at the end

• store the address of the head node to `next` of newNode (making `newNode` the last node)
• point the current last node to `newNode`
• make `newNode` as the last node

## Deletion on a Circular Linked List

Suppose we have a double-linked list with elements 1, 2, and 3.

### 1. If the node to be deleted is the only node

• free the memory occupied by the node
• store NULL in `last`

### 2. If last node is to be deleted

• find the node before the last node (let it be `temp`)
• store the address of the node next to the last node in `temp`
• free the memory of last
• make `temp` as the last node

### 3. If any other nodes are to be deleted

• travel to the node to be deleted (here we are deleting node 2)
• let the node before node 2 be `temp`
• store the address of the node next to 2 in `temp`
• free the memory of 2

## Circular Linked List Code in Python, Java, C, and C++

``````# Python code to perform circular linked list operations

class Node:
def __init__(self, data):
self.data = data
self.next = None

def __init__(self):
self.last = None

if self.last != None:
return self.last

# allocate memory to the new node and add data to the node
newNode = Node(data)

# assign last to newNode
self.last = newNode

self.last.next = self.last
return self.last

# add node to the front

# check if the list is empty
if self.last == None:

# allocate memory to the new node and add data to the node
newNode = Node(data)

# store the address of the current first node in the newNode
newNode.next = self.last.next

# make newNode as last
self.last.next = newNode

return self.last

# add node to the end
# check if the node is empty
if self.last == None:

# allocate memory to the new node and add data to the node
newNode = Node(data)

# store the address of the last node to next of newNode
newNode.next = self.last.next

# point the current last node to the newNode
self.last.next = newNode

# make newNode as the last node
self.last = newNode

return self.last

# insert node after a specific node

# check if the list is empty
if self.last == None:
return None

newNode = Node(data)
p = self.last.next
while p:

# if the item is found, place newNode after it
if p.data == item:

# make the next of the current node as the next of newNode
newNode.next = p.next

# put newNode to the next of p
p.next = newNode

if p == self.last:
self.last = newNode
return self.last
else:
return self.last
p = p.next
if p == self.last.next:
print(item, "The given node is not present in the list")
break

# delete a node
def deleteNode(self, last, key):

# If linked list is empty
if last == None:
return

# If the list contains only a single node
if (last).data == key and (last).next == last:

last = None

temp = last
d = None

# if last node is to be deleted
if (last).data == key:

# find the node before the last node
while temp.next != last:
temp = temp.next

# point temp node to the next of last i.e. first node
temp.next = (last).next
last = temp.next

# travel to the node to be deleted
while temp.next != last and temp.next.data != key:
temp = temp.next

# if node to be deleted was found
if temp.next.data == key:
d = temp.next
temp.next = d.next

return last

def traverse(self):
if self.last == None:
print("The list is empty")
return

newNode = self.last.next
while newNode:
print(newNode.data, end=" ")
newNode = newNode.next
if newNode == self.last.next:
break

# Driver Code
if __name__ == "__main__":

cll.traverse()

last = cll.deleteNode(last, 8)
print()
cll.traverse()``````
``````// Java code to perform circular linked list operations

static class Node {
int data;
Node next;
};

static Node addToEmpty(Node last, int data) {
if (last != null)
return last;

// allocate memory to the new node
Node newNode = new Node();

// assign data to the new node
newNode.data = data;

// assign last to newNode
last = newNode;

newNode.next = last;

return last;
}

// add node to the front
static Node addFront(Node last, int data) {
if (last == null)

// allocate memory to the new node
Node newNode = new Node();

// add data to the node
newNode.data = data;

// store the address of the current first node in the newNode
newNode.next = last.next;

last.next = newNode;

return last;
}

// add node to the end
static Node addEnd(Node last, int data) {
if (last == null)

// allocate memory to the new node
Node newNode = new Node();

// add data to the node
newNode.data = data;

// store the address of the head node to next of newNode
newNode.next = last.next;

// point the current last node to the newNode
last.next = newNode;

// make newNode as the last node
last = newNode;

return last;
}

static Node addAfter(Node last, int data, int item) {
if (last == null)
return null;

Node newNode, p;
p = last.next;
do {
// if the item is found, place newNode after it
if (p.data == item) {
// allocate memory to the new node
newNode = new Node();

// add data to the node
newNode.data = data;

// make the next of the current node as the next of newNode
newNode.next = p.next;

// put newNode to the next of p
p.next = newNode;

// if p is the last node, make newNode as the last node
if (p == last)
last = newNode;
return last;
}
p = p.next;
} while (p != last.next);

System.out.println(item + "The given node is not present in the list");
return last;

}

// delete a node
static Node deleteNode(Node last, int key) {
// if linked list is empty
if (last == null)
return null;

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

Node temp = last, d = new Node();

// if last is to be deleted
if (last.data == key) {
// find the node before the last node
while (temp.next != last) {
temp = temp.next;
}

// point temp node to the next of last i.e. first node
temp.next = last.next;
last = temp.next;
}

// travel to the node to be deleted
while (temp.next != last && temp.next.data != key) {
temp = temp.next;
}

// if node to be deleted was found
if (temp.next.data == key) {
d = temp.next;
temp.next = d.next;
}
return last;
}

static void traverse(Node last) {
Node p;

if (last == null) {
System.out.println("List is empty.");
return;
}

p = last.next;

do {
System.out.print(p.data + " ");
p = p.next;

}
while (p != last.next);

}

public static void main(String[] args) {
Node last = null;

traverse(last);

deleteNode(last, 8);
traverse(last);
}
}``````
``````// C code to perform circular linked list operations

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

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

struct Node* addToEmpty(struct Node* last, int data) {
if (last != NULL) return last;

// allocate memory to the new node
struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));

// assign data to the new node
newNode->data = data;

// assign last to newNode
last = newNode;

last->next = last;

return last;
}

// add node to the front
struct Node* addFront(struct Node* last, int data) {
// check if the list is empty
if (last == NULL) return addToEmpty(last, data);

// allocate memory to the new node
struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));

// add data to the node
newNode->data = data;

// store the address of the current first node in the newNode
newNode->next = last->next;

last->next = newNode;

return last;
}

// add node to the end
struct Node* addEnd(struct Node* last, int data) {
// check if the node is empty
if (last == NULL) return addToEmpty(last, data);

// allocate memory to the new node
struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));

// add data to the node
newNode->data = data;

// store the address of the head node to next of newNode
newNode->next = last->next;

// point the current last node to the newNode
last->next = newNode;

// make newNode as the last node
last = newNode;

return last;
}

// insert node after a specific node
struct Node* addAfter(struct Node* last, int data, int item) {
// check if the list is empty
if (last == NULL) return NULL;

struct Node *newNode, *p;

p = last->next;
do {
// if the item is found, place newNode after it
if (p->data == item) {
// allocate memory to the new node
newNode = (struct Node*)malloc(sizeof(struct Node));

// add data to the node
newNode->data = data;

// make the next of the current node as the next of newNode
newNode->next = p->next;

// put newNode to the next of p
p->next = newNode;

// if p is the last node, make newNode as the last node
if (p == last) last = newNode;
return last;
}

p = p->next;
} while (p != last->next);

printf("\nThe given node is not present in the list");
return last;
}

// delete a node
void deleteNode(struct Node** last, int key) {
// if linked list is empty
if (*last == NULL) return;

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

struct Node *temp = *last, *d;

// if last is to be deleted
if ((*last)->data == key) {
// find the node before the last node
while (temp->next != *last) temp = temp->next;

// point temp node to the next of last i.e. first node
temp->next = (*last)->next;
free(*last);
*last = temp->next;
}

// travel to the node to be deleted
while (temp->next != *last && temp->next->data != key) {
temp = temp->next;
}

// if node to be deleted was found
if (temp->next->data == key) {
d = temp->next;
temp->next = d->next;
free(d);
}
}

void traverse(struct Node* last) {
struct Node* p;

if (last == NULL) {
printf("The list is empty");
return;
}

p = last->next;

do {
printf("%d ", p->data);
p = p->next;

} while (p != last->next);
}

int main() {
struct Node* last = NULL;

traverse(last);

deleteNode(&last, 8);

printf("\n");

traverse(last);

return 0;
}``````
``````// C++ code to perform circular linked list operations

#include <iostream>

using namespace std;

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

struct Node* addToEmpty(struct Node* last, int data) {
if (last != NULL) return last;

// allocate memory to the new node
struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));

// assign data to the new node
newNode->data = data;

// assign last to newNode
last = newNode;

last->next = last;

return last;
}

// add node to the front
struct Node* addFront(struct Node* last, int data) {
// check if the list is empty
if (last == NULL) return addToEmpty(last, data);

// allocate memory to the new node
struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));

// add data to the node
newNode->data = data;

// store the address of the current first node in the newNode
newNode->next = last->next;

last->next = newNode;

return last;
}

// add node to the end
struct Node* addEnd(struct Node* last, int data) {
// check if the node is empty
if (last == NULL) return addToEmpty(last, data);

// allocate memory to the new node
struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));

// add data to the node
newNode->data = data;

// store the address of the head node to next of newNode
newNode->next = last->next;

// point the current last node to the newNode
last->next = newNode;

// make newNode as the last node
last = newNode;

return last;
}

// insert node after a specific node
struct Node* addAfter(struct Node* last, int data, int item) {
// check if the list is empty
if (last == NULL) return NULL;

struct Node *newNode, *p;

p = last->next;
do {
// if the item is found, place newNode after it
if (p->data == item) {
// allocate memory to the new node
newNode = (struct Node*)malloc(sizeof(struct Node));

// add data to the node
newNode->data = data;

// make the next of the current node as the next of newNode
newNode->next = p->next;

// put newNode to the next of p
p->next = newNode;

// if p is the last node, make newNode as the last node
if (p == last) last = newNode;
return last;
}

p = p->next;
} while (p != last->next);

cout << "\nThe given node is not present in the list" << endl;
return last;
}

// delete a node
void deleteNode(Node** last, int key) {
// if linked list is empty
if (*last == NULL) return;

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

Node *temp = *last, *d;

// if last is to be deleted
if ((*last)->data == key) {
// find the node before the last node
while (temp->next != *last) temp = temp->next;

// point temp node to the next of last i.e. first node
temp->next = (*last)->next;
free(*last);
*last = temp->next;
}

// travel to the node to be deleted
while (temp->next != *last && temp->next->data != key) {
temp = temp->next;
}

// if node to be deleted was found
if (temp->next->data == key) {
d = temp->next;
temp->next = d->next;
free(d);
}
}

void traverse(struct Node* last) {
struct Node* p;

if (last == NULL) {
cout << "The list is empty" << endl;
return;
}

p = last->next;

do {
cout << p->data << " ";
p = p->next;

} while (p != last->next);
}

int main() {
struct Node* last = NULL;

traverse(last);

deleteNode(&last, 8);
cout << endl;

traverse(last);

return 0;
}``````

 Circular Linked List Complexity Time Complexity Space Complexity Insertion Operation O(1) or O(n) O(1) Deletion Operation O(1) O(1)

1. Complexity of Insertion Operation

• The insertion operations that do not require traversal have the time complexity of `O(1)`.
• And, an insertion that requires traversal has a time complexity of `O(n)`.
• The space complexity is `O(1)`.

2. Complexity of Deletion Operation

• All deletion operations run with a time complexity of `O(1)`.
• And, the space complexity is `O(1)`.