What is the time complexity of inserting a node in the beginning and end of circular linked list

Introduction

A circular linked list is a linked list where the last node points to the first node instead of NULL. This linked list comes with a pointer END which points to the last element. Since the last element points to the first element, this enables quick traversal from the last element to the first. The circular linked list also enables traversal of the entire linked list starting from any one point.

Table of Contents Show

Introduction
Circular Linked List
Circular Singly Linked List | Insertion
Linked List | Set 2 (Inserting a node)

The circular linked list can be represented as follows:

We shall now analyze the time and space complexity of the various operations that can be performed on a circular linked list, such as traversal, insertion, and deletion.

Circular Linked List

In this article, you will learn what circular linked list is and its types with implementation.

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:

1. Circular Singly Linked List

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

Circular Linked List Representation

2. Circular Doubly Linked List

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.

Circular Doubly Linked List Representation

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

Circular Singly Linked List | Insertion

We have discussed Singly and Circular Linked List in the following post:
Singly Linked List
Circular Linked List

Why Circular? In a singly linked list, for accessing any node of the linked list, we start traversing from the first node. If we are at any node in the middle of the list, then it is not possible to access nodes that precede the given node. This problem can be solved by slightly altering the structure of a singly linked list. In a singly linked list, the next part (pointer to next node) is NULL. If we utilize this link to point to the first node, then we can reach the preceding nodes. Refer to this for more advantages of circular linked lists.
The structure thus formed is a circular singly linked list and looks like this:

In this post, the implementation and insertion of a node in a Circular Linked List using a singly linked list are explained.

Implementation
To implement a circular singly linked list, we take an external pointer that points to the last node of the list. If we have a pointer last pointing to the last node, then last -> next will point to the first node.

The pointer last points to node Z and last -> next points to node P.

Why have we taken a pointer that points to the last node instead of the first node?
For the insertion of a node at the beginning, we need to traverse the whole list. Also, for insertion at the end, the whole list has to be traversed. If instead of start pointer, we take a pointer to the last node, then in both cases there won’t be any need to traverse the whole list. So insertion at the beginning or at the end takes constant time, irrespective of the length of the list.

Insertion
A node can be added in three ways:

Insertion in an empty list
Insertion at the beginning of the list
Insertion at the end of the list
Insertion in between the nodes

Insertion in an empty List
Initially, when the list is empty, the last pointer will be NULL.

After inserting node T,

After insertion, T is the last node, so the pointer last points to node T. And Node T is the first and the last node, so T points to itself.
Function to insert a node into an empty list,

C++

struct Node *addToEmpty(struct Node *last, int data)
{

// This function is only for empty list

if (last != NULL)

return last;

// Creating a node dynamically.

struct Node *temp =

(struct Node*)malloc(sizeof(struct Node));

// Assigning the data.

temp -> data = data;

last = temp;

// Note : list was empty. We link single node

// to itself.

temp -> next = last;

return last;
}

Java

static Node addToEmpty(Node last, int data)
{

// This function is only for empty list

if (last != null)

return last;

// Creating a node dynamically.

Node temp = new Node();

// Assigning the data.

temp.data = data;

last = temp;

// Note : list was empty. We link single node

// to itself.

temp.next = last;

return last;
}
// This code is contributed by gauravrajput1

Python3

# This function is only for empty list

def addToEmpty(self, data):

if (self.last != None):

return self.last

# Creating the newnode temp

temp = Node(data)

self.last = temp

# Creating the link

self.last.next = self.last

return self.last

# this code is contributed by shivanisinghss2110

static Node addToEmpty(Node last, int data)
{

// This function is only for empty list

if (last != null)

return last;

// Creating a node dynamically.

Node temp =

new Node();

// Assigning the data.

temp.data = data;

last = temp;

// Note : list was empty. We link single node

// to itself.

temp.next = last;

return last;
}
// This code contributed by umadevi9616

Javascript

<script>

function addToEmpty(last , data)
{

// This function is only for empty list

if (last != null)

return last;

// Creating a node dynamically.

var temp = new Node();

// Assigning the data.

temp.data = data;

last = temp;

// Note : list was empty. We link single node

// to itself.

temp.next = last;

return last;
}
// This code contributed by umadevi9616 
</script>

Insertion at the beginning of the list
To insert a node at the beginning of the list, follow these steps:
1. Create a node, say T.
2. Make T -> next = last -> next.
3. last -> next = T.

After insertion,

Function to insert nodes at the beginning of the list,

C++

struct Node *addBegin(struct Node *last, int data)
{

if (last == NULL)

return addToEmpty(last, data);

// Creating a node dynamically.

struct Node *temp

= (struct Node *)malloc(sizeof(struct Node));

// Assigning the data.

temp -> data = data;

// Adjusting the links.

temp -> next = last -> next;

last -> next = temp;

return last;
}

Java

static Node addBegin(Node last, int data)
{

if (last == null)

return addToEmpty(last, data);

// Creating a node dynamically

Node temp = new Node();

// Assigning the data

temp.data = data;

// Adjusting the links

temp.next = last.next;

last.next = temp;

return last;
}
// This code is contributed by rutvik_56

Python3

def addBegin(self, data):

if (self.last == None):

return self.addToEmpty(data)

temp = Node(data)

temp.next = self.last.next

self.last.next = temp

return self.last

# this code is contributed by shivanisinghss2110

static Node addBegin(Node last, int data)
{

if (last == null)

return addToEmpty(last, data);

// Creating a node dynamically

Node temp = new Node();

// Assigning the data

temp.data = data;

// Adjusting the links

temp.next = last.next;

last.next = temp;

return last;
}
// This code is contributed by Pratham76

Javascript

<script>

function addBegin(last , data)
{

if (last == null)

return addToEmpty(last, data);

// Creating a node dynamically.

var temp = new Node();

// Assigning the data.

temp.data = data;

// Adjusting the links.

temp.next = last.next;

last.next = temp;

return last;
}

// This code contributed by Shivani
</script>

Insertion at the end of the list
To insert a node at the end of the list, follow these steps:
1. Create a node, say T.
2. Make T -> next = last -> next;
3. last -> next = T.
4. last = T.

After insertion,

Function to insert a node at the end of the List

C++

struct Node *addEnd(struct Node *last, int data)
{

if (last == NULL)

return addToEmpty(last, data);

// Creating a node dynamically.

struct Node *temp =

(struct Node *)malloc(sizeof(struct Node));

// Assigning the data.

temp -> data = data;

// Adjusting the links.

temp -> next = last -> next;

last -> next = temp;

last = temp;

return last;
}

Java

static Node addEnd(Node last, int data)

{

if (last == null)

return addToEmpty(last, data);

// Creating a node dynamically. 

Node temp = new Node();
// Assigning the data.

temp.data = data;

// Adjusting the links. 

temp.next = last.next;

last.next = temp;

last = temp;

return last;

}

// This code is contributed by shivanisinghss2110

Python3

def addEnd(self, data):

if (self.last == None):

return self.addToEmpty(data)

# Assigning the data.

temp = Node(data)

# Adjusting the links.

temp.next = self.last.next

self.last.next = temp

self.last = temp

return self.last

# This code is contributed by shivanisinghss2110

static Node addEnd(Node last, int data)
{

if (last == null)

return addToEmpty(last, data);

// Creating a node dynamically.

Node temp = new Node();

// Assigning the data.

temp.data = data;

// Adjusting the links.

temp.next = last.next;

last.next = temp;

last = temp;

return last;
}
// This code is contributed by shivanisinghss2110

Javascript

<script>

function addEnd(last, data) {

if (last == null) return addToEmpty(last, data);

var temp = new Node();

temp.data = data;

temp.next = last.next;

last.next = temp;

last = temp;

return last;

}

// this code is contributed by shivanisinghss2110

</script>

Insertion in between the nodes
To insert a node in between the two nodes, follow these steps:
1. Create a node, say T.
2. Search for the node after which T needs to be inserted, say that node is P.
3. Make T -> next = P -> next;
4. P -> next = T.
Suppose 12 needs to be inserted after the node has the value 10,

After searching and insertion,

Function to insert a node at the end of the List,

C++

struct Node *addAfter(struct Node *last, int data, int item)
{

if (last == NULL)

return NULL;

struct Node *temp, *p;

p = last -> next;

// Searching the item.

do

{

if (p ->data == item)

{

// Creating a node dynamically.

temp = (struct Node *)malloc(sizeof(struct Node));

// Assigning the data.

temp -> data = data;

// Adjusting the links.

temp -> next = p -> next;

// Adding newly allocated node after p.

p -> next = temp;

// Checking for the last node.

if (p == last)

last = temp;

return last;

}

p = p -> next;

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

cout << item << " not present in the list." << endl;

return last;
}

Java

static Node addAfter(Node last, int data, int item)
{

if (last == null)

return null;

Node temp, p;

p = last.next;

do

{

if (p.data == item)

{

temp = new Node();

temp.data = data;

temp.next = p.next;

p.next = temp;

if (p == last)

last = temp;

return last;

}

p = p.next;

} while(p != last.next);

System.out.println(item + " not present in the list.");

return last;
}
// This code is contributed by shivanisinghss2110

Python3

def addAfter(self, data, item):

if (self.last == None):

return None

temp = Node(data)

p = self.last.next

while p:

if (p.data == item):

temp.next = p.next

p.next = temp

if (p == self.last):

self.last = temp

return self.last

else:

return self.last

p = p.next

if (p == self.last.next):

print(item, "not present in the list")

break

# This code is contributed by shivanisinghss2110

static Node addAfter(Node last, int data, int item)
{

if (last == null)

return null;

Node temp, p;

p = last.next;

do

{

if (p.data == item)

{

temp = new Node();

temp.data = data;

temp.next = p.next;

p.next = temp;

if (p == last)

last = temp;

return last;

}

p = p.next;

} while(p != last.next);

Console.WriteLine(item + " not present in the list.");

return last;

}
// This code is contributed by shivanisinghss2110

Javascript

<script>

function addAfter(last, data, item) {

if (last == null) return null;

var temp, p;

p = last.next;

do {

if (p.data == item) {

temp = new Node();

temp.data = data;

temp.next = p.next;

p.next = temp;

if (p == last) last = temp;

return last;

}

p = p.next;

} while (p != last.next);

document.write(item + " not present in the list. <br>");

return last;

}

// This code is contributed by shivanisinghss2110

</script>

The following is a complete program that uses all of the above methods to create a circular singly linked list.

C++

#include<bits/stdc++.h>

using namespace std;

struct Node
{

int data;

struct Node *next;
};

struct Node *addToEmpty(struct Node *last, int data)
{

// This function is only for empty list

if (last != NULL)

return last;

// Creating a node dynamically.

struct Node *temp =

(struct Node*)malloc(sizeof(struct Node));

// Assigning the data.

temp -> data = data;

last = temp;

// Creating the link.

last -> next = last;

return last;
}

struct Node *addBegin(struct Node *last, int data)
{

if (last == NULL)

return addToEmpty(last, data);

struct Node *temp =

(struct Node *)malloc(sizeof(struct Node));

temp -> data = data;

temp -> next = last -> next;

last -> next = temp;

return last;
}

struct Node *addEnd(struct Node *last, int data)
{

if (last == NULL)

return addToEmpty(last, data);

struct Node *temp =

(struct Node *)malloc(sizeof(struct Node));

temp -> data = data;

temp -> next = last -> next;

last -> next = temp;

last = temp;

return last;
}

struct Node *addAfter(struct Node *last, int data, int item)
{

if (last == NULL)

return NULL;

struct Node *temp, *p;

p = last -> next;

do

{

if (p ->data == item)

{

temp = (struct Node *)malloc(sizeof(struct Node));

temp -> data = data;

temp -> next = p -> next;

p -> next = temp;

if (p == last)

last = temp;

return last;

}

p = p -> next;

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

cout << item << " not present in the list." << endl;

return last;
}

void traverse(struct Node *last)
{

struct Node *p;

// If list is empty, return.

if (last == NULL)

{

cout << "List is empty." << endl;

return;

}

// Pointing to first Node of the list.

p = last -> next;

// Traversing the list.

do

{

cout << p -> data << " ";

p = p -> next;

}

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

int main()
{

struct Node *last = NULL;

last = addToEmpty(last, 6);

last = addBegin(last, 4);

last = addBegin(last, 2);

last = addEnd(last, 8);

last = addEnd(last, 12);

last = addAfter(last, 10, 8);

traverse(last);

return 0;
}

Java

class GFG
{

static class Node
{

int data;

Node next;
};

static Node addToEmpty(Node last, int data)
{

// This function is only for empty list

if (last != null)

return last;

// Creating a node dynamically.

Node temp = new Node();

// Assigning the data.

temp.data = data;

last = temp;

// Creating the link.

last.next = last;

return last;
}

static Node addBegin(Node last, int data)
{

if (last == null)

return addToEmpty(last, data);

Node temp = new Node();

temp.data = data;

temp.next = last.next;

last.next = temp;

return last;
}

static Node addEnd(Node last, int data)
{

if (last == null)

return addToEmpty(last, data);

Node temp = new Node();

temp.data = data;

temp.next = last.next;

last.next = temp;

last = temp;

return last;
}

static Node addAfter(Node last, int data, int item)
{

if (last == null)

return null;

Node temp, p;

p = last.next;

do

{

if (p.data == item)

{

temp = new Node();

temp.data = data;

temp.next = p.next;

p.next = temp;

if (p == last)

last = temp;

return last;

}

p = p.next;

} while(p != last.next);

System.out.println(item + " not present in the list.");

return last;
}

static void traverse(Node last)
{

Node p;

// If list is empty, return.

if (last == null)

{

System.out.println("List is empty.");

return;

}

// Pointing to first Node of the list.

p = last.next;

// Traversing the list.

do

{

System.out.print(p.data + " ");

p = p.next;

}

while(p != last.next);
}
// Driven code

public static void main(String[] args)
{

Node last = null;

last = addToEmpty(last, 6);

last = addBegin(last, 4);

last = addBegin(last, 2);

last = addEnd(last, 8);

last = addEnd(last, 12);

last = addAfter(last, 10, 8);

traverse(last);
}
}
/* This code contributed by PrinciRaj1992 */

Python3

class Node:

def __init__(self, data):

self.data = data

self.next = None

class CircularLinkedList:

def __init__(self):

self.last = None

# This function is only for empty list

def addToEmpty(self, data):

if (self.last != None):

return self.last

# Creating the newnode temp

temp = Node(data)

self.last = temp

# Creating the link

self.last.next = self.last

return self.last

def addBegin(self, data):

if (self.last == None):

return self.addToEmpty(data)

temp = Node(data)

temp.next = self.last.next

self.last.next = temp

return self.last

def addEnd(self, data):

if (self.last == None):

return self.addToEmpty(data)

temp = Node(data)

temp.next = self.last.next

self.last.next = temp

self.last = temp

return self.last

def addAfter(self, data, item):

if (self.last == None):

return None

temp = Node(data)

p = self.last.next

while p:

if (p.data == item):

temp.next = p.next

p.next = temp

if (p == self.last):

self.last = temp

return self.last

else:

return self.last

p = p.next

if (p == self.last.next):

print(item, "not present in the list")

break

def traverse(self):

if (self.last == None):

print("List is empty")

return

temp = self.last.next

while temp:

print(temp.data, end = " ")

temp = temp.next

if temp == self.last.next:

break
# Driver Code

if __name__ == '__main__':

llist = CircularLinkedList()

last = llist.addToEmpty(6)

last = llist.addBegin(4)

last = llist.addBegin(2)

last = llist.addEnd(8)

last = llist.addEnd(12)

last = llist.addAfter(10,8)

llist.traverse()
# This code is contributed by
# Aditya Singh

using System;

public class GFG
{

public class Node
{

public int data;

public Node next;
};

static Node addToEmpty(Node last, int data)
{

// This function is only for empty list

if (last != null)

return last;

// Creating a node dynamically.

Node temp = new Node();

// Assigning the data.

temp.data = data;

last = temp;

// Creating the link.

last.next = last;

return last;
}

static Node addBegin(Node last, int data)
{

if (last == null)

return addToEmpty(last, data);

Node temp = new Node();

temp.data = data;

temp.next = last.next;

last.next = temp;

return last;
}

static Node addEnd(Node last, int data)
{

if (last == null)

return addToEmpty(last, data);

Node temp = new Node();

temp.data = data;

temp.next = last.next;

last.next = temp;

last = temp;

return last;
}

static Node addAfter(Node last, int data, int item)
{

if (last == null)

return null;

Node temp, p;

p = last.next;

do

{

if (p.data == item)

{

temp = new Node();

temp.data = data;

temp.next = p.next;

p.next = temp;

if (p == last)

last = temp;

return last;

}

p = p.next;

} while(p != last.next);

Console.WriteLine(item + " not present in the list.");

return last;

}

static void traverse(Node last)
{

Node p;

// If list is empty, return.

if (last == null)

{

Console.WriteLine("List is empty.");

return;

}

// Pointing to first Node of the list.

p = last.next;

// Traversing the list.

do

{

Console.Write(p.data + " ");

p = p.next;

}

while(p != last.next);

}

// Driven code

public static void Main(String[] args)
{

Node last = null;

last = addToEmpty(last, 6);

last = addBegin(last, 4);

last = addBegin(last, 2);

last = addEnd(last, 8);

last = addEnd(last, 12);

last = addAfter(last, 10, 8);

traverse(last);
}
}
// This code contributed by Rajput-Ji

Javascript

<script>

class Node {

constructor() {

this.data = 0;

this.next = null;

}

}

function addToEmpty(last, data) {

// This function is only for empty list

if (last != null) return last;

// Creating a node dynamically.

var temp = new Node();

// Assigning the data.

temp.data = data;

last = temp;

// Creating the link.

last.next = last;

return last;

}

function addBegin(last, data) {

if (last == null) return addToEmpty(last, data);

var temp = new Node();

temp.data = data;

temp.next = last.next;

last.next = temp;

return last;

}

function addEnd(last, data) {

if (last == null) return addToEmpty(last, data);

var temp = new Node();

temp.data = data;

temp.next = last.next;

last.next = temp;

last = temp;

return last;

}

function addAfter(last, data, item) {

if (last == null) return null;

var temp, p;

p = last.next;

do {

if (p.data == item) {

temp = new Node();

temp.data = data;

temp.next = p.next;

p.next = temp;

if (p == last) last = temp;

return last;

}

p = p.next;

} while (p != last.next);

document.write(item + " not present in the list. <br>");

return last;

}

function traverse(last) {

var p;

// If list is empty, return.

if (last == null) {

document.write("List is empty.<br>");

return;

}

// Pointing to first Node of the list.

p = last.next;

// Traversing the list.

do {

document.write(p.data + " ");

p = p.next;

} while (p != last.next);

}

// Driven code

var last = null;

last = addToEmpty(last, 6);

last = addBegin(last, 4);

last = addBegin(last, 2);

last = addEnd(last, 8);

last = addEnd(last, 12);

last = addAfter(last, 10, 8);

traverse(last);

</script>

Output:

2 4 6 8 10 12

This article is contributed by Anuj Chauhan. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to . See your article appearing on the GeeksforGeeks main page and help other Geeks.
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Article Tags :

Linked List

circular linked list

Practice Tags :

Linked List

circular linked list

Read Full Article

Linked List | Set 2 (Inserting a node)

We have introduced Linked Lists in the previous post. We also created a simple linked list with 3 nodes and discussed linked list traversal.
All programs discussed in this post consider the following representations of linked list.

C++

// A linked list node 

class Node
{ 

public:

int data;

Node *next;
}; 
// This code is contributed by rathbhupendra

// A linked list node

struct Node
{

int data;

struct Node *next;
};

Java

// Linked List Class

class LinkedList
{

Node head; // head of list

/* Node Class */

class Node

{

int data;

Node next;

// Constructor to create a new node

Node(int d) {data = d; next = null; }

}
}

Python

# Node class

class Node:

# Function to initialize the node object

def __init__(self, data):

self.data = data # Assign data

self.next = None # Initialize next as null
# Linked List class

class LinkedList:

# Function to initialize the Linked List object

def __init__(self):

self.head = None

/* Linked list Node*/

public class Node
{

public int data;

public Node next;

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

Javascript

<script>
// Linked List Class

var head; // head of list

/* Node Class */

class Node {

// Constructor to create a new node

constructor(d) {

this.data = d;

this.next = null;

}

}
// This code is contributed by todaysgaurav 
</script>

In this post, methods to insert a new node in linked list are discussed. A node can be added in three ways
1) At the front of the linked list
2) After a given node.
3) At the end of the linked list.