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Types of Linked List

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A linked list is a linear data structure, in which the elements are not stored at contiguous memory locations. The elements in a linked list are linked using pointers. In simple words, a linked list consists of nodes where each node contains a data field and a reference(link) to the next node in the list. 

Types Of Linked List:

1. Singly Linked List

It is the simplest type of linked list in which every node contains some data and a pointer to the next node of the same data type. 

The node contains a pointer to the next node means that the node stores the address of the next node in the sequence. A single linked list allows the traversal of data only in one way. Below is the image for the same:

Below is the structure of the singly linked list

C++




// Node of a singly linked list
class Node {
public:
    int data;
  
    // Pointer to next node in LL
    Node* next;
};


Java




// Node of a singly linked list
static class Node {
    int data;
  
    // Pointer to next node in LL
    Node next;
};
  
// this code is contributed by shivani


Python3




# Node of a singly linked list
class Node:
    def __init__(self, data):
        self.data = data
        self.next = None


C#




// Structure of a singly linked list Node
public class Node {
    public int data;
  
    // Pointer to next node in LL
    public Node next;
};
  
// this code is contributed by shivanisinghss2110


Javascript




// Node of a singly linked list
class Node
{
    constructor()
    {
        this.data=0;
          
        // Pointer to next node
        this.next=null;
    }
}
  
// This code is contributed by SHUBHAMSINGH10


Creation and Traversal of Singly Linked List:

C++




// C++ program to illustrate creation
// and traversal of Singly Linked List
  
#include <bits/stdc++.h>
using namespace std;
  
// Structure of Node
class Node {
public:
    int data;
    Node* next;
};
  
// Function to print the content of
// linked list starting from the
// given node
void printList(Node* n)
{
  
    // Iterate till n reaches NULL
    while (n != NULL) {
  
        // Print the data
        cout << n->data << " ";
        n = n->next;
    }
}
  
// Driver Code
int main()
{
    Node* head = NULL;
    Node* second = NULL;
    Node* third = NULL;
  
    // Allocate 3 nodes in the heap
    head = new Node();
    second = new Node();
    third = new Node();
  
    // Assign data in first node
    head->data = 1;
  
    // Link first node with second
    head->next = second;
  
    // Assign data to second node
    second->data = 2;
    second->next = third;
  
    // Assign data to third node
    third->data = 3;
    third->next = NULL;
  
    printList(head);
  
    return 0;
}


Java




// Java program to illustrate
// creation and traversal of
// Singly Linked List
class GFG {
  
    // Structure of Node
    static class Node {
        int data;
        Node next;
    };
  
    // Function to print the content of
    // linked list starting from the
    // given node
    static void printList(Node n)
    {
        // Iterate till n reaches null
        while (n != null) {
            // Print the data
            System.out.print(n.data + " ");
            n = n.next;
        }
    }
  
    // Driver Code
    public static void main(String[] args)
    {
        Node head = null;
        Node second = null;
        Node third = null;
  
        // Allocate 3 nodes in
        // the heap
        head = new Node();
        second = new Node();
        third = new Node();
  
        // Assign data in first
        // node
        head.data = 1;
  
        // Link first node with
        // second
        head.next = second;
  
        // Assign data to second
        // node
        second.data = 2;
        second.next = third;
  
        // Assign data to third
        // node
        third.data = 3;
        third.next = null;
  
        printList(head);
    }
}
  
// This code is contributed by Princi Singh


Python3




# structure of Node
class Node:
    def __init__(self, data):
        self.data = data
        self.next = None
  
  
class LinkedList:
    def __init__(self):
        self.head = None
        self.last_node = None
  
    # function to add elements to linked list
    def append(self, data):
        # if linked list is empty then last_node will be none so in if condition head will be created
        if self.last_node is None:
            self.head = Node(data)
            self.last_node = self.head
        # adding node to the tail of linked list
        else:
            self.last_node.next = Node(data)
            self.last_node = self.last_node.next
  
# function to print the content of linked list
    def display(self):
        current = self.head
      # traversing the linked list
        while current is not None:
          # at each node printing its data
            print(current.data, end=' ')
           # giving current next node
            current = current.next
        print()
  
# Driver code
if __name__ == '__main__':
    L = LinkedList()
    # adding elements to the linked list
    L.append(1)
    L.append(2)
    L.append(3)
    # displaying elements of linked list
    L.display()


C#




// C# program to illustrate
// creation and traversal of
// Singly Linked List
using System;
  
class GFG {
  
    // Structure of Node
    public class Node {
        public int data;
        public Node next;
    };
  
    // Function to print the content of
    // linked list starting from the
    // given node
    static void printList(Node n)
    {
  
        // Iterate till n reaches null
        while (n != null) {
  
            // Print the data
            Console.Write(n.data + " ");
            n = n.next;
        }
    }
  
    // Driver Code
    public static void Main(String[] args)
    {
        Node head = null;
        Node second = null;
        Node third = null;
  
        // Allocate 3 nodes in
        // the heap
        head = new Node();
        second = new Node();
        third = new Node();
  
        // Assign data in first
        // node
        head.data = 1;
  
        // Link first node with
        // second
        head.next = second;
  
        // Assign data to second
        // node
        second.data = 2;
        second.next = third;
  
        // Assign data to third
        // node
        third.data = 3;
        third.next = null;
  
        printList(head);
    }
}
  
// This code is contributed by Amit Katiyar


Javascript




// JavaScript program to illustrate
// creation and traversal of
// Singly Linked List
  
// Structure of Node
class Node
{
    constructor()
    {
        this.data=0;
        this.next=null;
    }
}
  
// Function to print the content of
// linked list starting from the
// given node
function printList(n)
{
    // Iterate till n reaches null
  while (n != null)
  {
    // Print the data
    document.write(n.data + " ");
    n = n.next;
  }
}
  
// Driver Code
let head = null;
let second = null;
let third = null;
  
// Allocate 3 nodes in
// the heap
head = new Node();
second = new Node();
third = new Node();
  
// Assign data in first
// node
head.data = 1;
  
// Link first node with
// second
head.next = second;
  
// Assign data to second
// node
second.data = 2;
second.next = third;
  
// Assign data to third
// node
third.data = 3;
third.next = null;
  
printList(head);
  
  
// This code is contributed by unknown2108


Output

1 2 3 

Time Complexity: O(N)
Auxiliary Space: O(N)

2. Doubly Linked List

A doubly linked list or a two-way linked list is a more complex type of linked list that contains a pointer to the next as well as the previous node in sequence. 

Therefore, it contains three parts of data, a pointer to the next node, and a pointer to the previous node. This would enable us to traverse the list in the backward direction as well. Below is the image for the same:

Structure of Doubly Linked List:

C++




// Node of a doubly linked list
struct Node {
    int data;
  
    // Pointer to next node in DLL
    struct Node* next;
  
    // Pointer to the previous node in DLL
    struct Node* prev;
};


Java




// Doubly linked list
// node
static class Node {
    int data;
  
    // Pointer to next node in DLL
    Node next;
  
    // Pointer to the previous node in DLL
    Node prev;
};
  
// This code is contributed by shivani


Python3




# structure of Node
class Node:
    def __init__(self, data):
        self.previous = None
        self.data = data
        self.next = None


C#




// Doubly linked list
// node
public class Node {
    public int data;
  
    // Pointer to next node in DLL
    public Node next;
  
    // Pointer to the previous node in DLL
    public Node prev;
};
  
// This code is contributed by shivanisinghss2110


Javascript




<script>
// Class for Doubly Linked List
    var head; // head of list
  
    /* Doubly Linked list Node */
    class Node {
        // Constructor to create a new node
            // next and prev is by default initialized as null
            constructor(val) {
                this.data = val;
                this.prev = null;
                this.next = null;
            }
        }
          
// This code contributed by Susobhan Akhuli
</script>


Creation and Traversal of Doubly Linked List:

C++




// C++ program to illustrate creation
// and traversal of Doubly Linked List
  
#include <bits/stdc++.h>
using namespace std;
  
// Doubly linked list node
class Node {
public:
    int data;
    Node* next;
    Node* prev;
};
  
// Function to push a new element in
// the Doubly Linked List
void push(Node** head_ref, int new_data)
{
    // Allocate node
    Node* new_node = new Node();
  
    // Put in the data
    new_node->data = new_data;
  
    // Make next of new node as
    // head and previous as NULL
    new_node->next = (*head_ref);
    new_node->prev = NULL;
  
    // Change prev of head node to
    // the new node
    if ((*head_ref) != NULL)
        (*head_ref)->prev = new_node;
  
    // Move the head to point to
    // the new node
    (*head_ref) = new_node;
}
  
// Function to traverse the Doubly LL
// in the forward & backward direction
void printList(Node* node)
{
    Node* last;
  
    cout << "\nTraversal in forward"
         << " direction \n";
    while (node != NULL) {
  
        // Print the data
        cout << " " << node->data << " ";
        last = node;
        node = node->next;
    }
  
    cout << "\nTraversal in reverse"
         << " direction \n";
    while (last != NULL) {
  
        // Print the data
        cout << " " << last->data << " ";
        last = last->prev;
    }
}
  
// Driver Code
int main()
{
    // Start with the empty list
    Node* head = NULL;
  
    // Insert 6.
    // So linked list becomes 6->NULL
    push(&head, 6);
  
    // Insert 7 at the beginning. So
    // linked list becomes 7->6->NULL
    push(&head, 7);
  
    // Insert 1 at the beginning. So
    // linked list becomes 1->7->6->NULL
    push(&head, 1);
  
    cout << "Created DLL is: ";
    printList(head);
  
    return 0;
}


Java




// Java program to illustrate
// creation and traversal of
// Doubly Linked List
  
import java.util.*;
class GFG {
  
    // Doubly linked list
    // node
    static class Node {
        int data;
        Node next;
        Node prev;
    };
  
    static Node head_ref;
  
    // Function to push a new
    // element in the Doubly
    // Linked List
    static void push(int new_data)
    {
        // Allocate node
        Node new_node = new Node();
  
        // Put in the data
        new_node.data = new_data;
  
        // Make next of new node as
        // head and previous as null
        new_node.next = head_ref;
        new_node.prev = null;
  
        // Change prev of head node to
        // the new node
        if (head_ref != null)
            head_ref.prev = new_node;
  
        // Move the head to point to
        // the new node
        head_ref = new_node;
    }
  
    // Function to traverse the
    // Doubly LL in the forward
    // & backward direction
    static void printList(Node node)
    {
        Node last = null;
  
        System.out.print("\nTraversal in forward"
                         + " direction \n");
        while (node != null) {
            // Print the data
            System.out.print(" " + node.data + " ");
            last = node;
            node = node.next;
        }
  
        System.out.print("\nTraversal in reverse"
                         + " direction \n");
  
        while (last != null) {
            // Print the data
            System.out.print(" " + last.data + " ");
            last = last.prev;
        }
    }
  
    // Driver Code
    public static void main(String[] args)
    {
        // Start with the empty list
        head_ref = null;
  
        // Insert 6.
        // So linked list becomes
        // 6.null
        push(6);
  
        // Insert 7 at the beginning.
        // So linked list becomes
        // 7.6.null
        push(7);
  
        // Insert 1 at the beginning.
        // So linked list becomes
        // 1.7.6.null
        push(1);
  
        System.out.print("Created DLL is: ");
        printList(head_ref);
    }
}
  
// This code is contributed by Princi Singh


Python3




# Python3 program to illustrate
# creation and traversal of
# Doubly Linked List
  
# structure of Node
class Node:
    def __init__(self, data):
        self.previous = None
        self.data = data
        self.next = None
  
  
class DoublyLinkedList:
    def __init__(self):
        self.head = None
        self.start_node = None
        self.last_node = None
  
    # function to add elements to doubly linked list
    def append(self, data):
        # is doubly linked list is empty then last_node will be none so in if condition head will be created
        if self.last_node is None:
            self.head = Node(data)
            self.last_node = self.head
        # adding node to the tail of doubly linked list
        else:
            new_node = Node(data)
            self.last_node.next = new_node
            new_node.previous = self.last_node
            new_node.next = None
            self.last_node = new_node
  
    # function to printing and traversing the content of doubly linked list from left to right and right to left
    def display(self, Type):
        if Type == 'Left_To_Right':
            current = self.head
            while current is not None:
                print(current.data, end=' ')
                current = current.next
            print()
        else:
            current = self.last_node
            while current is not None:
                print(current.data, end=' ')
                current = current.previous
            print()
  
# Driver code
if __name__ == '__main__':
    L = DoublyLinkedList()
    L.append(1)
    L.append(2)
    L.append(3)
    L.append(4)
    L.display('Left_To_Right')
    L.display('Right_To_Left')


C#




// C# program to illustrate
// creation and traversal of
// Doubly Linked List
  
using System;
  
class GFG {
  
    // Doubly linked list
    // node
    public class Node {
        public int data;
        public Node next;
        public Node prev;
    };
  
    static Node head_ref;
  
    // Function to push a new
    // element in the Doubly
    // Linked List
    static void push(int new_data)
    {
  
        // Allocate node
        Node new_node = new Node();
  
        // Put in the data
        new_node.data = new_data;
  
        // Make next of new node as
        // head and previous as null
        new_node.next = head_ref;
        new_node.prev = null;
  
        // Change prev of head node to
        // the new node
        if (head_ref != null)
            head_ref.prev = new_node;
  
        // Move the head to point to
        // the new node
        head_ref = new_node;
    }
  
    // Function to traverse the
    // Doubly LL in the forward
    // & backward direction
    static void printList(Node node)
    {
        Node last = null;
  
        Console.Write("\nTraversal in forward"
                      + " direction \n");
  
        while (node != null) {
  
            // Print the data
            Console.Write(" " + node.data + " ");
            last = node;
            node = node.next;
        }
  
        Console.Write("\nTraversal in reverse"
                      + " direction \n");
  
        while (last != null) {
  
            // Print the data
            Console.Write(" " + last.data + " ");
            last = last.prev;
        }
    }
  
    // Driver Code
    public static void Main(String[] args)
    {
  
        // Start with the empty list
        head_ref = null;
  
        // Insert 6.
        // So linked list becomes
        // 6.null
        push(6);
  
        // Insert 7 at the beginning.
        // So linked list becomes
        // 7.6.null
        push(7);
  
        // Insert 1 at the beginning.
        // So linked list becomes
        // 1.7.6.null
        push(1);
  
        Console.Write("Created DLL is: ");
        printList(head_ref);
    }
}
  
// This code is contributed by Amit Katiyar


Javascript




<script>
// Javascript program to illustrate creation
// and traversal of Doubly Linked List
  
// Class for Doubly Linked List
  
    var head; // head of list
  
    // Doubly Linked list Node
    class Node {
  
        // Constructor to create a new node
        // next and prev are by default initialized as null
constructor(d) {
            this.data = d;
            this.next = null;
            this.prev = null;
        }
    }
  
    // Adding a node at the front of the list
    function push(new_data) {
        /*
        * 1. allocate node 2. put in the data
        */
        var new_Node = new Node(new_data);
  
        /* 3. Make next of new node as head and previous as NULL */
        new_Node.next = head;
        new_Node.prev = null;
  
        /* 4. change prev of head node to new node */
        if (head != null)
            head.prev = new_Node;
  
        /* 5. move the head to point to the new node */
        head = new_Node;
    }
      
    // This function prints contents of
    // linked list starting from the given node
    function printlist(node) {
        var last = null;
        document.write("<br/>Traversal in forward Direction<br/>");
        while (node != null) {
            document.write(node.data + " ");
            last = node;
            node = node.next;
        }
        document.write();
        document.write("<br/>Traversal in reverse direction<br/>");
        while (last != null) {
            document.write(last.data + " ");
            last = last.prev;
        }
    }
  
    // Driver program to test above functions
      
        // Start with the empty list
          
        // Insert 6. So linked list becomes 6->NULL
        push(6);
  
        // Insert 7 at the beginning. So
        // linked list becomes 7->6->NULL
        push(7);
  
        // Insert 1 at the beginning. So
        // linked list becomes 1->7->6->NULL
        push(1);
  
        document.write("Created DLL is: ");
        printlist(head);
  
// This code is contributed by Susobhan Akhuli
</script>


Output

Created DLL is: 
Traversal in forward direction 
 1  7  6 
Traversal in reverse direction 
 6  7  1

Time Complexity:
The time complexity of the push() function is O(1) as it performs constant-time operations to insert a new node at the beginning of the doubly linked list. The time complexity of the printList() function is O(n) where n is the number of nodes in the doubly linked list. This is because it traverses the entire list twice, once in the forward direction and once in the backward direction. Therefore, the overall time complexity of the program is O(n).

Space Complexity:
The space complexity of the program is O(n) as it uses a doubly linked list to store the data, which requires n nodes. Additionally, it uses a constant amount of auxiliary space to create a new node in the push() function. Therefore, the overall space complexity of the program is O(n).

3. Circular Linked List

A circular linked list is that in which the last node contains the pointer to the first node of the list. 

While traversing a circular linked list, we can begin at any node and traverse the list in any direction forward and backward until we reach the same node we started. Thus, a circular linked list has no beginning and no end. Below is the image for the same:

Below is the structure of the Circular Linked List:

C++




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


Java




// Structure for a node
static class Node {
    int data;
  
    // Pointer to next node in CLL
    Node next;
};
  
// This code is contributed by shivanisinghss2110


Python3




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


C#




// Structure for a node
public class Node {
    public int data;
  
    // Pointer to next node in CLL
    public Node next;
};
  
// This code is contributed by shivanisinghss2110


Javascript




<script>
    /* Circular Linked list Node */
    class Node {
        // Constructor to create a new node
        // next and data are by default initialized as null and 0 respectively
        constructor() {
            this.data = 0;
            this.next = null;
        }
    }
// This code contributed by Susobhan Akhuli
</script>


Creation and Traversal of Circular Linked List:

C++




// C++ program to illustrate creation
// and traversal of Circular LL
  
#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 Circular LL
void push(Node** head_ref, int data)
{
    Node* ptr1 = new Node();
    Node* temp = *head_ref;
    ptr1->data = data;
    ptr1->next = *head_ref;
  
    // If linked list is not NULL then
    // set the next of last node
    if (*head_ref != NULL) {
        while (temp->next != *head_ref) {
            temp = temp->next;
        }
        temp->next = ptr1;
    }
  
    // For the first node
    else
        ptr1->next = ptr1;
  
    *head_ref = ptr1;
}
  
// Function to print nodes in the
// Circular Linked List
void printList(Node* head)
{
    Node* temp = head;
    if (head != NULL) {
        do {
  
            // Print the data
            cout << temp->data << " ";
            temp = temp->next;
        } while (temp != head);
    }
}
  
// Driver Code
int main()
{
    // Initialize list as empty
    Node* head = NULL;
  
    // Created linked list will
    // be 11->2->56->12
    push(&head, 12);
    push(&head, 56);
    push(&head, 2);
    push(&head, 11);
  
    cout << "Contents of Circular"
         << " Linked List\n ";
    
      // Function call
    printList(head);
  
    return 0;
}


Java




// Java program to illustrate
// creation and traversal of
// Circular LL
  
import java.util.*;
class GFG {
  
    // Structure for a
    // node
    static class Node {
        int data;
        Node next;
    };
  
    // Function to insert a node
    // at the beginning of Circular
    // LL
    static Node push(Node head_ref, int data)
    {
        Node ptr1 = new Node();
        Node temp = head_ref;
        ptr1.data = data;
        ptr1.next = head_ref;
  
        // If linked list is not
        // null then set the next
        // of last node
        if (head_ref != null) {
            while (temp.next != head_ref) {
                temp = temp.next;
            }
            temp.next = ptr1;
        }
  
        // For the first node
        else
            ptr1.next = ptr1;
  
        head_ref = ptr1;
        return head_ref;
    }
  
    // Function to print nodes in
    // the Circular Linked List
    static void printList(Node head)
    {
        Node temp = head;
        if (head != null) {
            do {
                // Print the data
                System.out.print(temp.data + " ");
                temp = temp.next;
            } while (temp != head);
        }
    }
  
    // Driver Code
    public static void main(String[] args)
    {
        // Initialize list as empty
        Node head = null;
  
        // Created linked list will
        // be 11.2.56.12
        head = push(head, 12);
        head = push(head, 56);
        head = push(head, 2);
        head = push(head, 11);
  
        System.out.print("Contents of Circular"
                         + " Linked List\n ");
        
        // Function call
        printList(head);
    }
}
  
// This code is contributed by gauravrajput1


Python3




# Python3 program to illustrate
# creation and traversal of
# Circular LL
  
# structure of Node
class Node:
    def __init__(self, data):
        self.data = data
        self.next = None
  
  
class CircularLinkedList:
    def __init__(self):
        self.head = None
        self.last_node = None
  
    # function to add elements to circular linked list
    def append(self, data):
        # is circular linked list is empty then last_node will be none so in if condition head will be created
        if self.last_node is None:
            self.head = Node(data)
            self.last_node = self.head
        # adding node to the tail of circular linked list
        else:
            self.last_node.next = Node(data)
            self.last_node = self.last_node.next
            self.last_node.next = self.head
  
    # function to print the content of circular linked list
    def display(self):
        current = self.head
        while current is not None:
            print(current.data, end=' ')
            current = current.next
            if current == self.head:
                break
        print()
  
# Driver code
if __name__ == '__main__':
    L = CircularLinkedList()
    L.append(12)
    L.append(56)
    L.append(2)
    L.append(11)
          
    # Function call
    L.display()


C#




// C# program to illustrate
// creation and traversal of
// Circular LL
  
using System;
  
class GFG {
  
    // Structure for a
    // node
    public class Node {
        public int data;
        public Node next;
    };
  
    // Function to insert a node
    // at the beginning of Circular
    // LL
    static Node push(Node head_ref, int data)
    {
        Node ptr1 = new Node();
        Node temp = head_ref;
        ptr1.data = data;
        ptr1.next = head_ref;
  
        // If linked list is not
        // null then set the next
        // of last node
        if (head_ref != null) {
            while (temp.next != head_ref) {
                temp = temp.next;
            }
            temp.next = ptr1;
        }
  
        // For the first node
        else
            ptr1.next = ptr1;
  
        head_ref = ptr1;
        return head_ref;
    }
  
    // Function to print nodes in
    // the Circular Linked List
    static void printList(Node head)
    {
        Node temp = head;
  
        if (head != null) {
            do {
  
                // Print the data
                Console.Write(temp.data + " ");
                temp = temp.next;
            } while (temp != head);
        }
    }
  
    // Driver Code
    public static void Main(String[] args)
    {
  
        // Initialize list as empty
        Node head = null;
  
        // Created linked list will
        // be 11.2.56.12
        head = push(head, 12);
        head = push(head, 56);
        head = push(head, 2);
        head = push(head, 11);
  
        Console.Write("Contents of Circular "
                      + "Linked List\n ");
  
          // Function call
        printList(head);
    }
}
  
// This code is contributed by gauravrajput1


Javascript




<script>
    class Node {
        constructor() {
            this.data = 0;
            this.next = null;
        }
    }
  
  
function push(head, data) {
      
    // If linked list is NULL then
    if (head == null) {
        // Creating a node dynamically.
        var temp = new Node();
          
        // Assigning the data.
        temp.data = data;
          
        // Creatring the links.
        head = temp;
        head.next = head;
    }
      
    // If linked list is not NULL then
    else{
        // Creating a node dynamically.    
        var temp = new Node();
          
        // Assigning the data.
        temp.data = data;
          
        // Reset the links.
        temp.next = head.next;
        head.next = temp;
    }
    return head;
}
  
function printList(head) {
    var p;
    // If list is empty, return.    
    if (head == null) {
        document.write("List is empty.<br>");
        return;
    }
    // Pointing to first Node of the list.
    p = head.next;
    // Traversing the list.    
    do {
        document.write(p.data + " ");
        p = p.next;
    } while (p != head.next);
}
  
// Driver code
var head = null;
  
// Created linked list will
// be 11->2->56->12
head = push(head, 12);
head = push(head, 56);
head = push(head, 2);
head = push(head, 11);
  
  
document.write("Contents of Circular Linked List<br>");
printList(head);
  
// This code contributed by Susobhan Akhuli
</script>


Output

Contents of Circular Linked List
 11 2 56 12

Time Complexity:

Insertion at the beginning of the circular linked list takes O(1) time complexity.
Traversing and printing all nodes in the circular linked list takes O(n) time complexity where n is the number of nodes in the linked list.
Therefore, the overall time complexity of the program is O(n).

Auxiliary Space:

The space required by the program depends on the number of nodes in the circular linked list.
In the worst-case scenario, when there are n nodes, the space complexity of the program will be O(n) as n new nodes will be created to store the data.
Additionally, some extra space is required for the temporary variables and the function calls.
Therefore, the auxiliary space complexity of the program is O(n).

4. Doubly Circular linked list

A Doubly Circular linked list or a circular two-way linked list is a more complex type of linked list that contains a pointer to the next as well as the previous node in the sequence. The difference between the doubly linked and circular doubly list is the same as that between a singly linked list and a circular linked list. The circular doubly linked list does not contain null in the previous field of the first node. Below is the image for the same:

Below is the structure of the Doubly Circular Linked List:

C++




// Node of doubly circular linked list
struct Node {
  
    int data;
  
    // Pointer to next node in DCLL
    struct Node* next;
  
    // Pointer to the previous node in DCLL
    struct Node* prev;
};


Java




// Structure of a Node
static class Node
{
    int data;
      
    // Pointer to next node in DCLL
    Node next;
      
    // Pointer to the previous node in DCLL
    Node prev;
};
  
//this code is contributed by shivanisinghss2110


Python3




# structure of Node
class Node:
    def __init__(self, data):
        self.previous = None
        self.data = data
        self.next = None


C#




// Structure of a Node
public class Node
{
    public  int data;
      
    // Pointer to next node in DCLL
    public Node next;
      
    // Pointer to the previous node in DCLL
    public Node prev;
};
  
// This code is contributed by shivanisinghss2110


Javascript




<script>
    // head list
    var start = null;
      
    // class of a Node
    class Node {
        constructor() {
            this.data = 0;
            this.next = null;
            this.prev = null;
        }
    }
      
    // This code is contributed by Susobhan Akhuli
</script>


Creation and Traversal of Doubly Circular Linked List:

C++




// C++ program to illustrate creation
// & traversal of Doubly Circular LL
  
#include <bits/stdc++.h>
using namespace std;
  
// Structure of a Node
struct Node {
    int data;
    struct Node* next;
    struct Node* prev;
};
  
// Function to insert Node at
// the beginning of the List
void insertBegin(struct Node** start, int value)
{
    // If the list is empty
    if (*start == NULL) {
        struct Node* new_node = new Node;
        new_node->data = value;
        new_node->next = new_node->prev = new_node;
        *start = new_node;
        return;
    }
  
    // Pointer points to last Node
    struct Node* last = (*start)->prev;
  
    struct Node* new_node = new Node;
  
    // Inserting the data
    new_node->data = value;
  
    // Update the previous and
    // next of new node
    new_node->next = *start;
    new_node->prev = last;
  
    // Update next and previous
    // pointers of start & last
    last->next = (*start)->prev = new_node;
  
    // Update start pointer
    *start = new_node;
}
  
// Function to traverse the circular
// doubly linked list
void display(struct Node* start)
{
    struct Node* temp = start;
  
    printf("\nTraversal in"
           " forward direction \n");
    while (temp->next != start) {
        printf("%d ", temp->data);
        temp = temp->next;
    }
    printf("%d ", temp->data);
  
    printf("\nTraversal in "
           "reverse direction \n");
    Node* last = start->prev;
    temp = last;
  
    while (temp->prev != last) {
  
        // Print the data
        printf("%d ", temp->data);
        temp = temp->prev;
    }
    printf("%d ", temp->data);
}
  
// Driver Code
int main()
{
    // Start with the empty list
    struct Node* start = NULL;
  
    // Insert 5
    // So linked list becomes 5->NULL
    insertBegin(&start, 5);
  
    // Insert 4 at the beginning
    // So linked list becomes 4->5
    insertBegin(&start, 4);
  
    // Insert 7 at the end
    // So linked list becomes 7->4->5
    insertBegin(&start, 7);
  
    printf("Created circular doubly"
           " linked list is: ");
    display(start);
  
    return 0;
}


Java




// Java program to illustrate creation
// & traversal of Doubly Circular LL
  
import java.util.*;
  
class GFG {
  
    // Structure of a Node
    static class Node {
        int data;
        Node next;
        Node prev;
    };
  
    // Start with the empty list
    static Node start = null;
  
    // Function to insert Node at
    // the beginning of the List
    static void insertBegin(int value)
    {
        // If the list is empty
        if (start == null) {
            Node new_node = new Node();
            new_node.data = value;
            new_node.next = new_node.prev = new_node;
            start = new_node;
            return;
        }
  
        // Pointer points to last Node
        Node last = (start).prev;
  
        Node new_node = new Node();
  
        // Inserting the data
        new_node.data = value;
  
        // Update the previous and
        // next of new node
        new_node.next = start;
        new_node.prev = last;
  
        // Update next and previous
        // pointers of start & last
        last.next = (start).prev = new_node;
  
        // Update start pointer
        start = new_node;
    }
  
    // Function to traverse the circular
    // doubly linked list
    static void display()
    {
        Node temp = start;
  
        System.out.printf("\nTraversal in"
                          + " forward direction \n");
        while (temp.next != start) {
            System.out.printf("%d ", temp.data);
            temp = temp.next;
        }
        System.out.printf("%d ", temp.data);
  
        System.out.printf("\nTraversal in "
                          + "reverse direction \n");
        Node last = start.prev;
        temp = last;
  
        while (temp.prev != last) {
  
            // Print the data
            System.out.printf("%d ", temp.data);
            temp = temp.prev;
        }
        System.out.printf("%d ", temp.data);
    }
  
    // Driver Code
    public static void main(String[] args)
    {
  
        // Insert 5
        // So linked list becomes 5.null
        insertBegin(5);
  
        // Insert 4 at the beginning
        // So linked list becomes 4.5
        insertBegin(4);
  
        // Insert 7 at the end
        // So linked list becomes 7.4.5
        insertBegin(7);
  
        System.out.printf("Created circular doubly"
                          + " linked list is: ");
        display();
    }
}
  
// This code is contributed by shikhasingrajput


Python3




# Python3 program to illustrate creation
# & traversal of Doubly Circular LL
  
# structure of Node
class Node:
    def __init__(self, data):
        self.previous = None
        self.data = data
        self.next = None
  
  
class DoublyLinkedList:
    def __init__(self):
        self.head = None
        self.start_node = None
        self.last_node = None
  
    # function to add elements to doubly linked list
    def append(self, data):
        # is doubly linked list is empty then last_node will be none so in if condition head will be created
        if self.last_node is None:
            self.head = Node(data)
            self.last_node = self.head
        # adding node to the tail of doubly linked list
        else:
            new_node = Node(data)
            self.last_node.next = new_node
            new_node.previous = self.last_node
            new_node.next = self.head
            self.head.previous = new_node
            self.last_node = new_node
  
    # function to print the content of doubly linked list
    def display(self, Type='Left_To_Right'):
        if Type == 'Left_To_Right':
            current = self.head
            while current.next is not None:
                print(current.data, end=' ')
                current = current.next
                if current == self.head:
                    break
            print()
        else:
            current = self.last_node
            while current.previous is not None:
                print(current.data, end=' ')
                current = current.previous
                if current == self.last_node.next:
                    print(self.last_node.next.data, end=' ')
                    break
            print()
  
  
if __name__ == '__main__':
    L = DoublyLinkedList()
    L.append(1)
    L.append(2)
    L.append(3)
    L.append(4)
    L.display('Left_To_Right')
    L.display('Right_To_Left')


C#




// C# program to illustrate creation
// & traversal of Doubly Circular LL
  
using System;
  
public class GFG {
  
    // Structure of a Node
    public
  
        class Node {
        public
  
            int data;
        public
  
            Node next;
        public
  
            Node prev;
    };
  
    // Start with the empty list
    static Node start = null;
  
    // Function to insert Node at
    // the beginning of the List
    static void insertBegin(int value)
    {
        Node new_node = new Node();
  
        // If the list is empty
        if (start == null) {
  
            new_node.data = value;
            new_node.next = new_node.prev = new_node;
            start = new_node;
            return;
        }
  
        // Pointer points to last Node
        Node last = (start).prev;
  
        // Inserting the data
        new_node.data = value;
  
        // Update the previous and
        // next of new node
        new_node.next = start;
        new_node.prev = last;
  
        // Update next and previous
        // pointers of start & last
        last.next = (start).prev = new_node;
  
        // Update start pointer
        start = new_node;
    }
  
    // Function to traverse the circular
    // doubly linked list
    static void display()
    {
        Node temp = start;
  
        Console.Write("\nTraversal in"
                      + " forward direction \n");
        while (temp.next != start) {
            Console.Write(temp.data + " ");
            temp = temp.next;
        }
        Console.Write(temp.data + " ");
  
        Console.Write("\nTraversal in "
                      + "reverse direction \n");
        Node last = start.prev;
        temp = last;
  
        while (temp.prev != last) {
  
            // Print the data
            Console.Write(temp.data + " ");
            temp = temp.prev;
        }
        Console.Write(temp.data + " ");
    }
  
    // Driver Code
    public static void Main(String[] args)
    {
  
        // Insert 5
        // So linked list becomes 5.null
        insertBegin(5);
  
        // Insert 4 at the beginning
        // So linked list becomes 4.5
        insertBegin(4);
  
        // Insert 7 at the end
        // So linked list becomes 7.4.5
        insertBegin(7);
  
        Console.Write("Created circular doubly"
                      + " linked list is: ");
        display();
    }
}
  
// This code is contributed by 29AjayKumar


Javascript




<script>
    // JavaScript program to illustrate creation
    // & traversal of Doubly Circular LL
    var start = null;
      
    // Structure of a Node
    class Node {
        constructor() {
            this.data = 0;
            this.next = null;
            this.prev = null;
        }
    }
      
    // Function to insert at the end
    function insertEnd(value) {
        var new_node;
      
        // If the list is empty, create a single node
        // circular and doubly list
        if (start == null) {
            new_node = new Node();
            new_node.data = value;
            new_node.next = new_node.prev = new_node;
            start = new_node;
            return;
        }
      
        // If list is not empty
      
        // Find last node
        var last = start.prev;
      
        // Create Node dynamically
        new_node = new Node();
        new_node.data = value;
      
        // Start is going to be next of new_node
        new_node.next = start;
      
        // Make new node previous of start
        start.prev = new_node;
      
        // Make last previous of new node
        new_node.prev = last;
      
        // Make new node next of old last
        last.next = new_node;
    }
      
    // Function to insert Node at the beginning
    // of the List,
    function insertBegin(value) {
        // Pointer points to last Node
        var last = start.prev;
      
        var new_node = new Node();
        new_node.data = value; // Inserting the data
      
        // setting up previous and next of new node
        new_node.next = start;
        new_node.prev = last;
      
        // Update next and previous pointers of start
        // and last.
        last.next = start.prev = new_node;
      
        // Update start pointer
        start = new_node;
    }
      
    function display() {
        var temp = start;
      
        document.write("<br>Traversal in forward direction <br>");
        while (temp.next != start) {
            document.write(temp.data + " ");
            temp = temp.next;
        }
        document.write(temp.data);
      
        document.write("<br>Traversal in reverse direction <br>");
        var last = start.prev;
        temp = last;
        while (temp.prev != last) {
            document.write(temp.data + " ");
            temp = temp.prev;
        }
        document.write(temp.data);
    }
      
    /* Driver code*/
    // Start with the empty list
    var start = null;
      
    // Insert 5. So linked list becomes 5.null
    insertEnd(5);
      
    // Insert 4 at the beginning. So linked
    // list becomes 4.5
    insertBegin(4);
      
    // Insert 7 at the end. So linked list
    // becomes 7.4.5.null
    insertBegin(7);
      
    document.write("Created circular doubly linked list is: ");
    display();
      
    // This code is contributed by Susobhan Akhuli
</script>


Output

Created circular doubly linked list is: 
Traversal in forward direction 
7 4 5 
Traversal in reverse direction 
5 4 7

Time Complexity:

Insertion at the beginning of a doubly circular linked list takes O(1) time complexity.
Traversing the entire doubly circular linked list takes O(n) time complexity, where n is the number of nodes in the linked list.
Therefore, the overall time complexity of the program is O(n).

Auxiliary space:

The program uses a constant amount of auxiliary space, i.e., O(1), to create and traverse the doubly circular linked list.
The space required to store the linked list grows linearly with the number of nodes in the linked list.
Therefore, the overall auxiliary space complexity of the program is O(1).

5. Header Linked List: 

A header linked list is a special type of linked list that contains a header node at the beginning of the list. 

So, in a header linked list START will not point to the first node of the list but START will contain the address of the header node. Below is the image for Grounded Header Linked List:

Below is the Structure of the Grounded Header Linked List:

C++




// Structure of the list
struct link {
    int info;
  
    // Pointer to the next node
    struct link* next;
};


Java




// Structure of the list
static class link {
    int info;
      
     // Pointer to the next node
    link next;
};
  
// this code is contributed by shivanisinghss2110


Python3




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


C#




// Structure of the list
public class link {
    public int info;
      
    // Pointer to the next node
    public link next;
};
  
// this code is contributed by shivanisinghss2110


Javascript




<script>
    // Class for a node
    class Node {
            // Constructor to create a new node
            constructor() {
                this.data = 0;
                // Pointer to next node
                this.next = null;
            }
        }
          
    // This code contributed by Susobhan Akhuli 
</script>


Creation and Traversal of Header Linked List:

C++




// C++ program to illustrate creation
// and traversal of Header Linked List
  
#include <bits/stdc++.h>
  
// Structure of the list
struct link {
    int info;
    struct link* next;
};
  
// Empty List
struct link* start = NULL;
  
// Function to create header of the
// header linked list
struct link* create_header_list(int data)
{
  
    // Create a new node
    struct link *new_node, *node;
    new_node = (struct link*)malloc(sizeof(struct link));
    new_node->info = data;
    new_node->next = NULL;
  
    // If it is the first node
    if (start == NULL) {
  
        // Initialize the start
        start = (struct link*)malloc(sizeof(struct link));
        start->next = new_node;
    }
    else {
  
        // Insert the node in the end
        node = start;
        while (node->next != NULL) {
            node = node->next;
        }
        node->next = new_node;
    }
    return start;
}
  
// Function to display the
// header linked list
struct link* display()
{
    struct link* node;
    node = start;
    node = node->next;
  
    // Traverse until node is
    // not NULL
    while (node != NULL) {
  
        // Print the data
        printf("%d ", node->info);
        node = node->next;
    }
    printf("\n");
  
    // Return the start pointer
    return start;
}
  
// Driver Code
int main()
{
    // Create the list
    create_header_list(11);
    create_header_list(12);
    create_header_list(13);
  
    // Print the list
    printf("List After inserting"
           " 3 elements:\n");
    display();
    create_header_list(14);
    create_header_list(15);
  
    // Print the list
    printf("List After inserting"
           " 2 more elements:\n");
    display();
  
    return 0;
}


Java




// Java program to illustrate creation
// and traversal of Header Linked List
  
class GFG {
    // Structure of the list
    static class link {
        int info;
        link next;
    };
  
    // Empty List
    static link start = null;
  
    // Function to create header of the
    // header linked list
    static link create_header_list(int data)
    {
  
        // Create a new node
        link new_node, node;
        new_node = new link();
        new_node.info = data;
        new_node.next = null;
  
        // If it is the first node
        if (start == null) {
  
            // Initialize the start
            start = new link();
            start.next = new_node;
        }
        else {
  
            // Insert the node in the end
            node = start;
            while (node.next != null) {
                node = node.next;
            }
            node.next = new_node;
        }
        return start;
    }
  
    // Function to display the
    // header linked list
    static link display()
    {
        link node;
        node = start;
        node = node.next;
  
        // Traverse until node is
        // not null
        while (node != null) {
  
            // Print the data
            System.out.printf("%d ", node.info);
            node = node.next;
        }
        System.out.printf("\n");
  
        // Return the start pointer
        return start;
    }
  
    // Driver Code
    public static void main(String[] args)
    {
        // Create the list
        create_header_list(11);
        create_header_list(12);
        create_header_list(13);
  
        // Print the list
        System.out.printf("List After inserting"
                          + " 3 elements:\n");
        display();
        create_header_list(14);
        create_header_list(15);
  
        // Print the list
        System.out.printf("List After inserting"
                          + " 2 more elements:\n");
        display();
    }
}
  
// This code is contributed by 29AjayKumar


Python3




# Python3 program to illustrate creation
# and traversal of Header Linked List
  
# structure of Node
class Node:
    def __init__(self, data):
        self.data = data
        self.next = None
  
  
class LinkedList:
    def __init__(self):
        self.head = Node(0)
        self.last_node = self.head
  
    # function to add elements to header linked list
    def append(self, data):
        self.last_node.next = Node(data)
        self.last_node = self.last_node.next
  
    # function to print the content of header linked list
    def display(self):
        current = self.head.next
        # traversing the header linked list
        while current is not None:
            # at each node printing its data
            print(current.data, end=' ')
            # giving current next node
            current = current.next
        # print(self.head.data)
        print()
  
# Driver code
if __name__ == '__main__':
    L = LinkedList()
    # adding elements to the header linked list
    L.append(1)
    L.append(2)
    L.append(3)
    L.append(4)
    # displaying elements of header linked list
    L.display()


C#




// C# program to illustrate creation
// and traversal of Header Linked List
  
using System;
  
public class GFG {
    // Structure of the list
    public class link {
        public int info;
        public link next;
    };
  
    // Empty List
    static link start = null;
  
    // Function to create header of the
    // header linked list
    static link create_header_list(int data)
    {
  
        // Create a new node
        link new_node, node;
        new_node = new link();
        new_node.info = data;
        new_node.next = null;
  
        // If it is the first node
        if (start == null) {
  
            // Initialize the start
            start = new link();
            start.next = new_node;
        }
        else {
  
            // Insert the node in the end
            node = start;
            while (node.next != null) {
                node = node.next;
            }
            node.next = new_node;
        }
        return start;
    }
  
    // Function to display the
    // header linked list
    static link display()
    {
        link node;
        node = start;
        node = node.next;
  
        // Traverse until node is
        // not null
        while (node != null) {
  
            // Print the data
            Console.Write("{0} ", node.info);
            node = node.next;
        }
        Console.Write("\n");
  
        // Return the start pointer
        return start;
    }
  
    // Driver Code
    public static void Main(String[] args)
    {
        // Create the list
        create_header_list(11);
        create_header_list(12);
        create_header_list(13);
  
        // Print the list
        Console.Write("List After inserting"
                      + " 3 elements:\n");
        display();
        create_header_list(14);
        create_header_list(15);
  
        // Print the list
        Console.Write("List After inserting"
                      + " 2 more elements:\n");
        display();
    }
}
  
// This code is contributed by 29AjayKumar


Javascript




<script>
// JavaScript program to illustrate creation
// and traversal of Header Linked List
  
// Structure of the list
class Link {
    constructor(info, next) {
        this.info = info;
        this.next = next;
    }
}
  
// Empty List
let start = null;
  
// Function to create header of the
// header linked list
function createHeaderList(data) {
  
    // Create a new node
    let newNode = new Link(data, null);
  
    // If it is the first node
    if (start == null) {
  
        // Initialize the start
        start = new Link(null, newNode);
    } else {
  
        // Insert the node in the end
        let node = start;
        while (node.next != null) {
            node = node.next;
        }
        node.next = newNode;
    }
    return start;
}
  
// Function to display the
// header linked list
function display() {
    let node = start;
    node = node.next;
  
    // Traverse until node is
    // not NULL
    while (node != null) {
  
        // Print the data
        document.write(node.info+" ");
        node = node.next;
    }
  
    // Return the start pointer
    return start;
}
  
// Create the list
createHeaderList(11);
createHeaderList(12);
createHeaderList(13);
  
// Print the list
document.write("List After inserting 3 elements:<br>");
display();
createHeaderList(14);
createHeaderList(15);
  
// Print the list
document.write("<br>List After inserting 2 more elements:<br>");
display();
  
// This code contributed by Susobhan Akhuli 
</script>


Output

List After inserting 3 elements:
11 12 13 
List After inserting 2 more elements:
11 12 13 14 15

Time Complexity:

The time complexity of creating a new node and inserting it at the end of the linked list is O(1).
The time complexity of traversing the linked list to display its contents is O(n), where n is the number of nodes in the list.
Therefore, the overall time complexity of creating and traversing a header linked list is O(n).

Auxiliary Space:

The space complexity of the program is O(n), where n is the number of nodes in the linked list.
This is because we are creating n nodes, each with a fixed amount of space required for storing the node information and a pointer to the next node.
Therefore, the overall auxiliary space complexity of the program is O(n).

Additional Types:

  1. Multiply Linked List: Multiply Linked List is a data structure in which each node of the list contains multiple pointers. It is a type of linked list which has multiple linked lists in one list. Each node has multiple pointers which can point to different nodes in the list and can also point to nodes outside the list. The data stored in a Multiply Linked List can be easily accessed and modified, making it a very efficient data structure. The nodes in a Multiply Linked List can be accessed in any order, making it suitable for applications such as graphs, trees, and cyclic lists.


Last Updated : 29 Jan, 2024
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