Linked list is a linear data structure consisting of nodes, where each node contains a value and a reference to the next (and possibly previous) node. This structure allows for dynamic memory allocation and easy insertion and deletion of elements. There are various types of linked lists which differ in their structure and functionality. This article discusses all types of linked lists, as well as the applications and representation of each linked list.

## Types of Linked Lists

Each variant of linked list possesses its own unique characteristics and varies from other linked lists in terms of how it is constructed and how it operates. The section below provides a comprehensive explanation of all types of linked lists.

### 1. Singly Linked List

Here’s a simplified explanation of a singly linked list:

- A singly linked list is a basic type of data structure that consists of a series of nodes.
- Each node in the singly linked list has two components: a data value and a pointer to the next node.
- The first node in the singly linked list is called the head, and the last node is called the tail. The tail’s pointer points to null, indicating the end of the list.
- A singly linked list is traversed only in one direction, from the head to the tail, as only unidirectional traversal is possible.
- Singly linked lists are often used in computer programming to implement other data structures, such as stacks and queues, and to represent relationships between objects.

The image below clearly depicts the appearance of the singly linked list.

**Structure of Singly Linked List Node**

The code below defines a structure for a singly linked list node.

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

class Node { public: int data; // Pointer to next node in LL Node* next; };

class Node { public int data; Node next; }

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

**Creation and Traversal of Singly Linked List**

Below is the program that demonstrates the creation and traversal of a singly linked list.

#include<stdio.h> #include<stdlib.h> // Structure of Node struct Node { int data; struct Node* next; }; // This function will print data present in the linked list from // start to end void printList(struct Node* n) { // move till n is NULL while (n != NULL) { // Print the data printf("%d ",n->data); n = n->next; } } // Driver Code int main() { struct Node* head = NULL; struct Node* second = NULL; struct Node* third = NULL; // create 3 nodes with data head = new_Node(10); second = new_Node(12); third = new_Node(37); // create a linke from first node to second node head->next = second; // create a linke from second node to third node second->next = third; // make last node’s next as NULL third->next = NULL; printList(head); return 0; }

#include <bits stdc++.h=""> using namespace std; // Structure of Node class Node { public: int data; Node* next; Node(int x){ data = x; next = NULL; } }; // This function will print data present in the linked list from // start to end void printList(Node* n) { // move till n is 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; // create 3 nodes with data head = new Node(10); second = new Node(12); third = new Node(37); // create a linke from first node to second node head->next = second; // create a linke from second node to third node second->next = third; // make last node’s next as NULL third->next = NULL; printList(head); return 0; }

class SinglyLinkedList { public int data; SinglyLinkedList next; SinglyLinkedList(int data) { this.data=data; } static void printList(SinglyLinkedList n) { while(n!=null) { System.out.print(n.data+" "); n=n.next; } } public static void main(String[] args) { SinglyLinkedList head=null; SinglyLinkedList second=null; SinglyLinkedList third=null; head =new SinglyLinkedList(10); second=new SinglyLinkedList(12); third=new SinglyLinkedList(37); head.next=second; second.next=third; third.next=null; printList(head); } }

class Node: def __init__(self, data=None, next=None): self.data = data self.next = next # This function will print data present in the linked list from start to end def printList(head): while (head != None): print( head.data , end=" ") head = head.next head = None second = None third = None # create 3 nodes with data head = Node(10) second = Node(12) third = Node(37) # create a link from first node to second node head.next = second # create a link from second node to third node second.next = third printList(head)

**Output**

`10 12 37`

**Complexity Analysis of Creation and Traversal of Singly Linked List**

Here’s the time and space complexity analysis of the above program:

**Time Complexity:**

- The creation of each node takes constant time O(1).
- The linking of the nodes takes constant time O(1).
- The traversal of the linked list using the "printList" function takes linear time O(n), where n is the number of nodes in the linked list.

Therefore, the overall time complexity of this program is O(n).

**Space Complexity:**

- The space complexity of this program depends on the number of nodes in the linked list.
- Each node requires a constant amount of space for its "data" and "next" members.
- The head, second, and third pointers require constant space.

Therefore, the overall space complexity of this program is O(n), where n is the number of nodes in the linked list.

### 2. Doubly Linked List

Here’s a simplified explanation of a doubly linked list:

- Doubly linked list is similar to singly linked list, but has an additional pointer that points to the previous node.
- Each node in the doubly linked list has three parts: data of the node, a pointer to the next node which has the address of the next node, and another pointer to the previous node which has the address of the previous node.
- The first node in the doubly linked list is known as the head node, while the last node is called the tail node. The first node’s previous pointer points to the null value, and the last node’s next pointer points to the null value.
- Doubly linked list is a bi-directional linked list, which means you can traverse it either from head to tail or from tail to head. Here, the pointer to the next node is generally referred to as "next" and the information to the previous node is called "prev".

The image below provides a clear illustration of how doubly linked lists are represented.

**Structure of Doubly Linked List Node**

The code below defines a structure for a doubly linked list node.

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

class Node { public: int data; // Pointer to next node in LL Node* next,*prev; Node(int x){ data = x; next = NULL; prev = NULL; } };

class Node { public: int data; // Pointer to next node in LL Node* next,*prev; Node(int x){ data = x; next = NULL; prev = NULL; } };

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

**Creation and Traversal of Doubly Linked List**

Below is the program that demonstrates the creation and traversal of a doubly linked list.

#include <stdio.h> #include<stdlib.h> struct node { struct node *prev; int data; struct node *next; } void push(Node** head_ref, int new_data) { // create a new node with given data struct Node* new_node = (struct Node*)malloc(sizeof(struct Node)); // assign head node’s address to next of new node new_node->next = (*head_ref); // assign NULL to prev of new node new_node->prev = NULL; // update the previous of old node as new node if ((*head_ref) != NULL) (*head_ref)->prev = new_node; // update the head node of list as new node (*head_ref) = new_node; } // This function will print data present in the linked list from // start to end and also in reverse order void printList(struct Node* node) { struct Node* last; printf("\nTraversal in forward direction \n"; while (node != NULL) { // Print the data pritnf("%d ,node->data);; last = node; node = node->next; } printf("\nTraversal in reverse direction \n"; while (last != NULL) { // Print the data printf("%d ,last->data); last = last->prev; } } // Driver Code int main() { // Start with the empty list struct Node* head = NULL; // Insert 10. // So linked list becomes 10->NULL push(&head, 10); // Insert 44 at the beginning. So // linked list becomes 44->10->NULL push(&head, 44); // Insert 11 at the beginning. So // linked list becomes 11->44->10->NULL push(&head, 11); printf("Created DLL is: "); printList(head); return 0; }

#include <bits stdc++.h=""> using namespace std; // Doubly linked list node class Node { public: int data; Node* next; Node* prev; Node(int x){ data = x; prev = NULL; next = NULL; } }; // This function will add a new node in front of the list void push(Node** head_ref, int new_data) { // create a new node with given data Node* new_node = new Node(new_data); // assign head node’s address to next of new node new_node->next = (*head_ref); // assign NULL to prev of new node new_node->prev = NULL; // update the previous of old node as new node if ((*head_ref) != NULL) (*head_ref)->prev = new_node; // update the head node of list as new node (*head_ref) = new_node; } // This function will print data present in the linked list from // start to end and also in reverse order 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 10. // So linked list becomes 10->NULL push(&head, 10); // Insert 44 at the beginning. So // linked list becomes 44->10->NULL push(&head, 44); // Insert 11 at the beginning. So // linked list becomes 11->44->10->NULL push(&head, 11); cout << "Created DLL is: "; printList(head); return 0; }

class Node: def __init__(self, data=None, next=None, prev=None): self.data = data self.next = next self.prev = prev # This function will add a new node in front of the list def push(head, new_data): # create a new node with given data new_node = Node(new_data) # assign head node’s address to next of new node new_node.next = head # update the previous of old node as new node if head is not None: head.prev = new_node # update the head node of list as new node head = new_node return new_node # This function will print data present in the linked list from start to end def printList(node): print("Traversal in forward direction") while node: print(node.data,end=" ") last = node node = node.next print("\nTraversal in reverse direction",) while last: print(last.data,end=" ") last = last.prev # Start with the empty list head = None # Insert 10. # So linked list becomes 10->NULL head = push(head,10) # Insert 44 at the beginning. So # linked list becomes 44->10->NULL head = push(head,44) # Insert 11 at the beginning. So # linked list becomes 11->44->10->NULL head = push(head,11) print("Created DLL is:") printList(head)

**Output**

```
Created DLL is:
Traversal in forward direction
11 44 10
Traversal in reverse direction
10 44 11
```

**Complexity Analysis of Creation and Traversal of Doubly Linked List**

Here’s the time and space complexity analysis of the above program:

**Time Complexity:**

The time complexity of the program is O(n), where n is the number of nodes in the doubly linked list. Also, each node insertion operation takes O(1) time.

**Space Complexity:**

The space complexity of the program is O(n), where n is the number of nodes in the doubly linked list. This is because the program uses dynamic memory allocation to create nodes for the linked list, and each node takes O(1) space.

### 3. Circular Linked List

Here’s an explanation of circular linked list:

- A circular linked list is a type of linked list where the last node points to the first node, creating a circular structure.
- A circular linked list can only be traversed in one direction, making it a unidirectional linked list.
- Compared to a singly linked list, a circular linked list has no end and can theoretically go on forever, but the traversal must still start at the head node.

The image below provides a clear illustration of how doubly linked lists are represented.

**Structure of Circular Linked List Node**

The code below defines a structure for a doubly linked list node.

class Node { public: int data; // Pointer to next node in LL Node* next; };

**Creation and Traversal of Circular Linked List**

Below is the program that demonstrates the creation and traversal of circular linked list.

#include <bits stdc++.h=""> using namespace std; // Structure for a node class Node { public: int data; Node* next; Node(int x){ data = x; next = NULL; } }; // This function will insert a node at the beginning of the // list void push(Node** head_ref, int data) { Node* ptr1 = new Node(data); Node* temp = *head_ref; ptr1->next = *head_ref; if (*head_ref != NULL) { while (temp->next != *head_ref) { temp = temp->next; } temp->next = ptr1; } else ptr1->next = ptr1; *head_ref = ptr1; } // This function will print data of all nodes in the list void printList(Node* head) { Node* temp = head; if (head != NULL) { do { // Print the data cout << temp->data << " "; temp = temp->next; } while (temp != head); } } // Main function int main() { Node* head = NULL; push(&head, 14); push(&head, 35); push(&head, 5); push(&head, 9); //created list will be 9->5->35->14 cout << "Contents of Circular" << " Linked List\n "; printList(head); return 0; }

**Output**

```
Contents of Circular Linked List
9 5 35 14
```

**Complexity Analysis of Creation and Traversal of Doubly Linked List**

Here’s the time and space complexity analysis of the above program:

**Time Complexity:**

The time complexity of the push function is O(n) in the worst case, where n is the number of nodes in the circular linked list. This is because in the worst case scenario, the function will need to traverse the entire linked list to find the last node and update its next pointer to point to the newly inserted node.

The time complexity of the printList function is also O(n), where n is the number of nodes in the circular linked list. This is because the function will need to traverse the entire linked list to print the data of each node.

**Space Complexity:** O(n), where ‘n’ is the number of nodes present in the circular linked list.

### 4. Doubly Circular Linked List

Here’s an explanation of Doubly Circular Linked List.

- A doubly circular linked list is the combination of both a circular linked list and a doubly linked list.
- Each node in the doubly circular linked list has three parts: one for data, the second for storing the address of the next node, and the last for storing the address of the previous node.
- A special feature of a doubly circular linked list is that, like a circular linked list, its last node points to the head of the linked list.
- A doubly circular linked list can be traversed in both directions, making it a bi-directional linked list.

The image below provides a clear illustration of how doubly circular linked lists are represented.

**Structure of Doubly Circular Linked List Node**

The code below defines a structure for a doubly circular linked list node.

class Node { public: int data; // Pointer to next node in LL Node* next,*prev; Node(int x){ data = x; next = NULL; prev = NULL; } };

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

**Creation and Traversal of Doubly Circular Linked List**

Below is the program that demonstrates the creation and traversal of doubly circular linked list.

#include <bits stdc++.h=""> using namespace std; // Structure of a Node class Node { public: int data; // Pointer to next node in LL Node* next,*prev; Node(int x){ data = x; next = NULL; prev = NULL; } }; // This function will insert a node at the beginning of the // list void insertBegin(Node** start, int value) { // when list is empty if (*start == NULL) { Node* new_node = new Node(value); new_node->next = new_node->prev = new_node; *start = new_node; return; } // last node Node* last = (*start)->prev; Node* new_node = new Node(value); // update the prev and next pointers 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; } // This function will print the data in nodes of our list void display(Node* start) { 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 Node* start = NULL; // Insert 7 // So linked list becomes 7->NULL insertBegin(&start, 7); // Insert 5 at the beginning // So linked list becomes 5->7 insertBegin(&start, 5); // Insert 10 at the end // So linked list becomes 10->5->7 insertBegin(&start, 10); printf("Created circular doubly" " linked list is: "); display(start); return 0; }

**Output**

```
Created circular doubly linked list is:
Traversal in forward direction
10 5 7
Traversal in reverse direction
7 5 10
```

**Complexity Analysis of Creation and Traversal of Doubly Circular Linked List**

Here’s the time and space complexity analysis of the above program:

**Time Complexity:**

The time complexity of the insertBegin function is O(1) because it involves only constant-time operations, regardless of the size of the linked list. The display function iterates over all nodes of the linked list. Therefore, its time complexity is O(n), where n is the number of nodes in the linked list.

**Space Complexity:**

The space complexity of the program is O(n), where n is the number of nodes in the linked list.

**Conclusion**

In conclusion, linked lists are an essential data structure in computer science that allow for efficient data storage and traversal. The four main types of linked lists include singly linked lists, doubly linked lists, circular linked lists, and doubly circular linked lists. Each type has its own unique features and advantages, and understanding the differences between them is important in choosing the appropriate data structure for a given application. If you want to solve more questions on Linked List, which are curated by our expert mentors at PrepBytes, you can follow this link Linked List.

## FAQs related to Linked List

Here are some frequently asked questions on types of linked list.

**Q1: What is a singly linked list and how does it differ from other types of linked lists?**

**Ans:** A singly linked list is a type of linked list where each node contains a data element and a pointer to the next node in the list. It differs from other types of linked lists, such as doubly linked lists and circular linked lists, in that it only has one pointer per node.

**Q2: What is a doubly linked list and what are its advantages over a singly linked list?**

**Ans:** A doubly linked list is a type of linked list where each node contains a data element and two pointers – one to the next node in the list and one to the previous node. Its advantages over a singly linked list include the ability to traverse the list in both directions and the ability to easily delete nodes from the list.

**Q3: What is a circular linked list and what are some use cases for it?**

**Ans:** A circular linked list is a type of linked list where the last node points back to the first node, forming a loop. It is useful in situations where a list needs to be continuously traversed, such as in a queue or circular buffer.

**Q4: What is a XOR linked list and what are its advantages over other types of linked lists?**

**Ans:** An XOR linked list is a type of linked list where each node contains a single pointer that is the XOR of the previous and next nodes. Its advantages over other types of linked lists include the ability to save space by using only one pointer per node and the ability to traverse the list in both directions.

**Q5: What is a lock-free linked list and how does it differ from other types of linked lists?**

**Ans:** A lock-free linked list is a type of linked list where multiple threads can concurrently access and modify the list without using locks or other synchronization mechanisms. It differs from other types of linked lists in that it is designed to be thread-safe without the use of locks.