Operations of Doubly Linked List with Implementation

A Doubly Linked List (DLL) contains an extra pointer, typically called the previous pointer, together with the next pointer and data which are there in a singly linked list. 
 

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Below are operations on the given DLL:
 

1. Add a node at the front of DLL: The new node is always added before the head of the given Linked List. And the newly added node becomes the new head of DLL & maintaining a global variable for counting the total number of nodes at that time.
    
2. Traversal of a Doubly linked list
3. Insertion of a node: This can be done in three ways: 
   
   • At the beginning: The new created node is insert in before the head node and head points to the new node.
   • At the end: The new created node is insert at the end of the list and tail points to the new node.
   • At a given position: Traverse the given DLL to that position(let the node be X) then do the following: 
     
     1. Change the next pointer of new Node to the next pointer of Node X.
     2. Change the prev pointer of next Node of Node X to the new Node.
     3. Change the next pointer of node X to new Node.
     4. Change the prev pointer of new Node to the Node X.
4. Deletion of a node: This can be done in three ways: 
   
   • At the beginning: Move head to the next node to delete the node at the beginning and make previous pointer of current head to NULL .
   • At the last: Move tail to the previous node to delete the node at the end and make next pointer of tail node to NULL.
   • At a given position: Let the prev node of Node at position pos be Node X and next node be Node Y, then do the following: 
     
     1. Change the next pointer of Node X to Node Y.
     2. Change the previous pointer of Node Y to Node X.

Below is the implementation of all the operations:
 

Linked List: 2 4 9 1 21 22 

Linked List after inserting 1 at beginning: 1 2 4 9 1 21 22 
Linked List after inserting 0 at end: 1 2 4 9 1 21 22 0 
Linked List after inserting 44 after 3rd Node: 1 2 4 44 9 1 21 22 0 

Linked List after deleting node at beginning: 2 4 44 9 1 21 22 0 
Linked List after deleting node at end: 2 4 44 9 1 21 22 
Linked List after deleting node at position 5: 2 4 44 9 21 22 

Time and Space of Complexity of Each Operation :

Add a node at the front of DLL:
Time Complexity: O(1)
Space Complexity: O(1)

Traversal of a Doubly linked list:
Time Complexity: O(n)
Space Complexity: O(1)

Insertion of a node at the beginning:
Time Complexity: O(1)
Space Complexity: O(1)

Insertion of a node at the end:
Time Complexity: O(1)
Space Complexity: O(1)

Insertion of a node at a given position:
Time Complexity: O(n)
Space Complexity: O(1)

Deletion of a node at the beginning:
Time Complexity: O(1)
Space Complexity: O(1)

Deletion of a node at the end:
Time Complexity: O(1)
Space Complexity: O(1)

Deletion of a node given the position:
Time Complexity: O(n)
Space Complexity: O(1)