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Doubly Linked List
A doubly linked list is a type of linked data structure that allows traversal in both directions (forward and backward directions). It differs from singly linked list in that, singly linked list does not support backward traversal. Every node in a doubly linked list contains a data part and two pointers; next pointer that points to the next node and the prev pointer that points to the previous node in the list. A doubly linked list also has two dummy nodes (head and tail) known as sentinels (guard nodes) that contains no data of the sequence. The first element of a doubly linked list has its prev pointer pointing to head and the last element has its next node pointing to tail.
Without a tail pointer, you cannot directly access the last element without having to first traverse the entire list all the way from the beginning.
Steps to create a doubly linked list
To create an empty list,
- create head and tail nodes (nodes without data) first
- let the next pointer of the head point to the tail node
- let the prev pointer of the tail point to the head node.
For a non-empty list,
- let the next pointer of the head point to the first real element of the sequence
- let the prev pointer of the tail point to the last real element of the sequence
Key operations
- Insertion (insert at the beginning, at the end or anywhere in the middle)
- deletion (delete from beginning, end or anywhere in the middle)
To add an element(node) at the beginning of the list, let the;
- next pointer of the new element (node) point to the first element (the one the head currently points to)
- next pointer of the head point to this new element you want to add
- prev pointer of the element (node) you want to add point to head.
To add an alement (node) to the end of the list, let the;
- prev pointer of the new element you want to add point to the last element (the one before the tail)
- next pointer of the last element (the one before the tail) point to the new element you want to add
- prev pointer of the tail point to the new element.
To delete an element from the beginning, let the;
- next pointer of the head point to the second element in the list (node after the one head pointers to).
- prev pointer of the second element point to the head
To delete from the end of the list, let the;
- prev pointer of the tail point to the element before the last node
- next pointer of the element before the last node point to the tail
Note: If there is only one element in the list, deletion from both directions happens by pointing the next pointer of head to tail and prev pointer of tail to head.
Deletion anywhere in the middle happens by letting the prev pointer and the next pointer of the node after and before the one you want to delete point to each other respectively.
To insert anywhere in the middle, let the;
- next pointer of the element you want to insert point to the node at the position you want to insert it
- prev pointer of the element you want to insert point to node before the position you want to insert it
- prev pointer of the node at the position you want to insert point to the new element
- next pointer of the node before the position you want to insert point to the new element.
Deletion and insertion at the beginning or end of the list is a constant operation and has a O(1) runtime. Deletion or insertion anywhere in the middle however has a O(n) runtime.