Which of the following operations is not possible in a doubly linked list?Insertion at the beginningInsertion at the endDeletion from the middleDirect access to an element by index

The operation that is not possible in a doubly linked list is "Direct access to an element by index".

Here's why:

1. Insertion at the beginning: This is possible in a doubly linked list. You just need to create a new node, set its next pointer to the current head, set the previous pointer of the current head to the new node, and then update the head to the new node.

2. Insertion at the end: This is also possible. You need to create a new node, set its previous pointer to the current tail, set the next pointer of the current tail to the new node, and then update the tail to the new node.

3. Deletion from the middle: This is possible as well. You need to find the node to be deleted, update the next pointer of the node before it to the node after it, update the previous pointer of the node after it to the node before it, and then delete the node.

4. Direct access to an element by index: This is not possible in a doubly linked list. Linked lists, whether singly or doubly, do not provide direct access to the elements by their index. To access an element, you need to traverse the list from the head (or tail, in a doubly linked list) until you reach the desired element. This operation takes O(n) time, where n is the length of the list.