Which of the following operations is performed more efficiently by doubly…

Concept

The time for a linked-list update depends on which neighbouring nodes are already reachable. A singly linked node stores only a next link, whereas a doubly linked node stores both next and previous links.

When the target node itself is given, a backward link can remove the need to search for its predecessor; operations that already have the required node or must inspect every node gain no such asymptotic advantage.

Application

1. Let x be the given node. Deleting x requires changing its predecessor’s next link so that it bypasses x.

2. In a singly linked list, x does not identify its predecessor. Starting from the head to locate that predecessor takes O(n) time in the general case.

3. In a doubly linked list, x.prev gives the predecessor directly. Updating x.prev.next and, when present, x.next.prev takes O(1) time.

4. Therefore, deleting a node whose location is given is performed more efficiently by a doubly linked list.

Cross-check and contrast

• Searching an unsorted list may inspect every node in either representation, so it is O(n) in both.

• Inserting after a known node already has the splice point, so it is O(1) in both.

• Traversing to process every node necessarily visits all nodes, so it is O(n) in both.

Result: deleting a node whose location is given is the operation with the asymptotic efficiency advantage.