What is the time complexity of the enqueue operation in a queue implemented using a linked list?O(1)O(n)O(log n)O(n log n)

Break Down the Problem

1. Understanding the Queue Data Structure: A queue follows the First In First Out (FIFO) principle. We need to analyze how the enqueue operation behaves when the queue is implemented using a linked list.
2. Exploring Linked List Implementation: In a linked list, each element (node) contains a value and a reference to the next node. We typically maintain a reference to both the head (start) and the tail (end) of the list to facilitate operations.

Relevant Concepts

1. Enqueue Operation: The enqueue operation involves adding a new element to the end of the queue.

Analysis and Detail

1. To perform an enqueue operation on a linked list, we:

   1. Create a new node for the element to be added.
   2. Update the next reference of the current tail node to point to this new node.
   3. Then, update the tail reference of the queue to be the new node.
   • Since both updating the references and creating a new node take constant time, the operation does not depend on the number of elements already in the queue.

Verify and Summarize

• For a queue implemented using a linked list, the enqueue operation consistently takes $O(1)$ time, as it requires a fixed number of steps regardless of the queue's size.

Final Answer

The time complexity of the enqueue operation in a queue implemented using a linked list is $O(1)$.