How do you implement a queue using a linked list?

A queue can be implemented using a linked list by adding elements at the end and removing them from the beginning.

A queue is a data structure that follows the First-In-First-Out (FIFO) principle. This means that the first element that was added to the queue will be the first one to be removed. In a linked list, each element points to the next one, making it a dynamic data structure.

To implement a queue using a linked list, you would need two pointers: one for the front of the queue and one for the rear. The front pointer is used to remove elements from the queue, while the rear pointer is used to add elements.

When an element is added (enqueued), it is placed at the end of the queue. This is done by creating a new node, setting its value to the element, and then updating the 'next' pointer of the current last node to point to this new node. The rear pointer is then updated to point to this new node.

When an element is removed (dequeued), it is taken from the front of the queue. This is done by moving the front pointer to the next node in the list. The node that was previously at the front is no longer referenced by the queue and can be deleted.

It's important to handle the cases where the queue is empty. When adding an element to an empty queue, both the front and rear pointers should point to the new node. When removing an element from an empty queue, an error should be returned or the operation should be ignored.

In terms of time complexity, both enqueue and dequeue operations are O(1), meaning they take constant time regardless of the size of the queue. This is because we are only ever dealing with the front and rear of the queue, and these operations do not require traversing the entire list.

In conclusion, implementing a queue using a linked list involves managing two pointers to the front and rear of the list, and correctly handling additions and removals according to the FIFO principle.