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A queue is implemented using a non-circular singly linked list. The queue has a head pointer and a tail pointer, as shown in the figure. Let n denote the number of nodes in the queue. Let enqueue be implemented by inserting a new node at the head, and dequeue be implemented by deletion of a node from the tail. Which one of the following is the time complexity of the most time-efficient implementation of enqueue and dequeue, respectively, for this data structure?

A queue is implemented using a non-circular singly linked list. The queue has a head pointer and a tail pointer, as shown in the figure. Let n denote the number of nodes in the queue. Let enqueue be implemented by inserting a new node at the head, and dequeue be implemented by deletion of a node from the tail. Which one of the following is the time complexity of the most time-efficient implementation of enqueue and dequeue, respectively, for this data structure? Correct Answer θ(1), θ(n)

Enquene: Inserting new node in front.

next =  Head

Head = P

Hence two-pointer operations will take O(1) time.

Dequeue:

As the list is singly linked, we have to traverse up to the second last node for pointer manipulation, which will take O(n) time.

Enqueue:

Create a Node P.

P-->Data = Data

P-->Next = Head

Head = P

Complexity = Only pointer manipulatuon so constant = O(1)

Dequeue:temp = head;

 While( temp-Next-->Next != NULL)

{       

 temp = temp-Next;       

 }

temp-->next = NULL;

Tail = temp;

Complexity = Traversing list and then free last node and keep track of Tail pointer = O(n)

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