Question

Suppose the following operations are performed on an empty queue: enqueue (5) enqueue (7) enqueue( 9 ) enqueue (12)

Short answer

Answer: The resulting queue after performing the given enqueue operations is [5, 7, 9, 12].

Step-by-step solution

Initialize an empty queue

Begin with an empty queue represented as [ ].

Perform the first enqueue operation

Enqueue the number 5 into the queue: enqueue(5). The queue now looks like this [5].

Perform the second enqueue operation

Enqueue the number 7 into the queue: enqueue(7). The queue now looks like this [5, 7].

Perform the third enqueue operation

Enqueue the number 9 into the queue: enqueue(9). The queue now looks like this [5, 7, 9].

Perform the fourth enqueue operation

Enqueue the number 12 into the queue: enqueue(12). The queue now looks like this [5, 7, 9, 12]. After performing all the enqueue operations, the final queue is [5, 7, 9, 12].

Key concepts

Queue Operations

In computer science, a queue is a simple, yet incredibly useful data structure. Picture it like a real-life line at a ticket counter. People get added to the end of the line and leave from the front. This is exactly how a queue operates with its First-In-First-Out (FIFO) principle. A queue is based on two main operations: enqueue and dequeue.

• Enqueue: Adds an element to the end of the queue.
• Dequeue: Removes an element from the front of the queue.

Queues are implemented in many programming applications, especially for situations that require sequential processing, such as task scheduling, error handling, and data streaming. This structure is often part of broader systems requiring order and fairness in servicing requests.

Enqueue Operation

The enqueue operation is essential to the function of a queue as it allows new elements to enter the queue. Think of the enqueue process as analogous to people joining the back of a line. During this operation, an item is inserted at the rear, and it waits its turn to be processed or removed wilfully When performing an enqueue operation, certain considerations must be kept in mind:

• The queue should have enough space to hold the new element. In cases of static arrays, space might not be sufficient.
• In dynamic scenarios, additional procedures might be needed to allocate more space if the queue is full.

Given a schedule of enqueue operations, like inserting numbers 5, 7, 9, and 12, each gets added sequentially to the existing queue, maintaining their order.

Queue Implementation

Implementing a queue can be quite straightforward, yet the choice of implementation can make a difference in efficiency. Queues can be implemented in several ways, including using arrays or linked lists.

• Arrays: This is a simple method where elements are stored in contiguous memory locations. Adding elements (enqueue) is straightforward, but it requires shifting elements on dequeue operations, which might not be optimal.
• Linked Lists: This structure is flexible, allowing for efficient enqueue and dequeue operations without the need to shift other elements as each node points to its successor.
• Circular Queue: This is a more advanced implementation using arrays, effectively allowing the queue to wrap around, optimizing the use of storage space.

Choosing a particular implementation depends on the specific needs of the application, be it memory efficiency or speed of operations. For instance, if rapid insertion and deletion are essential, linked lists or circular queues are preferable.