Question

Suppose the following operations are performed on an empty queue: enqueue(5) : enqueue (7) : enqueue (9): enqueue (12): Insert numbers in the following diagram to show what will be stored in the static queue after the operations have executed.

Short answer

Answer: The state of the queue after performing these enqueue operations is [5, 7, 9, 12] with 5 at the front and 12 at the rear.

Step-by-step solution

Understand the Enqueue Operation

To solve this exercise, we need to understand the behavior of an enqueue operation. In a queue, elements are added (enqueued) at the end and removed (dequeued) from the front. When an item is enqueued, it becomes the last element in the queue.

Enqueue Operations on an Empty Queue

We start with an empty queue and perform the following operations in order: 1. enqueue(5): The queue becomes [5]. 2. enqueue(7): The queue becomes [5, 7]. 3. enqueue(9): The queue becomes [5, 7, 9]. 4. enqueue(12): The queue becomes [5, 7, 9, 12].

Present the Final Queue State

After performing all enqueue operations on the empty queue, the current state of the queue is [5, 7, 9, 12]. In the following diagram, we can represent the elements in the queue as: Front --> 5 -> 7 -> 9 -> 12 <-- Rear The diagram shows the order of elements in the queue after executing all the given operations and how the enqueue operation added the elements at the rear end sequentially.

Key concepts

Enqueue Operation

Imagine you're in a line at a movie theater, waiting to buy tickets. The process of joining the line is very similar to the enqueue operation in a queue data structure. When you enqueue an element, you add it to the rear of the queue, just like joining the end of the line.

Each new element occupies a space after the last element that was added. If you think of your queue as a train queue, each new element is the next person getting on the train. Let's break it down with the example given:

* **enqueue(5)** - The queue is empty initially, so 5 becomes the first element.
* **enqueue(7)** - The queue now has [5], and 7 joins at the end, making it [5, 7].
* **enqueue(9)** - Adding 9 to the back makes the queue [5, 7, 9].
* **enqueue(12)** - Lastly, 12 is added, resulting in [5, 7, 9, 12].

Remember, like the people queue at a theater, the queue grows only from the rear.

Static Queue

Understanding a static queue is crucial for handling queues efficiently. A static queue is like having a fixed-length line with specific seats, such as a bus with fixed seating. The queue has a limited size, and once it's full, you can't add more elements without first removing some.

A static queue is implemented using arrays, providing a fixed number of slots for your elements. Once the operation begins, each enqueue fills a slot until all are filled. This can be beneficial in cases where memory is a constraint, or when you need predictable memory usage.

Consider what happens when a static queue reaches its capacity. Any additional enqueue operations will fail unless you remove elements from the front to make space at the rear. This limitation means you must manage your queue size and usage carefully to avoid overflow.

Queue Operations

Queue operations are fundamental in the management of the queue data structure, consisting primarily of enqueue and dequeue processes.

When you perform an **enqueue** operation, you're adding an element to the rear of the queue. It's like adding a new person at the end of a queue line. On the flip side, the **dequeue** operation removes the front element. Imagine someone stepping off the line after buying tickets; they are at the front and get removed first.

Additional operations often include:

• **Peek/Front**: Viewing the first element without removing it.
• **isEmpty**: Checking if the queue is empty.
• **isFull**: For static queues, checking if the queue has no more room for new elements.

These operations together facilitate efficient management of elements, ensuring that processing follows the First In, First Out (FIFO) principle, facilitating orderly processing without disruption. The structured access provided by these operations helps maintain data order and allows for predictable resource management, crucial in various algorithm implementations.