Question

Suppose three items, R, S, and T, are placed in a queue in that order. Then one item is removed from the queue before a fourth item, \(\mathrm{X}\), is placed in the queue. Then one item is removed from the queue, the items \(\mathrm{Y}\) and \(\mathrm{Z}\) are placed in the queue, and then the queue is emptied by removing one item at a time. List all the items in the order in which they were removed.

Short answer

R, S, T, X, Y, Z

Step-by-step solution

Understand the Initial Queue State

Initially, three items R, S, and T are placed in a queue. The order in the queue is: R, S, T.

Removing First Item Before Adding X

An item is removed from the queue first. According to the order of a queue (FIFO - First In, First Out), the item R is removed, leaving the queue with: S, T.

Adding Item X to the Queue

Now, item X is placed in the queue. The new order of the queue is: S, T, X.

Removing Second Item

The next item to be removed from the queue is the next front item, which is S, leaving the queue with: T, X.

Adding Items Y and Z

Items Y and Z are now added sequentially to the queue. The queue order becomes: T, X, Y, Z.

Emptying the Queue

One by one, items are removed from the queue according to the FIFO principle: first, T is removed, then X, followed by Y, and finally Z. The removal order is: T, X, Y, Z.

Key concepts

Queue

Imagine you are waiting in line for your favorite ice cream. This line is similar to a queue in computer science. A queue is a crucial data structure that operates in a specific order, which is similar to a timeline. In a queue, the items enter from one end, called the 'rear', and exit from the opposite end, known as the 'front'. This structure allows elements to come in and out in a strictly controlled manner.
This feature makes queues perfect for scenarios where tasks need to be managed in turn. Think about call centers, printing services, or even the execution of tasks by the operating system. Whenever these tasks arrive, they are added at the rear, and whenever they are processed, they are removed from the front. This is why we think of a queue as putting items in line, which guarantees each item enters and exits only through these two designated ends.

• Ordered structure of adding (rear) and removing (front)
• Operates efficiently for managing sequencing needs
• Highly applicable in various real-world applications like task scheduling or managing print jobs

FIFO (First In, First Out)

Remember the phrase "first come, first served"? That's almost exactly how a queue works, and it's formally known as FIFO -- First In, First Out. When an item is added to the queue, we say it is 'enqueued'. When an item exits, it is 'dequeued'. This principle ensures that the first element added is also the first one to be removed.
Consider a scenario: three elements, say R, S, and T, join the queue in this order. According to FIFO logic, the element R, which was the first to enter, will be the first to get out. This step-by-step processing closely mimics many real-life lines, like standing in line at a bank. FIFO aids in processing requests or tasks in the sequence they are received, preventing newer tasks from jumping ahead and leading to predictable and fair task management.

• FIFO ensures orderly processing
• Ensures fairness and timeliness
• Highly predictable and easy-to-manage queue behavior

Algorithm Steps

Understanding an algorithm is like following a recipe, where each ingredient and action leads towards the final dish. Let's break down the steps taken with our queue, as carefully illustrated in the exercise. Initially, we have three items, R, S, and T, that join the queue, forming the initial sequence. The first move involves removing the frontmost item, R, following the FIFO principle.
Next, we introduce a new item, X, into the queue, which positions after T. The sequence of removing and adding continues, with S now exiting (as it's at the front), and Y and Z being added. To empty the queue, we continue removing items according to FIFO - T, followed by X, Y, and Z.
This algorithm showcases the dynamic ability of queues to handle complex sequences of operations:

• Inserting and removing items in logical stages
• Maintaining order using FIFO logic
• Efficient processing and management of tasks and elements

By closely following these sequential steps, understanding and implementing the operations on a queue becomes clear and manageable.