Question

The following algorithm (used for Exercises 34-36) is a count-controlled loop going from 1 through 5 . At each iteration, the loop counter is either printed or put on a queue, depending on the result of Boolean function RanFun(). (The behavior of RanFun() is immaterial.) At the end of the loop, the items on the queue are dequeued and printed. Because of the logical properties of a queue, this algorithm cannot print certain sequences of the values of the loop counter. You are given an output and asked if the algorithm could generate the output. Respond as follows: A. True B. False C. Not enough information The following output is possible using a queue: 13513 .

Short answer

B. False

Step-by-step solution

Understanding Queue Logic

A queue follows a FIFO (First In, First Out) structure. When an element is added to the queue, it is placed at the end, and when an element is removed, it is taken from the front. Only sequences that reflect this order can be formed from the queue.

Understanding the Loop Counter Sequence

The loop counter runs from 1 to 5, and for each iteration, the counter could either be printed directly or placed into the queue, according to the result of the function RanFun(). The queue's sequence must reflect the order in which items are added and removed.

Examining the Sequence: 13513

The sequence shows elements being repeated and mixed in a way that needs careful FIFO verification. For each digit after an earlier printed digit, such as '1' appearing after '3' and '5', one must check if it reflects possible queue order and removal. However, '3' before '1' indicates '1' left without using FIFO. Thus the sequence doesn't fit possible queue logic.

Key concepts

Count-Controlled Loop

A count-controlled loop is a type of loop that executes a fixed number of times, controlled by a counter. For example, a loop that runs from 1 to 5 will repeat five times. This is crucial in automating repetitive tasks where the number of iterations is known. Count-controlled loops are common in programming. They help perform the same action or set of actions repeatedly.
In programming languages like Python or Java, a for-loop is a typical count-controlled loop. It allows programmers to specify the start and end points of the loop counter. Here’s a simple syntax: `for i in range(1, 6):`.
In the exercise, the count-controlled loop iterates from 1 to 5. Each number can be either printed immediately or placed into a queue based on a boolean function "RanFun()". The nature of the loop ensures that each number from 1 to 5 is processed once. This looping mechanism is critical in ensuring the completeness and predictability of the algorithm.

Queue Logic

Queue logic revolves around understanding how elements are managed in a queue. A queue operates based on the FIFO principle, which stands for "First In, First Out". This means that the first element added to the queue will be the first one to be removed.
Imagine standing in line at a movie theater. The first person to arrive is also the first to get a ticket and leave. This logic ensures an orderly processing of elements, making queues ideal for managing items in order.
In algorithm scenarios, queues are often used to manage processes or objects in the sequence they were created. Our exercise employs a queue to store loop counter numbers based on the outcome of a Boolean function. The logic of the queue is crucial in understanding what sequences can or cannot be formed once the loop is done, influencing the possible outputs significantly.

FIFO Structure

The FIFO structure, or "First In, First Out," is a foundational concept in many areas of computing and business operations. In the context of a queue, FIFO ensures that the first item added is the first to be removed. This mirrors natural processes such as lining up at a checkout counter.
In the exercise, the queue serves as a storage for numbers depending on the result from the function "RanFun()". When numbers are placed into the queue, their order must obey FIFO. This creates constraints around the possible sequences that could be printed after all numbers are processed through the queue.
For instance, once a number enters the queue, it must wait for previous numbers to exit before it can be printed. This orderly sequence helps maintain data consistency and predictability, which is essential in ensuring that certain output patterns, like the one described, adhere to or violate the FIFO principles.

Boolean Function

A Boolean function is a function that returns a Boolean value, either true or false. These functions are essential in decision-making processes within algorithms. For example, they can control the flow of an algorithm by evaluating conditions and branching logic accordingly.
In our exercise, the Boolean function "RanFun()" determines whether a number is printed directly or placed into a queue. Although the details of "RanFun()" are immaterial, each true or false outcome dictates how the loop counter's number will be processed.
These decisions alter how the sequence of numbers develops, directly affecting the possible outputs. Although the internal logic of "RanFun()" may be unknown, its impact is pivotal in exploring the protocol of our given loop-queue scenario. Understanding Boolean functions helps us see how certain logical conditions can lead to different paths in an algorithm, thus affecting the final result.