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: 13542 .

Short answer

B. False

Step-by-step solution

Understand the Loop Structure

The loop runs from 1 to 5, iterating over each integer in that range. During each iteration, the current integer can either be printed immediately or placed into a queue based on the result of the function RanFun().

Analyze Queue Properties

A queue operates in a First-In-First-Out (FIFO) manner, which means that numbers are removed in the same order they were added. Thus, once a number is placed in the queue, it cannot appear in output before any other number that was placed after it.

Sequence and Printing Conditions

For the output sequence '13542' to occur, '1', '3', and '5' must be printed when they occur in the loop, assuming immediate printing. '4' must be placed in the queue first, and '2' must be placed after '4' in the queue.

Check Output Possibility

To produce the specified output, '1' would be printed first immediately, '3' next, followed by '5'. However, if '4' and '2' are placed into the queue in that order, they will be dequeued and printed in the same order as '42'. This contradicts the order given in the sequence '13542' required by the question.

Conclusion Based on Queue Behavior

Based on the FIFO nature of a queue, the output sequence '13542' is not possible because '4' placed before '2' in the queue should be printed before '2'. Thus, the sequence is inaccurate.

Key concepts

Count-Controlled Loop

A count-controlled loop is a type of loop in programming where the number of iterations is predetermined. It typically uses a counter to track how many times the loop has executed. For example, if a loop is set to run five times, it will iterate exactly five times unless interrupted by a condition inside the loop.
This method is often used when you know the exact number of elements or the specific number of times you need to repeat a block of code. Count-controlled loops are common because they simplify the iteration process by automatically incrementing a counter.

• Consistent operation: The loop performs a consistent set of operations a defined number of times.
• Easy to set up: Simply determine the start and end conditions, and the loop takes care of the rest.

In the context of the exercise, the loop runs from 1 through 5, meaning it will iterate exactly five times, executing the loop block with the current counter value each time.

Queue Data Structure

A queue is a special type of data structure in computer science which follows the First-In-First-Out (FIFO) methodology. You can think of it like a line of people at a checkout counter, where the first person in line is the first to be served.
Queues are dynamic, allowing elements to be added (enqueued) at one end, called the rear, and removed (dequeued) from the other end, called the front.

• Enqueue: Add an item to the end of the queue.
• Dequeue: Remove an item from the front of the queue.
• Peek: View the item at the front without removing it.

In the algorithm presented, numbers are queued based on a certain condition. They remain there until the end of the loop when they are dequeued and printed. This explains why understanding queue operations is crucial to solving the given exercise.

FIFO Principle

FIFO stands for "First-In-First-Out", and is the principal methodology driving queue data structures. It stipulates that the first element added to the queue will be the first one to be removed. This rule is similar to standing in a lineup, where the first person to join is the first to leave.
This order is critical when considering sequences like those discussed in the exercise. It prevents certain output patterns from emerging because elements added to the queue later cannot exit before those enqueued earlier. Regarding the exercise's question, the FIFO principle contributes to the impossibility of producing a specific sequence. Once an item is placed in the queue, it must be removed in the same order it was entered before any that came after it are dequeued, thereby making specific output orders unachievable.

Boolean Function

A Boolean function in programming is a function that returns one of two possible values: true or false. These functions are essential for decision-making processes within programs, used heavily in control structures like loops, conditionals, and searches.
They act by evaluating specific conditions or scenarios, facilitating branching logic where different actions are taken based on whether the result of the function is true or false. In the given problem, a Boolean function named RanFun() determines whether a number is printed immediately or added to a queue. Despite its functionality being "immaterial" to the problem, understanding its role helps explain how different values are processed differently during loop execution.

• Conditional flow: Determines the path of execution within a loop based on the function's return value.
• Logical operations: Used to evaluate conditions which influence program behavior.

Recognizing the influence of the Boolean function is essential when predicting potential outputs and understanding parts of the algorithm's logic.