Algo&Complex-Prelim Exam

Consider a mathematical problem that requires finding the greatest common divisor (GCD) of two numbers using the Euclidean method. This problem-solving approach involves repeatedly subtracting the smaller number from the larger number until the numbers become equal. This can be classified as:

• A finite algorithm involving non-recursive steps

• An infinite algorithm with a finite solution

• A recursive algorithm with a finite number of steps

• A non-algorithmic solution

Which of the following situations would not be considered an algorithm?

• A step-by-step process to calculate the area of a circle

• A set of instructions that repeats indefinitely without reaching a conclusion

• A finite procedure to find the maximum number in a list

• A recursive method to solve the factorial of a number

Before building a skyscraper, engineers use software to test how it would respond to earthquakes and strong winds. Which application of algorithms is this?

• Optimization of Industrial Processes

• Structural Engineering

• Navigation

• Financial Analysis

A car manufacturing company wants to reduce production time while lowering costs. Which application of algorithms is being used?

• Optimization of Industrial Processes

• Financial Analysis

• Recommendation Systems

• Circuit Design

Google Maps suggests the shortest route between two cities. Which algorithmic problem is being solved?

• Graph Problem

• Optimization

• Searching

• Data Compression

After watching a movie on Netflix, the platform suggests similar films based on your viewing history. Which application of algorithms is working here?

• Recommendation Systems

• Navigation

• Circuit Design

• Structural Engineering

Which of the following best illustrates the need for "finiteness" in an algorithm?

• The algorithm should run indefinitely to find the most optimal solution.

• The algorithm must complete its task within a finite number of steps, ensuring that it does not run endlessly and always provides an answer.

• Finiteness is only needed when the algorithm deals with large datasets.

• Finiteness ensures that the algorithm can restart from the beginning after completing its task.

Why is it important for an algorithm to be "feasible"?

• The algorithm must rely on futuristic technology to ensure optimal performance.

• It should be simple, generic, and executable with available resources, ensuring that it can be practically implemented and used in real-world scenarios.

• Feasibility is not crucial as long as the algorithm works in theory.

• The algorithm should focus on complexity rather than practicality to be effective.

How does being "language-independent" benefit an algorithm?

• The algorithm needs to be rewritten for each programming language.

• It consists of plain instructions that can be implemented in any programming language, ensuring consistent results no matter the language used.

• Language independence limits the algorithm's applicability to only certain types of tasks.

• Algorithms should rely on specific languages to ensure better performance.

What does "definiteness" mean in the context of an algorithm, and why is it essential?

• It allows instructions to be ambiguous so that different programmers can interpret them based on their preferences.

• It ensures that every instruction is precise, unambiguous, and easy to interpret, so the algorithm's steps are clear and easily followed without confusion.

• Definiteness means that the algorithm can be altered by users based on their needs.

• It allows the algorithm to have varying interpretations depending on the situation.