Advanced Placement (AP) Computer Science

Which scenario describes an algorithm that is not reasonable in terms of time complexity?

1. It completes in constant time.

2. It takes a linear amount of steps relative to the input size.

3. It grows exponentially with the increase of input size.

4. It uses loops to reduce the number of executed steps.

The correct answer is: It grows exponentially with the increase of input size.

The scenario that describes an algorithm that is not reasonable in terms of time complexity is one that grows exponentially with the increase of input size. Algorithms with exponential time complexity are often denoted as O(2^n) or similar, where the time taken doubles with each additional input element. This means that even relatively small increases in the size of the input can lead to dramatically longer execution times. For example, if an algorithm requires 2^n steps, when n is 20, it would require over a million steps, and this number grows rapidly as n increases. This level of complexity is typically impractical for most real-world applications where input sizes can be relatively large. Algorithms with such exponential behavior are often infeasible for use in situations requiring efficient computation or real-time processing, leading to the conclusion that an algorithm with exponential growth is unreasonable for most purposes. In contrast, constant time (independent of input size), linear time (proportional to input size), and optimized looping techniques can be considered reasonable and viable for practical applications in algorithms.