Algorithms Analysis Practice Test 2025 - Free Algorithms Practice Questions and Study Guide

The degradation of an algorithm's performance from O(log n) to O(n) can occur in cases where the input data features significant repetition. In a scenario where the input data is highly repetitive, an algorithm that is designed to quickly narrow down its search based on unique elements may end up having to process multiple iterations over similar data points. For instance, if the algorithm tries to perform a search or sort operation on a dataset where many elements are duplicates, it may end up evaluating a greater number of elements than it would in a more diverse dataset.

This increased number of evaluations can lead to a linear relationship with respect to the size of the input (n), as opposed to the logarithmic relationship that typically applies when the elements are more diverse. Therefore, when repetition is significant, an algorithm's ability to efficiently halve the problem space at each step can be compromised, resulting in performance dropping to O(n) due to having to check a greater portion of the dataset.

In contrast, other options may not directly impact the algorithm's time complexity in the same way. For example, using a more complex algorithm could potentially lead to worse performance, but it may not transform O(log n) to O(n) directly. Similarly, recalculating the algorithm multiple times