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

The Big-O complexity of a linear search algorithm is correctly identified as O(n). In a linear search, the algorithm examines each element in the list or array sequentially until it finds the target value or reaches the end of the collection.

This means that in the worst-case scenario, the algorithm will need to look at every single element in the collection to determine whether the target is present or not. Therefore, if there are 'n' elements in the list, the number of comparisons and checks the algorithm must perform is directly proportional to 'n'. As such, the time complexity grows linearly with the size of the input, which is why we express this complexity as O(n).

Options like O(1), O(log n), and O(n^2) represent different growth rates not applicable to a linear search. O(1) indicates constant time complexity, O(log n) suggests a logarithmic search such as binary search, and O(n^2) implies a quadratic relationship which would be more characteristic of nested loops processing every pair of elements in the input. Thus, the linear search is best described by O(n).