Western Governors University (WGU) ICSC2100 C949 Data Structures and Algorithms I Practice Exam

When discussing time complexity, it's important to understand how different complexities represent growth patterns in relation to input size. The scenario described involves a situation where the cost of performing an operation increases only slightly as the input size grows. This is indicative of logarithmic time complexity.

Logarithmic growth, represented by O(log n), describes a situation where each time the input size doubles, the number of operations required increases by a constant amount. Essentially, this complexity arises in algorithms that efficiently halve the problem space with each iteration or recursive call. For instance, binary search operates in O(log n) as it continually divides the input in half until the target value is found, which is notably efficient compared to linear or polynomial growth.

In contrast, linear (O(n)) complexity increases directly in proportion to the input size, while polynomial (O(n^2)) and O(nm) complexities indicate much steeper increases as n or the size of the inputs grow, leading to significantly higher costs in operations. Thus, the situation described aligns well with logarithmic time complexity, making it the correct choice.