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

The time complexity that describes a function not scaling up as quickly as the input size increases is logarithmic time complexity, denoted as O(log n). This means that as the size of the input grows, the time it takes to complete the function increases at a much slower rate.

Logarithmic complexity typically arises in algorithms that effectively reduce the problem size with each step, such as binary search. In a binary search, for instance, the search space is halved with each iteration, leading to the logarithmic growth in time as the input size increases.

In contrast, the other complexities described represent faster growth rates. Linear time complexity, O(n), indicates that the time required grows proportionally with the input size. Quadratic time complexity, O(n^2), signifies that the time increases with the square of the input size, making it significantly less efficient for larger datasets. Lastly, O(nm), which indicates a multiplicative relation between two variables, can also represent a function that grows rapidly. Thus, O(log n) is the correct representation of a function that does not scale up as quickly as the input size grows, making it the most efficient among the choices provided.