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

The classification of functions in terms of their growth rates is fundamental in analyzing algorithms, especially when considering functions with multiple inputs. When a function relies on two inputs, each contributing independently to the overall complexity, it can be represented as the product of those inputs.

In this case, the resulting growth rate is denoted by O(nm), where 'n' and 'm' represent the sizes of the two input parameters. This signifies that the function's performance will scale linearly with respect to both inputs. For example, if one input size doubles while the other remains constant, the growth will reflect that increase, and vice versa.

Comparing this to O(n), O(log n), and O(n^2), those notations describe functions with different growth behaviors. O(n) represents linear growth with a single variable, O(log n) depicts logarithmic growth often seen in divide-and-conquer algorithms (such as binary search), and O(n^2) signifies quadratic growth typically found in algorithms with nested loops iterating over the same collection.

Thus, the classification as O(nm) effectively captures the complexity of a function influenced by two separate inputs, recognizing how both contribute to the overall performance as their sizes change. This understanding is crucial in the