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

Exponential growth in algorithm complexity is represented by O(2^n). This notation indicates that the time or space required increases exponentially as the size of the input (n) grows. In an exponential algorithm, each time the input size increases by 1, the resources required double, leading to a rapid increase in complexity.

For example, if n is the input size, then for n = 1, the actual growth is minimal, but for n = 10, the complexity might be 2^10, which equals 1024. This rapid increase is distinctive of exponential growth and can quickly render algorithms inefficient for larger input sizes. Many recursive algorithms exhibit this complexity, particularly when they solve problems by making multiple calls for each subset of the input, leading to a branching factor.

The other options illustrate different growth rates:

- O(n) represents linear growth, where the resources required increase directly in proportion to the input size.

- O(log n) represents logarithmic growth, where resource requirements grow slowly as the input size increases.

- O(n^2) signals quadratic growth, indicating that the resources grow at a rate proportional to the square of the input size—much slower compared to exponential growth but significantly faster than linear growth.

Understanding