Algorithms Analysis 2025 – 400 Free Practice Questions to Pass the Exam

The running time that doubles as the input size increases by one corresponds to an exponential growth pattern, specifically O(2^n). This complexity indicates that for every additional element (or increase of one in input size), the time required to complete the algorithm becomes exponentially greater.

For example, if you have an input size of n and the time complexity is O(2^n), then when you increase the input size to n+1, the running time will not just increment slightly but will rather double, as it results in evaluating two possible states for each element in the input. This contrasts significantly with other complexities listed, such as linear, logarithmic, or quadratic complexities, which do not exhibit such dramatic growth with slight increases in input size.

Understanding this exponential growth helps clarify why O(2^n) represents a significant increase in running time: it reflects scenarios such as recursive algorithms that solve problems by exploring all subsets or arrangements, leading to a combination of possibilities growing very rapidly with each additional input element.