Algorithms Analysis Practice Test

The reason the answer is O(n log n) lies in the specific characteristics of the algorithm's running time. When we describe an algorithm's time complexity as having linear growth with a logarithmic factor, we are indicating that the time taken increases proportionately with the size of the input (n) while also being influenced by a logarithmic component (log n).

This relationship can be understood by dividing the running time into two multipliers: one that grows linearly (which contributes the O(n) part) and another that contributes a logarithmic growth (log n). Hence, when both components are combined, the overall complexity becomes O(n log n).

For context, algorithms that exhibit this complexity are typically those that involve a linear scan through the data while repeatedly applying a logarithmic operation, such as in certain sorting algorithms (like mergesort) or algorithms that utilize divide-and-conquer strategies.

In contrast, other complexities like O(n), O(n²), and O(2^n) describe different growth behaviors: O(n) indicates direct linear growth without additional logarithmic factors, O(n²) indicates quadratic growth (which is significantly faster as n increases), and O(2^n) represents exponential growth that escalates rapidly with even small