Algorithms

Quicksort’s worst case occurs when the pivot divides the array into extremely unbalanced partitions, such as a sorted or reverse‑sorted list, leading to recursive calls of size n‑1 and n‑2; the total work sums to a quadratic series, giving O(n²) time. The choice O(n log n) describes the average case, not the worst case, so it is a common misconception.

This recurrence falls under Case 2 of the Master Theorem, where the driving function f(n) matches the algorithmic work, resulting in an extra logarithmic factor. Option A is incorrect because it fails to account for this log n factor when the two terms are asymptotically equal.

Binary search repeatedly divides the search interval in half, leading to a logarithmic time complexity of O(log n). A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.

• !Linear time, or O(n) (Option A), is incorrect because it describes a sequential search where every element is checked one by one.
• !The choice O(n log n) describes the average case, not the worst case, so it is a common misconception.
• !Option A is incorrect because it fails to account for this log n factor when the two terms are asymptotically equal.

Answer each from memory — you'll see instantly whether you're right and why.

Run a focused 10-question mini-mock on Algorithms and see it stick.