Discussion
What is the time complexity of the Quick Sort algorithm in the average case ?
Answer: B
Quick sort's average case is O(n log n).
Each partition step does linear work. With reasonably balanced splits the recursion is about log n levels deep, giving n log n in total, and averaged over random inputs or random pivots the expected number of comparisons is about 1.39 n log2 n.
\(O(n^{2})\) is quick sort's worst case, when the pivot is always the smallest or largest element, for example on sorted input with a first-element pivot. O(n) is too fast for any comparison sort, and O(log n) is the depth of the recursion, not the total work.
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