Discussion
The worst case running times of Insertion sort, Merge sort and Quick sort, respectively, are:
Answer: D
The worst case times are \(\Theta(n^{2})\), \(\Theta(n\log n)\), and \(\Theta(n^{2})\).
Insertion sort: on reverse-sorted input each element shifts past all the earlier ones, \(1 + 2 + \cdots + (n-1) = \Theta(n^{2})\). Merge sort: it always halves the array and merges in linear time, \(\Theta(n\log n)\) in every case. Quick sort: if the pivot is always the smallest or largest element (for example the first element of sorted input), each partition removes only one element, giving \(\Theta(n^{2})\).
Quick sort's \(\Theta(n\log n)\) is its average case, which is the trap in the other options; insertion sort's worst case is never \(n\log n\).
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