Question

(5 marks; questions to Reza) In Lecture 5, Travis said you can prove QuickSort takes N(n log n) time in the best case the same way he proved any comparison-based sorting algorithm takes (n log n) time in the worst case. Give that proof. Notice it doesn't follow directly: e.g., Insertion Sort takes O(n) time in the best case. You can assume QuickSort divides each array into elements less than or equal to the pivot (including the pivot itself) and elements greater than the pivot, so the recursion can be modelled as a binary tree on n leaves.

Answer 1

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Step1

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Step 2

Step3

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Step4

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Step 5

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Step 6

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Step7

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Step 8

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Step 9

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Step 10

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Step 11

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Step 12

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Step 13

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Step 14

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Step 15

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