GATE CS 2015 Set 1 — Question 14
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Algorithms → Asymptotic Analysis → Best, Worst, Average Case
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Question
Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting numbers? In the recurrence equations given in the options below, is a constant.
Correct answer
(B) T(n) = T(n-1) + T(1) + cn
Solution
In the worst case of Quicksort, the partition function splits the array into two subarrays of size and (or , depending on implementation, but effectively one element is placed and the rest are on one side). The partitioning step takes time (represented by ).The recurrence relation is:Since is a constant time operation, this simplifies to , which solves to .Option (A) represents the best case (or Merge Sort).
Option (C) represents .
Option (D) represents a binary search-like recurrence but with linear work.
Option (C) represents .
Option (D) represents a binary search-like recurrence but with linear work.
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