GATE | GATE-CS-2015 (Set 1) | Question 12

Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n(≥ 2) numbers? In the recurrence equations given in the options below, c is a constant.

(A) T(n) = 2T (n/2) + cn
(B) T(n) = T(n – 1) + T(0) + cn
(C) T(n) = 2T (n – 2) + cn
(D) T(n) = T(n/2) + cn


Answer: (B)

Explanation: In worst case, the chosen pivot is always placed at a corner position and recursive call is made for following.

a) for subarray on left of pivot which is of size n-1 in worst case.
b) for subarray on right of pivot which is of size 0 in worst case.

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