GATE | GATE-CS-2009 | Question 39

In quick sort, for sorting n elements, the (n/4)th smallest element is selected as pivot using an O(n) time algorithm. What is the worst case time complexity of the quick sort?
(A) \theta(n)
(B) \theta(nLogn)
(C) \theta(n^2)
(D) \theta(n^2 log n) </pre>

(A) A
(B) B
(C) C
(D) D

Answer: (B)

Explanation: Answer(B)
The recursion expression becomes:

T(n) = T(n/4) + T(3n/4) + cn

After solving the above recursion, we get \theta(nLogn).

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