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 the worst case, the chosen pivot is always placed at a corner position and recursive call is made for the 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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