GATE | Gate IT 2005 | Question 51

Let T(n) be a function defined by the recurrence

T(n) = 2T(n/2) + √n for n ≥ 2 and
T(1) = 1

Which of the following statements is TRUE?

(A) T(n) = θ(log n)
(B) T(n) = θ(√n)
(C) T(n) = θ(n)
(D) T(n) = θ(n log n)


Answer: (C)

Explanation: n^(log_ba) = n which is = n^(1-.5) = O(sqrt n)
then by applying case 1 of master method we get T(n) = Θ(n)

Please  refer https://www.geeksforgeeks.org/analysis-algorithm-set-4-master-method-solving-recurrences/ for more details.

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