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

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