Consider the following recurrence T n 3T n 5 lgn lgn What is the value of T n A Tex Theta n log 5 3 Tex B Tex Theta n log 3 5 Tex c Tex Theta n Log n Tex D Tex Theta Log n Tex

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Algorithms | Analysis of Algorithms (Recurrences) | Question 11

Consider the following recurrence
T(n) = 3T(n/5) + lgn * lgn

What is the value of T(n)?

(A) $\Theta(n ^ \log_5{3})$
(B) $\Theta(n ^ \log_3{5})$
(c) $\Theta(n Log n )$
(D) $\Theta( Log n )$
(A) A
(B) B
(C) C
(D) D

Answer: (A)

Explanation: By Case 1 of the Master Method, we have T(n) = Theta(n ^ (log5(3)) ). [^ is for power]

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