GATE | GATE CS 2021 | Set 1 | Question 40

Consider the following recurrence relation.

Which one of the following options is correct?
(A) T(n) = Θ(n^5/2)
(B) T(n) = Θ(nlogn)
(C) T(n) = Θ(n)
(D) T(n) = Θ((logn)^5/2)

Answer: (C)
Explanation: Given, recurrence relation can be written as,
T(n) = T(n/2) + T(2n/5) + 7n
T(n) = T((5/2)n/5) + T(2n/5) + 7n

Since, sum of numerator (5/2+2 = 4.5) is less than denominator (5), so time complexity would be function itself.

Hence, T(n) = Θ(7n) = Θ(n)
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