UGC-NET | UGC-NET CS 2017 Nov – III | Question 33

Consider the recurrence relation: Where b and c are constants. The order of the algorithm corresponding to above recurrence relation is:

(A)

n

(B)

n²

(C)

n log n

(D)

n³

Answer: (D)

Explanation:

We can use Master theorem to solve this recurrence relation:

T(n) = aT(n/2) + Θ(nklogpn)
In given question:
T(n) = 8T(n/2) + Cn
here a = 8 and b = 2 and k = 1.
 clearly a > bk 
So T(n) = Θ(nlogba )
T(n) = Θ(nlog2 8)
ie T(n) = Θ(n3)

So, option (D) is correct.

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