time complexity

Question

The running time of an algorithm T(n), where ‘n’ is the input size, is given by— T(n)=8⌈(n/2)+qn,if n>1⌉=p,if n=1
where p, q are constants. The order of this algorithm is—
(a) n2 (b) nn
(c) n3 (d) n

Answer 1

Thank you @Anirudh sir for the correction..!!  //Question was not clearly typed before. Thank for updating :)
Assuming that the question given is T(n )= 8 (n/2) + qn

n ^{log ₂ 8} = n³

and using Masters theorem, T(n) = Θ(n ³ )

Answer 2

answer given is n3 i.e,(c) but not know the reason

Comments

Using master theorem ans is n³ .

i.e. n^log₂8 = n³ > n²

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Thanks vkm for updating question clearly now!!

Answer 3

$T(n)=8T(\frac{n}{2})+qn$

Using master's theorem, we'll compare this will the standard formula:

$T(n)=aT(\frac{n}{b})+\theta(n^klog^pn)$, we find that
 $a=8, b=2, k=1,p=0$, and $a>b^k$

The Order of the recurrence becomes 

$\theta(n^{log_ba})\rightarrow\theta(n^{log_28})=\theta(n^3)$

Option (C).