Is the question ok?

The Gateway to Computer Science Excellence

+27 votes

Best answer

Option $C$** **is the answer. It can be done by Master's theorem.

$n^{\log_b a} = n^{\log_2 2} = n$.

$f(n) = \sqrt n = n^{\frac{1}{2}}$.

So, $f(n) = O\left(n^{\log_b a -\epsilon}\right)$ is true for any real $\epsilon$, $0 < \epsilon < \frac{1}{2}$. Hence Master theorem Case 1 satisfied,

$$T(n) = \Theta\left(n^{\log_b a}\right) = \Theta (n).$$

0 votes

- All categories
- General Aptitude 1.8k
- Engineering Mathematics 7.4k
- Digital Logic 2.9k
- Programming and DS 4.9k
- Algorithms 4.4k
- Theory of Computation 6.2k
- Compiler Design 2.1k
- Databases 4.1k
- CO and Architecture 3.4k
- Computer Networks 4.1k
- Non GATE 1.4k
- Others 1.7k
- Admissions 595
- Exam Queries 576
- Tier 1 Placement Questions 23
- Job Queries 72
- Projects 17

50,666 questions

56,159 answers

193,768 comments

93,763 users