1
GATE CSE 2006
+2
-0.6
Consider the following recurrence:
$$T\left( n \right){\rm{ }} = {\rm{ 2T(}}\left\lceil {\sqrt n } \right\rceil {\rm{) + }}\,{\rm{1 T(1) = 1}}$$
Which one of the following is true?
A
$$T\left( n \right){\rm{ }} = {\rm{ }}\theta \,{\rm{(loglogn)}}$$
B
$$T\left( n \right){\rm{ }} = {\rm{ }}\theta \,{\rm{(logn)}}$$
C
$$T\left( n \right){\rm{ }} = {\rm{ }}\theta \,{\rm{(}}\sqrt n {\rm{)}}$$
D
$$T\left( n \right){\rm{ }} = {\rm{ }}\theta \,{\rm{(}}n {\rm{)}}$$
2
GATE CSE 2006
+2
-0.6
The median of n elements can be found in O(n) time. Which one of the following is correct about the complexity of quick sort, in which median is selected as pivot?
A
$$\theta \,{\rm{(n)}}$$
B
$$\theta \,{\rm{(nlogn)}}$$
C
$$\theta \,{\rm{(n}}{}^2{\rm{)}}$$
D
$$\theta \,{\rm{(n}}{}^3{\rm{)}}$$
3
GATE CSE 2005
+2
-0.6
Suppose T(n) = 2T (n/2) + n, T(0) = T(1) = 1
Which one of the following is FALSE?
A
T(n) = O(n2)
B
$$T\left( n \right){\rm{ }} = {\rm{ }}\theta \left( {n{\rm{ }}\,log\,{\rm{ }}n} \right)$$
C
$$T\left( n \right){\rm{ }} = {\rm{ }}\Omega ({n^2})$$
D
T(n) = O(n log n)
4
GATE CSE 1997
+2
-0.6
Let T(n) be the function defined by $$T(1) =1, \: T(n) = 2T (\lfloor \frac{n}{2} \rfloor ) + \sqrt{n}$$
Which of the following statements is true?
A
$$T(n) = O \sqrt{n}$$
B
$$T(n)=O(n)$$
C
$$T(n) = O (\log n)$$
D
$$T(n) = O (\log n)$$
GATE CSE Subjects
Theory of Computation
Operating Systems
Algorithms
Digital Logic
Database Management System
Data Structures
Computer Networks
Software Engineering
Compiler Design
Web Technologies
General Aptitude
Discrete Mathematics
Programming Languages
Computer Organization
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