1

GATE CSE 2015 Set 3

MCQ (Single Correct Answer)

+2

-0.6

Let $$f\left( n \right) = n$$ and $$g\left( n \right) = {n^{\left( {1 + \sin \,\,n} \right)}},$$ where $$n$$ is a positive integer. Which of the following statements is/are correct?

$$\eqalign{ & \,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,f\left( n \right) = O\left( {g\left( n \right)} \right) \cr & \,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,\,\,f\left( n \right) = \Omega \left( {g\left( n \right)} \right) \cr} $$

2

GATE CSE 2015 Set 1

MCQ (Single Correct Answer)

+2

-0.6

An algorithm performs $${\left( {\log N} \right)^{1/2}}$$ find operations, N insert operations, $${\left( {\log N} \right)^{1/2}}$$ delete operations, and $${\left( {\log N} \right)^{1/2}}$$decrease-key operations on a set of data items with keys drawn from a linearly ordered set. For a delete operation, a pointer is provided to the record that must be deleted. For the decrease-key operation, a pointer is provided to the record that has its key decreased. Which one of the following data structures is the most suited for the algorithm to use, if the goal is to achieve the best total asymptotic complexity considering all the operations?

3

GATE CSE 2015 Set 1

MCQ (Single Correct Answer)

+2

-0.6

Consider the following C function.

```
int fun1 (int n) {
int i, j, k, p, q = 0;
for (i = 1; i < n; ++i)
{
p = 0;
for (j = n; j > 1; j = j/2)
++p;
for (k = 1; k < p; k = k * 2)
++q;
}
return q;
}
```

Which one of the following most closely approximates the return value of the function **fun1**?4

GATE CSE 2013

MCQ (Single Correct Answer)

+2

-0.6

The number of elements that can be stored in $$\Theta (\log n)$$ time using heap sort is

Questions Asked from Complexity Analysis and Asymptotic Notations (Marks 2)

Number in Brackets after Paper Indicates No. of Questions

GATE CSE 2021 Set 1 (2)
GATE CSE 2019 (1)
GATE CSE 2016 Set 2 (1)
GATE CSE 2015 Set 3 (1)
GATE CSE 2015 Set 1 (2)
GATE CSE 2013 (1)
GATE CSE 2011 (1)
GATE CSE 2008 (5)
GATE CSE 2007 (3)
GATE CSE 2005 (3)
GATE CSE 2004 (4)
GATE CSE 2003 (1)
GATE CSE 2002 (2)
GATE CSE 2000 (1)
GATE CSE 1994 (1)
GATE CSE 1993 (1)
GATE CSE 1990 (1)
GATE CSE 1987 (2)

GATE CSE Subjects

Discrete Mathematics

Programming Languages

Theory of Computation

Operating Systems

Computer Organization

Database Management System

Data Structures

Computer Networks

Algorithms

Compiler Design

Software Engineering

Web Technologies

General Aptitude