Browse papers
A

Section A: Long Answer Questions

Attempt any TWO questions.

3 questions·10 marks each
1long10 marks

Define minimum spanning tree. Write Kruskal's algorithm to find the MST of a connected weighted graph, illustrate it with an example and analyze its complexity.

graphmst
2long10 marks

Define asymptotic notations (Big-O, Big-Omega, Big-Theta). State the master theorem and use it to solve the recurrences T(n)=3T(n/2)+n and T(n)=2T(n/4)+sqrt(n).

asymptoticrecurrence
3long10 marks

Explain the complexity classes P, NP, NP-Hard and NP-Complete with examples. Discuss how a problem is proved to be NP-Complete using polynomial-time reduction.

np-completenesscomplexity-classes
B

Section B: Short Answer Questions

Attempt any EIGHT questions.

9 questions·5 marks each
4short5 marks

What are approximation algorithms? Explain the approximation algorithm for the vertex cover problem.

approximation
5short5 marks

Explain the branch and bound technique. How is it used to solve the travelling salesman problem?

branch-and-bound
6short5 marks

Differentiate between Breadth First Search (BFS) and Depth First Search (DFS) with examples and their time complexities.

graphbfs-dfs
7short5 marks

Solve the recurrence relation T(n) = 2T(n/2) + n using the substitution method and the recursion tree method.

recurrencesubstitution
8short5 marks

Explain the job sequencing with deadlines problem and solve it using the greedy approach for a given set of jobs.

greedyjob-scheduling
9short5 marks

Explain the naive string matching algorithm and the Rabin-Karp algorithm with their time complexities.

string-matching
10short5 marks

Write an algorithm for binary search using divide and conquer. Analyze its best-case, worst-case and average-case time complexity.

binary-search
11short5 marks

Explain the randomized quicksort algorithm and analyze its expected time complexity.

quicksort
12short5 marks

Write a greedy algorithm for the fractional knapsack problem and analyze its time complexity.

greedyknapsack