2004-05 MODEL PAPER

MCA 2.1.4

DESIGN AND ANALYSIS OF ALGORITHMS

First Question is Compulsory

Answer any four from the remaining

Answer all parts of any Question at one place.

Time: 3 Hrs.
Max. Marks: 100

1. Explain:
a. Asymtotic Notation.
b. Lower Bounds.
c. NP-hard Problems.
d. Minimal spanning Tree.
e. Convex Hull Problem.
f. Memory Functions.
g. Topological Sorting.

2. Describe divide and conquer strategy for multiplying two n-bit numbers. Derive its time complexity.

3. a. Explain quick sort Algorithm.
b. Show how the quick sort algorithm sorts the following sets of keys.
(1,1,1,1,1,1,1) and (5,5,8,3,4,3,2)

4. a. Explain how you can use greedy technique for Huffman coding.
b. Explain the greedy technique with knopsack problem as an example.

5. Explain problem Reduction using linear programming as an example.

6. Explain Dynamic Programming Technique for construction of optimal binary search trees with the help of an example.

7. Outline Template of a backtracking algorithm. Explain a backtracking solution to the Hamiltonian circuit problem.

8. Explain branch and bound technique. Apply it to the following instance of Assignment problem.