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University of Sargodha MS 1" Term Examination 2015 Subject: Computer Science Paper: Advanced Analysis of Algorithms (CS-5143) Maximum Marks: 80

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Paper text

University of Sargodha

MS 1" Term Examination 2015

Subject: Computer Science Paper: Advanced Analysis of Algorithms (CS-5143)

Maximum Marks: 80

Time Allowed: 3 Hours

Objective Part (Compulsory)

..No. 1. Write short answers for the following questions. (8x2-16)

1) Define asymptotic analysis.

2) Define Big-Oh notation.

3) What is fast algorithm?

(4) What properties does a problem hold for applying dynamic programming approach?

5h What are the steps for designing dynamic programming algorithm?

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What is the main idea of dynamic programning approach?

Define optimal substructure property.

Define longest common subsequence (LCS) problem.

Subjective Part

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(4x16=64)

Note: Attempt any four questions.

Q.No.2. Write Bellman-ford algorithm and elaborate it by performing dry run on the following

graph.

Q.No.3. Prove optimal substructure of shortest path stated as: Given a weighted directed graph

G = (V,

E) with weight function w: E → R, let p = < V1.... Uk > be a shortest path between

vertex v, and Uk and for any i,j such that 1 ≤ i ≤ / ≤ k, let pi = (V,,...,v, be subpath of p

from vertex v, to vertex v. Then ply is the shortest path from v, to v;.

CQ.No.4. Prove correctness of cut property.

ladni coterm countner on the own are show you prese by stop.

Q.No.5. Perform counting sort on the following array. Show your procedure step by step.

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Q.No. 6. Design a Huffman coding scheme ta encode a text file containing alphabets (A, B, C, D,

E, F,

G) with the following frequencies.

Alphabets

A

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G

Frequencies

10

20

30

40

50

60

70

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