Download GTU B.Tech 2020 Winter 5th Sem 2150703 Analysis And Design Of Algorithms Question Paper

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Subject Code: 2150703

GUJARAT TECHNOLOGICAL UNIVERSITY

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BE- SEMESTER-V (NEW) EXAMINATION - WINTER 2020

Subject Name: Analysis and Design of Algorithms

Time: 10:30 AM TO 12:30 PM

Instructions:

1. Attempt any FOUR questions out of EIGHT questions.

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2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

Q.1

1. Define O, O, T notations with example. (03)
2. Sort following functions in increasing order of running time for large values of n: n, log2n, 2n, nlogn, n². (03)

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3. (i) What are the different parameters to analyze any algorithm? (04)
   (ii) Solve the following using Master’s theorem:
   A. T(n) = 2T(n/4) + 1
   B. T(n) = 3T(n/3) + n

Q.2

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1. Explain Master Theorem for all three cases. (03)
2. (i) What is the smallest value of n such that an algorithm whose running time is 100n² runs faster than an algorithm whose running time is 2n on the same machine? (04)
   (ii) What is meaning of T(n) = O(1). Explain with suitable example.
3. Given the four matrices P5x4, Q4x6, R6x2, T2x7: Find the optimal sequence for the computation of multiplication operation. (07)

Q.3

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1. Mention the parameters for finding suitable algorithm among many candidate algorithms. Justify parameter with suitable example. (03)
2. i. Which version of algorithm is preferred when memory resources are limited, Iterative or recursive? Justify your answer. (04)
   ii. An asymptotically fast algorithm running on a slow computer is better than an asymptotically slow algorithm running on a fast computer for larger input size. (True/False) Justify your answer with supporting arguments.
3. Analyze Selection sort and Insertion Sort algorithms in best case and worst case scenarios. (07)

Q.4

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1. Merge sort algorithm have similar time complexity in best, average and worst case. (True/False). Justify your answer. (03)
2. Differentiate between greedy approach and Dynamic approach. (04)
3. How the selection of pivot affects the performance of Quick Sort? Discuss all possible scenarios. (07)

Q.5

1. How to solve knapsack problem using dynamic programming? (03)

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2. Given two strings from 26 symbols set, X="BITTER", Y = "BUTTER" obtain the longest common subsequence. (04)

Date: 22/01/2021

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Total Marks: 56

Q.6

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1. Explain the concept of amortized analysis with suitable example. (03)
2. Generate Huffman Code for symbols with probability as A1(0.5), A2(0.25), A3(0.125), A4(0.0625), A5(0.0625). (04)
3. Find the all pair shortest path using Floyd-Warshall Algorithm for directed graph. (07)

Q.7

1. How to solve 0-1 knapsack problem using dynamic programming? Consider Items having Value(Rs.)={60, 100, 120}, Weight(KG)={10, 20, 30} respectively, Weight Capacity = 50 KG. (03)

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2. Define terms: Articulation Point, Isolated, Adjacency (04)
3. Solve the following Task Assignment problem for minimization using following cost matrix. (Cost matrix represents cost of Task T performed by Person P. (07)
   

   	T1	T2	T3
   P1	10	20	25
   P2	20	23	26
   P3	12	16	25

Q.8

1. Find minimum spanning tree for the following undirected weighted graph using Kruskal’s algorithm. (03)

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2. What is the significance of Hashing in Rabin-Karp Pattern matching algorithm? (04)
3. Draw the Finite automata which accepts String over 26 letter alphabet of {A..Z} : ACACAGA (07)

Explain the concept of P, NP and NP-complete problem

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