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2003 Course Design & Analysis Of Algorithms

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Total No. of Questions : 12] P1350 [Total No. of Pages : 3 [3864]-401 B.E. (Computer) DESIGN AND ANALYSIS OF ALGORITHMS (2003 Course) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates : 1) Answer THREE questions from each section. 2) Answers to the TWO sections should be written in SEPARATE answer books. 3) Figures to the right indicate full marks. 4) Assume suitable data, if necessary. SECTION - I Q1) a) Explain what are different ways of measuring the running time of an algorithm? [8] b) With the help of an example, explain the general strategy/method that can be applied for analyzing the efficiency of Recursive and nonrecursive algorithms. [10] OR Q2) a) Prove by contradiction : There are infinitely many prime numbers.[8] b) Prove by mathematical induction on the integer n such that m = 2n.[8] c) State and justify whether the function : 100n + 6 = O(n) is CORRECT or INCORRECT. [2] Q3) a) Write an algorithm for Merge Sort algorithm. Draw the tree structure of the recursive calls made. [8] b) Explain the concept of Divide and Conquer technique and explain its three major variations. [8] OR Q4) a) Write a greedy algorithm to solve the knapsack problem and prove : if p1/w1 p2/w2 ........ pn/wn, then Greedy knapsack generates an optimal solution to the given instance of the knapsack problem. [8] b) Find an optimal solution for the following knapsack instance n = 7, m = 15, (p1, p2, .... p7) = (10, 5, 15, 7, 6, 18, 3) and (w1, w2, ..... w7) = (2, 3, 5, 7, 1, 4, 1) [8] P.T.O.

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