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2003 Course Design & Analysis of Algorithms

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Total No. of Questions : 12] P1327 [Total No. of Pages : 3 [3664]-334 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) Prove there exist two irrational numbers X and Y such that Xy is rational. [8] b) c) Prove by mathematical induction All horses are the same color . [8] State whether the function is CORRECT or INCORRECT and justify [2] your answer : 10n2 + 4n + 2 = O(n2). OR Q2) a) Easter Sunday is in principle the first Sunday after the full moon after the spring equinox. Is this rule sufficiently precise to be called an algorithm? Justify your answer. [6] b) Explain building a heap and maintaining the heap property. c) [6] Recursive permutation generator A(x0) = (.......(anx0 + an-1)x0+........a1)x0 + a0 Write an algorithm to evaluate a polynomial using Horner s rule. [6] Q3) a) Write an algorithm for recursively finding the maximum and minimum of the set of elements {a(i), a(i + 1)i......a(j)}. [8] b) Prove GREEDY-ACTIVITY-SELECTOR always produces solutions of maximum size for the activity-selection problem. [8] P.T.O.

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