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Posted By: Sra1 Member Level: Diamond Posted Date: 27 May 2008
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2007 Jawaharlal Nehru Technological University B.Tech Computer Science & Engineering DESIGN AND ANALYSIS OF ALGORITHMS (Supplimentary Examinations, Aug/Sep 2007) Question paper
Set No 3 ---------------- Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks
1. (a) Define omega notation. Explain the terms involved in it. Give an example. (b) Show that f1(n)×f2(n) = 0(g1(n)×g2(n) wheref1(n) = 0(g1(n) and f2(n) = 0(g2(n)). [10+6] 2. (a) Write and explain the control abstraction for Divide and conquer. (b) Suggest refinements to mergesort to make it in-place. [8+8] 3. (a) What is spanning tree? Explain the prim’s algorithm with an example. (b) Explain the terms Feasible solution, optimal solution and objective function. [10+6] 4. (a) For the Travelling sales person algorithm show that the time complexity is 0(n22n) and space complexity is O(n2n). (b) Write an algorithm of matrix chain multiplication. [8+8] 5. (a) Explain the properties of strongly connected components. (b) Write a non-recursive algorithm of In-order traversal of a tree and also analyze its time complexity. [6+10] 6. Describe Backtracking technique to m-coloring graph. Explain with an example [16] 7. (a) Explain the method of reduction to solve TSP problem using Branch and Bound. (b) Explain the principles of FIFO Branch and Bound. [8+8] 8. (a) Explain the classes of P and NP. (b) Write a nondeterministic Knapsack algorithm. [8+8]
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