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Posted By: kondapalli Member Level: Gold Posted Date: 01 May 2008
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2007 Jawaharlal Nehru Technological University M.Tech Computer Science Design and Analysis of Algorithms Question paper
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1.a) Organize the following classes into inheritance hierarchies and where appropriate create new classes : Student, Lecturer, technician, Admin, Office, Lab, Post graduate student, undergraduate Student, Lecture and Building using C++ Syntax.
b) Write a C++ program to generate a fibbonacci series overloading a prefix operator
2.a) Develop a probabilistic algorithm to find the value of the integral dxx?-2024
b) Give the Big-oh notation definition and briefly discuss the properties of such as notation with reference to commutative, Associate, reflexive, Symmetric and antisymmetric natures of the functions.
3.a) Show how matrix multiplication is carried out using the strassen’s method. Find the complexity of the Strassen’s method.
b) Write the Binary search algorithm for deletion.
4.a) Show how prim’s algorithm can be implemented using heap.
b) Explain the job sequencing with deadlines with an example using the Greedy approach.
5. Consider a 4 – stage system with device types d1, d2, d3, d4. Let C1 = 30, C2 = 15, C3 = 20, C4 = 10. The cost of the system is C = 135. The reliabilities of the device types are
r1 = 0.9, r2 = 0.8, r3 = 0.5, r4 = 0.6.
6.a) Consider building a B-tree of degree 4 that is balanced four-way tree where each node can hold 3 data value and have four branches. Suppose it needs to contain the following values
1,5,6,2,8,11,13,18,20,7,9
b) Show that the inorder and preorder sequences of a binary tree uniquely define the binary tree.
7. Solve the Traveling salesperson problem having the following cost-matrix using branch-and-bound technique.
8 7 3 12 8
3 8 6 14 9
5 8 8 6 18
9 3 5 8 11
18 14 9 8 8
8.a) What are non deterministic algorithms. Devise a non-deterministic algorithm for the satisfiability problem.
b) Prove that decision problem (CDP) ? node cover decision problem.
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