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r05220502 Design and Analysis of Algorithms

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www.andhracolleges.com The Complete Information About Colleges in Andhra Pradesh Code No: R05220502 Set No. 1 II B.Tech II Semester Regular Examinations, Apr/May 2007 DESIGN AND ANALYSIS OF ALGORITHMS (Computer Science & Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ www.andhracolleges.com (b) Show that n3 logn is w(n3 ). 2. (a) Determine the running time of mergesort for i. sorted input ii. reverse-ordered input iii. random-ordered i
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  Seminar Topics - Scholarships - Admission/Entrance Exam NotificationsUSA-UK-Australia-Germany-France-NewZealand Universities ListEngineering-MBA-MCA-Medical-Pharmacy-B.Ed-Law Colleges Information www.andhracolleges.com The Complete Information About Colleges in Andhra Pradesh www.andhracolleges.com Code No: R05220502 Set No. 1 II B.Tech II Semester Regular Examinations, Apr/May 2007DESIGN AND ANALYSIS OF ALGORITHMS(Computer Science & Engineering)Time: 3 hours Max Marks: 80Answer any FIVE QuestionsAll Questions carry equal marks ⋆ ⋆ ⋆ ⋆ ⋆ 1. (a) Write the non recursive algorithm for finding the Fibonacci sequence andderive its time complexity.(b) Show that n 3 logn is w ( n 3 ). [10+6]2. (a) Determine the running time of mergesort fori. sorted inputii. reverse-ordered inputiii. random-ordered input(b) Write deletion algorithm of binary search tree. [8+8]3. (a) Prove that the Greedy algorithm always finds an optimal schedule.(b) Explain the Kruskal’s algorithm with an example. [8+8]4. (a) For the Travelling sales person algorithm show that the time complexity is0( n 2 2 n ) and space complexity is O ( n 2 n ).(b) Write an algorithm of matrix chain multiplication. [8+8]5. (a) Explain the BFS algorithm with an example.(b) The Preorder and Postorder sequences of a binary tree do not uniquely definethe binary tree. Justify the answer. [8+8]6. (a) Write a recursive backtracking algorithm for sum of subsets problem.(b) Draw the search tree to color the graph with the three colors: red, blue, green.[8+8]7. (a) Explain the general method of Branch and Bound.(b) Explain the principles of LIFO Branch and Bound. [8+8]8. (a) Explain the satisfiability problem and write the algorithm for the same.(b) Differentiate between NP-complete and NP-Hard. [10+6] ⋆ ⋆ ⋆ ⋆ ⋆ 1 of 1  Seminar Topics - Scholarships - Admission/Entrance Exam NotificationsUSA-UK-Australia-Germany-France-NewZealand Universities ListEngineering-MBA-MCA-Medical-Pharmacy-B.Ed-Law Colleges Information www.andhracolleges.com The Complete Information About Colleges in Andhra Pradesh www.andhracolleges.com Code No: R05220502 Set No. 2 II B.Tech II Semester Regular Examinations, Apr/May 2007DESIGN AND ANALYSIS OF ALGORITHMS(Computer Science & Engineering)Time: 3 hours Max Marks: 80Answer any FIVE QuestionsAll Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Show that f(n)+g(n)=O ( n 2 ) where f  ( n ) = 3 n 2 − n + 4 and g(n)=nlogn+5(b) Explain how time complexity of an algorithm is computed. [8+8]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) Show that the greedy algorithm to minimize the mean completion time formultiprocessor Job scheduling.(b) Write an algorithm of Greedy Knapsack and Also analyze its time complexity.[8+8]4. (a) Write a pseudocode for a linear time algorithm that generates the optimalBinary search tree from the root table.(b) Find the minimum no of operations required for the following chain matrixmultiplication using dynamic programming.A(30,40) * B(40,5) * C(5,15) * D(15,6). [8+8]5. (a) Explain the properties of depth-first search.(b) Write a non-recursive algorithm of Post-order traversal of a tree and alsoanalyze its time complexity. [6+10]6. (a) Write an algorithm of finding all m-colorings of a graph.(b) Describe the 4-queens problem using backtracking. [8+8]7. Draw the portion of the state space tree generated by FIFO Branch and Bound forthe following instances.n=5, m=12, ( P  1 −−− P  5 ) = (10,15,6,8,4)( w 1 −−−− w 5 ) = (4,6,3,4,2)8. (a) Explain the satisfiability problem and write the algorithm for the same.(b) Differentiate between NP-complete and NP-Hard. [10+6] ⋆⋆⋆⋆⋆ 1 of 1  Seminar Topics - Scholarships - Admission/Entrance Exam NotificationsUSA-UK-Australia-Germany-France-NewZealand Universities ListEngineering-MBA-MCA-Medical-Pharmacy-B.Ed-Law Colleges Information www.andhracolleges.com The Complete Information About Colleges in Andhra Pradesh www.andhracolleges.com Code No: R05220502 Set No. 3 II B.Tech II Semester Regular Examinations, Apr/May 2007DESIGN AND ANALYSIS OF ALGORITHMS(Computer Science & Engineering)Time: 3 hours Max Marks: 80Answer any FIVE QuestionsAll Questions carry equal marks ⋆ ⋆ ⋆ ⋆ ⋆ 1. (a) Write the non-recursive algorithm for finding the fibonacci sequence and deriveits time complexity.(b) Show that f(n) = 4n 2 − 64n + 288 =Ω( n ) 2 . [10+6]2. (a) suppose a binary tree has leaves ℓ 1 ℓ 2 ....... l m at depths d 1 ,d 2 ....d m respectivelyprove that m  i =1 2 − di ≤ 1 and determine when the equality is true.(b) Write and explain the control abstraction algorithm of divide and conquer.[8+8]3. (a) Design an efficient algorithm for finding the length of a longest path in adirected acyclic graph by using Greedy method.(b) Prove that Kruskal’s algorithm finds a minimum spanning tree. [8+8]4. (a) Solve the all-pairs shortest path problem for the digraph with the weightmatrix  0 2 ∞ 1 86 0 3 2 ∞∞ ∞ 0 4 ∞∞ ∞ 2 0 33 ∞ ∞ ∞ 0  (b) What is Travelling sales person problem and what are its applications. [10+6]5. (a) Find the strongly connected components in the graph of figure 5a.Figure 5a1 of 2  Seminar Topics - Scholarships - Admission/Entrance Exam NotificationsUSA-UK-Australia-Germany-France-NewZealand Universities ListEngineering-MBA-MCA-Medical-Pharmacy-B.Ed-Law Colleges Information www.andhracolleges.com The Complete Information About Colleges in Andhra Pradesh www.andhracolleges.com Code No: R05220502 Set No. 3 (b) Write a non-recursive algorithm of Pre-order traversal of a tree and also ana-lyze its time complexity. [6+10]6. (a) Let w = { 15 , 7 , 20 , 5 , 18 , 10 , 12 } and m=35. Find all possible subsets of w thatsum to m. Draw the portion of the state space tree that is generated.(b) Write the control abstraction of backtracking. [10+6]7. (a) What is Bounding? Explain how these bound are useful in Branch and Boundmethods.(b) Describe the TSP in Branch and Bound. [8+8]8. (a) What is meant by Halting problem explain with an example.(b) Explain the classes of P and NP. [8+8] ⋆ ⋆ ⋆ ⋆ ⋆ 2 of 2
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