5105 BHARATHIDASAN ENGINEERING COLLEGE

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1 CS 6402 DESIGN AND ANALYSIS OF ALGORITHMS II CSE/IT /IV SEMESTER UNIT I PART A 1. Design an algorithm to compute the area and circumference of a circle?(dec 2016) 2. Define recurrence relation? (Dec 2016) 3. Give the Euclid s algorithm for computing gcd (m,n) (May 2016) 4. Compare the orders of growth of n(n-1)/2 and n 2 (May 2016) 5. The log nth smallest number of n unsorted numbers can be determined in O(n) average case time (true or false)? (Dec 2015) 6. Write the recursive Fibonacci series and its recurrence relation. (Dec 2015) 7. Write an algorithm to find the number of binary digits in the binary representation of a positive decimal integer. (May 2015) 8. Write down the properties of asymptotic notations.(may 2015) 9. Differentiate time complexity from space complexity? (May 2010) 10. Define omega notation (May 2010) (2004 R) 11. What do you mean by linear search algorithm? (May 2010) (2004 R) 12. Define the notation of algorithm?(dec 2009) 13. What is an algorithm? (Dec 2012) 14. What are the algorithm design techniques? (Nov 2009) 15. What is analysis of algorithm? (Dec 2009) 16. What is best case efficiency? (May 2009) 17. What is average case efficiency? (May 2009) 18. What is worst case efficiency? (May 2009) 19. What is asymptotic notation? (May 2009) 20. What is big-oh notion? What are properties of big-oh notation? (May 2011) 21. What is theta notation? (Nov 2009) (M.C.A ) 22. What is recursive equation? What are the general plans for recursive algorithms? (May 2010) 23. What are the drawbacks in using the standard unit of time, to measure the runtime of an algorithm? (Dec 2009) 24. What are the 6 step processes in algorithm problem solving? (Dec 2009) 25. What do you mean by order of growth? (May 2013)

2 1. Use the most appropriate notation to indicate the time efficiency class of sequential search algorithm in the worst case, best case and the average case? (Dec 2016) (8) 2. State the general plan for analysing the time efficiency of nonrecursive algorithms and explain with an example?(dec 2016) (8) 3. Solve the recurrence relation with example(may 2015) (16) 4. Give the definition and graphical representation of O notation (May 2015) (8) 5. Give the algorithm to check whether all the elements in a given array of n elements are distinct.find worst case complexity of the same. (May 2015) (8) 6. Give the recursive algorithm to finding the number of binary digits in n s binary representation, where n is a positive decimal integer. Find the recurrence relation and complexity?(may 2016) (8) 7. Write the insertion sort algorithm and estimates its running time?(dec 2015) (8) 8. Derive the worst case analysis of merge sort using example? (Dec 2015) (8) 9. Solve the asymptotic notation? (May 2010),(Dec 2011) (8) 10. Solve the properties of big oh notation? (May 2010) (8) 11. Explain how time complexity & space complexity is calculated. (May 2010) (16) 12. Explain how the removing condition is done from the conditional asymptotic notation and conditional asymptotic notation? (Dec 2011) (8) UNIT II PART A 1. Write an algorithm for brute force closest pair problem (Dec 2016) 2. What is worst case complexity of binary search? (Dec 2016) 3. Give the general method of divide and conquer method? (May 2016) 4. What is the closest pair problem? (May 2016) 5. Give the mathematical notation to determine if a convex direction is towards left or right and write the algorithm.(may 2015) 6. Prove that any comparison sort algorithm requires Ω (n log n) comparisons in the worst case. (May 2015) 7. Design a brute force algorithm for computing the value of polynomial and determine its worst case efficiency class.(dec 2015) 8. Derive the complexity of binary search algorithm.(dec 2015) 9. What is divide and conquer method? Compare and contrast DAC method?(may 2010) 10. What are the examples of divide and conquer method?

3 11. What is binary search? (May 2009) 12. What is brute force method? Give some examples of brute force method? (Dec 2009) 13. Define convex hull problem? 14. What is exhaustive search? 15. State the travelling salesman problem? (Nov 2011) 16. What is knapsack problem? (Nov 2011) 17. What is assignment problem? 18. What is time complexity of binary search? Give an example? (Dec 2009) 19. Trace the operation of binary search algorithm for the input if you are searching for the element.(dec 2009) 20. Give the time efficiency and drawback of merge sort algorithm? (May 2007) 21. What are the difference between quick sorts and merge sort? (Nov 2009) 22. Show the intermediate steps when the numbers123, 23, 1, 43, 54,36,75,34 are sorted using merge sort.(may 2011) 23. What is selection sort? (Dec 2006) 24. Find the number of comparisons made by the sequential search in the worst and best case.(dec 2007) 25. Give the recurrence equation for the worst case behaviour of merge sort? (May 2006) 1. Give the algorithm for quick sort with an example?(dec 2016) (16) 2. There are 4 people who need to be assigned to execute 4 jobs (one person per job) and the problem is to find an assignment with the minimum total cost. The assignment costs is given below, solve the assignment problem by exhaustive search.(dec 2016) (16) Job 1 Job 2 Job 3 Job 4 Person Person Person Person State and explain the merge sort algorithm and give the recurrence relation and efficiency?(may 2016) (16) 4. Explain the method used for performing multiplication of two large integers. Explain how divide and conquer method can be used to solve the same.(may 2016) (16) 5. Write the algorithm by binary search and compute its time complexity?(may 2015) (8) 6. Compute the Strassen s multiplication method?(may 2015) (8) 7. Explain the convex hull problem and solution?(dec 2015) (8)

4 8. Solve the brute force algorithm for whether the given string is specified pattern or not?(dec 2015) (8) 9. Discuss about brute-force algorithm with example? (Dec 2009) (8) 10. Explain exhaustive search problems of TSP, knapsack & assignment?(may 2009) (16) 11. What is closest pair problem? Write algorithm and example? (8) 12. Write short notes on multiplication of large integers?(dec 2009) (8) UNIT III PART A 1. What is meant by principle of optimality? (Dec 2016) 2. How to calculate the efficiency of Dijkstra s algorithm? (Dec 2016) 3. Define the single source shortest paths problem? (May 2016) 4. State the assignment problem? (May 2016) 5. State how binomial coefficient is computed? (May 2015) 6. What is the best algorithm for suited to identify topography graph. Mention its efficiency factors. (May 2015) 7. List out the memory functions used for dynamic programming? (Dec 2015) 8. Write down the optimization technique for wars hall s algorithm. State the rules and assumptions are implied. (Dec 2015) 9. Write an algorithm to find the shortest path between all pairs of node? (May 2011) 10. What are the problems that can be solved using dynamic programming? 11. State Floyd s algorithm? Where do you apply Floyd s algorithm? (May 2009) 12. Compare greedy and dynamic programming method? (Dec 2012) 13. What are the applications of greedy method? 14. What is minimum spanning tree? (May 2006) 15. What is a Huffman tree? 16. Give the time and space complexity of travelling salesman problem? (Dec 2006) 17. What is meant by optimal binary search tree? (May 2010) 18. Define optimal solution? (May 2010) 19. What is meant by memory function technique? 20. Define wars hall s algorithm? 21. What are advantages of optimal search tree? (May 2010) 22. Define knapsack problem? (Dec 2012) 23. What is feasible solution? (May 2010) 24. Write the general algorithm for greedy method control abstraction.(dec 2011)

5 25. What are the drawbacks of dynamic programming? 1. Solve the all pairs shortest path problem for the digraph with weight matrix? (Dec 2016) (16) 0 2 Infinitive Infinitive Infinitive Infinitive 0 4 Infinitive Infinitive Infinitive Infinitive Infinitive Infinitive 0 2. Apply kruskal s algorithm to find a minimum spanning tree? (Dec 2016) (16) 3. Discuss about the algorithm and pseudo code to find the minimum spanning tree using prim s algorithm. Find the minimum spanning tree for the graph and discuss about the efficiency of algorithm.(may 2016) (16) 4. Find all the solution to the travelling salesman problem by exhaustive search. (May 2016) (10) 5. Write the procedure code and solving Huffman codes?(may 2015) (16) 6. Write an algorithm and to construct for Optimal Binary search tree?(may 2015) (16) 7. Explain about wars hall s algorithm with suitable examples?(dec 2015) (16) 8. Write and explain the problem of computing binomial coefficient?(dec 2015) (16) 9. Explain the concept of memory function? (May 2016) (6) 10. Discuss about knapsack problem using knapsack problem? (May 2011) (16) 11. Explain Dijkstra s algorithm with example? (May 2010) (16) 12. Discuss about dynamic programming with example? (May 2010) (16) UNIT IV PART A 1. Define the iterative improvement technique.(dec 2016) 2. What is maximum cardinality matching? (Dec 2016) 3. What is state space graph? (May 2016) 4. State extreme point theorem? (May 2016) 5. What do you meant by perfect matching in bipartite graphs? (May 2015) 6. Define flow cut? (May 2015) 7. Determine the linear program? (Dec 2015) 8. What is network flow? (Dec 2015)

6 9. What are the examples of iterative improvement technique? (May 2009) 10. What are the applications of linear programming? (May 2009) 11. Define ford-fulkerson method? (Dec 2009) 12. What is augmenting paths? (Dec 2009) 13. What is residual network? (May 2010) 14. What is stable marriage problem? (Dec 2010) 15. Define linear programming? (Dec 2011) 16. Define simplex method? (May 2011) 1. State and probe Max-flow Min-cut theorem?(dec 2016),(Dec 2015) (8) 2. Summarize the steps of the simplex method?(dec 2016),(May 2016),(Dec 2015),(May 2015) (8) 3. Explain briefly about stable marriage problem?(dec 2016),(May 2015) (10) 4. Determine the time efficiency class of the stable marriage algorithm? (Dec 2016) (6) 5. Apply the shortest-augmenting-path algorithm to the network? (May 2016) (16) 6. How to compute maximum flow using ford-fulkerson method? (May 2009) (8) 7. Illustrate the workings of the maximum matching algorithm on the weighted tree? (8) 8. State and prove max-flow min-cut theorem? (May 2016) (8) 9. Illustrate the workings of the maximum matching algorithm on weighted tree? (Dec 2015) (12) 10. How do you compute maximum flow for the following graph using ford Fulkerson method? (May 2015) (10) 11. Write the procedure to initialize simplex which determines if a linear program is feasible or not? (Dec 2015) (4) UNIT V PART A 1. Write the formula for decision tree for searching a sorted array? (Dec 2016) 2. State the reason for terminating search path at the current node in branch and bound algorithm? (Dec 2016) 3. Give the purpose of lower bound and upper bound? (May 2016) 4. What is Euclidean minimum spanning tree problem? (May 2016) 5. Define Hamiltonian circuit problem? (May 2015) 6. How differ from NP-hard and NP-complete problem? (May 2015) 7. Draw a decision tree for three comparison values?(dec 2015)

7 8. Define backtracking? (Dec 2015) 9. What is state space tree? (Dec 2009) 10. State N-queen problem? 11. What are the strategies used in branch and bound technique? What is branch and bound? (May 2009) 12. State the travelling salesman problem? (Dec 2011) 13. Define branch and bound technique? (May 2010) 14. State sum of subset problem? (May 2010) 15. What is an approximation algorithm? 16. Define class P problem? (May 2011) 17. Define the class NP problem and NP completeness? (May 2011) 18. Define deterministic algorithms? 19. Define non-deterministic algorithms? 20. What is time complexity for Hamiltonian circuit problem? Draw the graph?(may 2011) 21. What is promising and non-promising node? 22. What is decision problem? 23. Define a live node? (May 2010) 24. Define an E-node? (May 2010) 25. Define a dead node? (May 2010) 1. Draw a decision tree and find the number of key comparisons in the worst and average case for the 3element bubble sort?(dec 2016) (8) 2. Write backtracking algorithm for 4 Queen s problem and discuss the possible solution (Dec 2016) (8) 3. Solve the knapsack problem by branch and bound algorithm=15. (Dec 2016) (16) Item Weight profit 1 5 $ $ $ $4 5 5 $ $2 4. Give five undecidable problems and explain the famous halting problem. (May 2016) (16) 5. State the subset sum problem and complete state-space tree of the backtracking algorithm applied to the instance A= {3, 56.7} and d=15 of the subset sum problem.(may 2016) (16) 6. Suggest an approximation algorithm for travelling salesperson problem.(may 2015) (8)

8 7. Explain how job assignment problem could be solved, given n tasks and n agents has a cost to complete each task, using branch and bound technique.(may 2015) (8) 8. Implement an algorithm for knapsack problem using NP-hard approach(dec 2015) (8) 9. The knight is placed on the first block of an empty board and moving according to the rules of chess, must visit each square exactly once using backtracking procedure?(dec 2015) (8) 10. Show that the Hamiltonian path problem reduces to the problem(dec 2015) (10) 11. What is an approximation algorithm?give example (Dec 2015) (4) 12. Explain state space problem using backtracking technique? (May 2011) (16) 13. Write and explain the techniques in branch and bound techniques? (Dec 2009) (16)

CLASS: II YEAR / IV SEMESTER CSE CS 6402-DESIGN AND ANALYSIS OF ALGORITHM UNIT I INTRODUCTION

CLASS: II YEAR / IV SEMESTER CSE CS 6402-DESIGN AND ANALYSIS OF ALGORITHM UNIT I INTRODUCTION 1. What is performance measurement? 2. What is an algorithm? 3. How the algorithm is good? 4. What are the