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Mahatma Gandhi University / MG University

May 2015 Question Paper

Course: B.Tech Computer Science and Engineering

Semester: 6

Subject Code: CS010 601

Subject: Design and Analysis of Algorithms

Time Duration: 3:00 hours

Full Marks: 100

Pass Marks: 40

Part A [5*3=15 marks]

1. What are asymptotic notations ? With a figure explain any two of them used for specifying best and worst-case complexities.

2. Using recurrence, derive the complexity of merge-sort algorithm. What is the method behind the algorithm ?

3. What is multistage graph problem ?

4. What is state space tree ? Give an example.

5. Give algorithm for topological sort.

Part B [5*5=25 marks]

6. State Master's Theorem for solving recurrence. Solve: (i) T(n)=3T(n/4)+nlogn by this method.

7. Using Divide and Conquer, give an algorithm for binary search.

8. Give Prim's algorithm for obtaining a minimum spanning tree. What is the loop-invariant in the algorithm ?

9. Explain Monte-Carlo Method.

10. Explain complexity of kth element selection.

Part C [5*12=60 marks]

11. (a) Define space and time complexity. Give an example. [4 marks]

(b) Define asymptotic upper bound of T(n)=2T(n/2)+n using substitution method. [4 marks]

(c) Use recursion tree to determine a good asymptotic upper bound on the recurrence T(n)=3T(n/2)+n. [4 marks]

OR

12. Write an algorithm to sort an array of n-elements using insertion sort and derive its best and worst case runtime complexities.

13. Explain quick sort algorithm. Derive its running time. Show the various steps in quick sorting of < 13, 4, -9, 25, 1, 6, 15, 32 >.

OR

14. Give Strassen's matrix multiplication method. Compare it with the usual matrix multiplication algorithm.

15. (a) What is principle of optimality ? [3 marks]

(b) Compare 0/1 Knapsack and fractional Knapsack problem. [4 marks]

(c) Explain job sequencing with deadlines. [5 marks]

OR

16. (a) What is greedy strategy ? [3 marks]

(b) Give a greedy solution for Knapsack problem. Can greedy method used for solving 0/1 Knapsack problem ? [5 marks]

(c) Compare Dynamic programming and divide and conquer method. [4 marks]

17. State the puzzle problem. What is the best method for solving it ? Also give its complexity.

OR

18. (a) Give FIFO and LIFO control abstractions in branch and bound method. [5 marks]

(b) What is backtracking ? Give any problem that can be solved by backtracking. [7 marks]

19. (a) Write short notes on deterministic and non-deterministic algorithms. [5 marks]

(b) How is comparison tree used in searching problems ? [4 marks]

(c) What is lower bound theory ? [3 marks]

OR

20. (a) Give Las-Vegas algorithm. [6 marks]

(b) Write the steps in Rabin-Karp algorithm. [6 marks]

Mahatma Gandhi University / MG University

May 2015 Question Paper

Course: B.Tech Computer Science and Engineering

Semester: 6

Subject Code: CS010 601

Subject: Design and Analysis of Algorithms

Time Duration: 3:00 hours

Full Marks: 100

Pass Marks: 40

Part A [5*3=15 marks]

1. What are asymptotic notations ? With a figure explain any two of them used for specifying best and worst-case complexities.

2. Using recurrence, derive the complexity of merge-sort algorithm. What is the method behind the algorithm ?

3. What is multistage graph problem ?

4. What is state space tree ? Give an example.

5. Give algorithm for topological sort.

Part B [5*5=25 marks]

6. State Master's Theorem for solving recurrence. Solve: (i) T(n)=3T(n/4)+nlogn by this method.

7. Using Divide and Conquer, give an algorithm for binary search.

8. Give Prim's algorithm for obtaining a minimum spanning tree. What is the loop-invariant in the algorithm ?

9. Explain Monte-Carlo Method.

10. Explain complexity of kth element selection.

Part C [5*12=60 marks]

11. (a) Define space and time complexity. Give an example. [4 marks]

(b) Define asymptotic upper bound of T(n)=2T(n/2)+n using substitution method. [4 marks]

(c) Use recursion tree to determine a good asymptotic upper bound on the recurrence T(n)=3T(n/2)+n. [4 marks]

OR

12. Write an algorithm to sort an array of n-elements using insertion sort and derive its best and worst case runtime complexities.

13. Explain quick sort algorithm. Derive its running time. Show the various steps in quick sorting of < 13, 4, -9, 25, 1, 6, 15, 32 >.

OR

14. Give Strassen's matrix multiplication method. Compare it with the usual matrix multiplication algorithm.

15. (a) What is principle of optimality ? [3 marks]

(b) Compare 0/1 Knapsack and fractional Knapsack problem. [4 marks]

(c) Explain job sequencing with deadlines. [5 marks]

OR

16. (a) What is greedy strategy ? [3 marks]

(b) Give a greedy solution for Knapsack problem. Can greedy method used for solving 0/1 Knapsack problem ? [5 marks]

(c) Compare Dynamic programming and divide and conquer method. [4 marks]

17. State the puzzle problem. What is the best method for solving it ? Also give its complexity.

OR

18. (a) Give FIFO and LIFO control abstractions in branch and bound method. [5 marks]

(b) What is backtracking ? Give any problem that can be solved by backtracking. [7 marks]

19. (a) Write short notes on deterministic and non-deterministic algorithms. [5 marks]

(b) How is comparison tree used in searching problems ? [4 marks]

(c) What is lower bound theory ? [3 marks]

OR

20. (a) Give Las-Vegas algorithm. [6 marks]

(b) Write the steps in Rabin-Karp algorithm. [6 marks]

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