Vikram Sarabhai Essays and Term Papers
MASTER OF COMPUTER APPLICATIONS (MCA)
MCA/ASSIGN/III/YEAR/2012
ASSIGNMENTS Year, 2012-13 (3rd Semester)
(MCS-031, MCS-032, MCS-033, MCS-034, MCS-035, MCSL-36)
There are ten questions in this assignment, which carries 80 marks. Rest 20 marks are for viva-voce. Answer all the questions. You may use illustration and diagrams to enhance the explanations. Please go through the guidelines regarding assignments given in the MCA Programme Guide for the format of presentation. The examples, whenever asked to be given, should be different from those that are discussed in the course material. Question1: Using Insertion Sort, sort the following sequence in increasing (10 marks) order and do the analysis of the algorithm: 35, 37, 18, 15, 40, 12 Question 2: Write a pseudocode for divide and conquer algorithm for finding the position of an array of n numbers and estimate the number of key comparisons made by your algorithm. (10 marks) Question 3: Apply quicksort to sort the following list: Q U I C K S O R T (10 marks) in alphabetical order. Find the element whose position is unchanged in the sorted list. Question 4: Write Strassen’s matrix multiplications algorithm for obtaining the product of two matrices. (10 marks) Question 5: (i) Define DFS. Explain briefly how it differs from BFS. (10 marks) (ii) Write pseudocode for DFS and calculate its time complexity Question 6: Apply Kruskal’s algorithm to find minimal spanning tree with an example. (10 marks) Question7: Arrange the following growth rates in increasing order: O (3n), O (n2), O (1), O (n log n) Question 8: Using Principle of Mathematical Induction, prove that the sum 20 + 21 +…+ 2n is 2n +1 – 1 for all n 1.
(4 marks)
(6 marks)
Question 9: Define Knapsack Problem and cite one instance of the problem. (5 marks) Question 10: Explain the essential idea of Dynamic Programming. How does Dynamic Programming differ from Divide and conquer approach for solving problems?
(5 marks)
3
Course Code
MCA/ASSIGN/III/YEAR/2012
ASSIGNMENTS Year, 2012-13 (3rd Semester)
(MCS-031, MCS-032, MCS-033, MCS-034, MCS-035, MCSL-36)
There are ten questions in this assignment, which carries 80 marks. Rest 20 marks are for viva-voce. Answer all the questions. You may use illustration and diagrams to enhance the explanations. Please go through the guidelines regarding assignments given in the MCA Programme Guide for the format of presentation. The examples, whenever asked to be given, should be different from those that are discussed in the course material. Question1: Using Insertion Sort, sort the following sequence in increasing (10 marks) order and do the analysis of the algorithm: 35, 37, 18, 15, 40, 12 Question 2: Write a pseudocode for divide and conquer algorithm for finding the position of an array of n numbers and estimate the number of key comparisons made by your algorithm. (10 marks) Question 3: Apply quicksort to sort the following list: Q U I C K S O R T (10 marks) in alphabetical order. Find the element whose position is unchanged in the sorted list. Question 4: Write Strassen’s matrix multiplications algorithm for obtaining the product of two matrices. (10 marks) Question 5: (i) Define DFS. Explain briefly how it differs from BFS. (10 marks) (ii) Write pseudocode for DFS and calculate its time complexity Question 6: Apply Kruskal’s algorithm to find minimal spanning tree with an example. (10 marks) Question7: Arrange the following growth rates in increasing order: O (3n), O (n2), O (1), O (n log n) Question 8: Using Principle of Mathematical Induction, prove that the sum 20 + 21 +…+ 2n is 2n +1 – 1 for all n 1.
(4 marks)
(6 marks)
Question 9: Define Knapsack Problem and cite one instance of the problem. (5 marks) Question 10: Explain the essential idea of Dynamic Programming. How does Dynamic Programming differ from Divide and conquer approach for solving problems?
(5 marks)
3
Course Code