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BCS042 SOLVED ASSIGNMENT 2016-2017 IGNOU BCA 4th SEM

1.
How can big O-notation be used to estimate the sum of the first n positive integers.








2.
Show how the following matrices should be multiplied using the Strassen's algorithm.






























4.
What is a recurrence relation ? Where it is used ? Write recurrence relation for the followings and explain it.
(i) Binary Search Algorithm
(ii) Merge Sort Algorithm
(iii) Fibonacci Series Algorithm
(iv) Quick Sort Algorithm











5.
What are the applications of spanning tree. Write Prim's algorithm and apply it to the following graph to find out total cost of a minimum spanning tree. Show all the intermediate steps. Also, discuss time complexity of Prim's algorithm.






















6.
Define what is an optimization problem ? What are the tasks performed in Greedy method to solve optimization problem. Design a Greedy algorithm for Knapsack problem. We are given n objects and a Knapsack or a bag object. It has a weight Wi and the Knapsack has capacity m. If a fraction Xi , 0 ≤ Xi ≤ 1, of object i is placed into the Knapsack, profit of PiXi is earned. The objective is to fill the Knapsack in such a way as to maximize the total profit earning.











7.
What are the properties of a shortest path. Write Bellman Ford's algorithm and apply it to the following graph.



Show all the intermediate steps of the algorithm.




















8.
Write Merge Sort algorithm and explain the operation of the algorithm with help of the following example. 70 30 20 80 40 90 25 50
















9.
Explain the following terms :
(i) Adjacency matrix
(ii) Convected graph
(iii) Asymptote
(iv) Time complexity
(v) Branch and broad


















10.
Write a Pseudocode to perform a Linear Search Algorithm. Calculate the total number of comparison-operations, assignment-operations and how many times the loop will execute for finding the smallest number in an arrary ?




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