MCA DCA7104 Analysis and Design of Algorithms

Description

SESSION	APril-2023
PROGRAM	MCA
SEMESTER	III
course CODE & NAME	DCA7104Analysis and Design of Algorithms
CREDITS	4
nUMBER OF ASSIGNMENTS & Marks	02 &30 Marks each

 

SET-I

 

1. A. Explain amortized analysis with the help of an example.

Ans 1a.

Amortized analysis is a method used in computational complexity theory, to find the average time taken per operation, over a worst-case sequence of operations. This is useful when a data structure undergoes a series of operations, and we want to analyze the time complexity not of one operation but of the whole series. The analysis assures that no particular operation will be too expensive in

 

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2. Discuss the recursion step to compute quicksort using Divide and Conquer strategy.

Ans 2.

Quicksort is a classic algorithm used for sorting arrays or lists. It was developed by British computer scientist Tony Hoare in 1959 and is still considered one of the most efficient sorting algorithms in many scenarios. It employs a divide-and-conquer strategy, which means it breaks the problem

 

 

3. A. Analyse Brute force String matching algorithm and obtain its time complexity

Ans 3a.

The Brute Force String Matching algorithm is a simple and straightforward technique for finding a substring within a string. It operates by aligning the search pattern at the start of the text and then moving the pattern one character at a time, checking for a match at each position.

Algorithm:

 

 

1. Write a recursive algorithm to compute GCD of two numbers using Euclid’s algorithm.

Ans 2B.

 

Euclid’s Algorithm is a time-tested method for computing the Greatest Common Divisor (GCD) of two numbers. The key principle behind this method is that the GCD of two numbers remains the same if the larger number is replaced by its difference with the smaller number. And with repeated application of this principle, we eventually find the GCD.

Euclid

 

SET-II

 

 

4. A. Differentiate between bottoms-up and top-down heap construction.

Ans 4a.

Heap construction is a process used to build a heap data structure from a given set of input data. It can be accomplished through two primary methods: Bottom-up and Top-down.

Bottom-Up Heap Construction:

Also known as the Williams method, the bottom-up heap construction technique works by building the heap

 

5. Explain the Floyd’s algorithm to find the shortest path with its complexity.

Ans 5.

Floyd’s algorithm

We can generate the distance matrix with an algorithm that is very similar to Warshall’s algorithm. It is called Floyd’s algorithm, after its inventor R. Floyd. It is applicable to both

 

6. A. How are Huffman codes constructed?

Ans 6A.

To assign codes start from root of the tree and assign 1 to every left branch and 0 to every right branch. We will now explain the process of tree creation. To find the code for a particular symbol, start from that symbol and traverse in direction towards the root. As soon as you encounter a branch assign the code to that branch (1/0); Suppose we need to find Huffman code for ‘C’; we start from ‘C’ and move toward root i.e., C -> EC -> DEC -> BDEC- >ABDEC; we get code 1