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Computer Science, Technology and Applications No part of this digital document may be reproduced, stored in a retrieval system or transmitted in any form or by any means. The publisher has taken reasonable care in the preparation of this digital document, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained herein. This digital document is sold with the clear understanding that the publisher is not engaged in rendering legal, medical or any other professional services. Computer Science, Technology and Applications Speech Recognition Technology and Applications Vasile-Florian Păiș (Editor) 2022. ISBN: 978-1-68507-929-1 (Hardcover) 2022. ISBN: 979-8-88697-179-8 (eBook) Internet of Everything: Smart Sensing Technologies T.Kavitha, V. Ajantha Devi, S. 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ISBN: 978-1-68507-916-1 (eBook) More information about this series can be found at https://novapublishers.com/product-category/series/computer-science- technology-and-applications/ Soubhik Chakraborty, Prashant Pranav, Naghma Khatoon and Sandip Dutta A Guide to Design and Analysis of Algorithms Copyright © 2023 by Nova Science Publishers, Inc. DOI: https://doi.org/10.52305/HVZD7283 All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. We have partnered with Copyright Clearance Center to make it easy for you to obtain permissions to reuse content from this publication. Simply navigate to this publication’s page on Nova’s website and locate the “Get Permission” button below the title description. 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Additional color graphics may be available in the e-book version of this book. Library of Congress Cataloging-in-Publication Data ISBN: (cid:28)(cid:26)(cid:28)(cid:16)(cid:27)(cid:16)(cid:27)(cid:27)(cid:25)(cid:28)(cid:26)(cid:16)(cid:23)(cid:22)(cid:19)(cid:16)(cid:19)(cid:11)(cid:72)(cid:37)(cid:82)(cid:82)(cid:78)(cid:12) Published by Nova Science Publishers, Inc. † New York Contents Preface .......................................................................................... vii Chapter 1 Introduction to the Design of Algorithms ........................1 Chapter 2 Divide and Conquer ........................................................11 Chapter 3 Greedy Algorithms ..........................................................19 Chapter 4 Dynamic Programming ...................................................27 Chapter 5 Backtracking ....................................................................45 Chapter 6 Branch and Bound ...........................................................51 Chapter 7 Introduction to the Analysis of Algorithms ...................67 Chapter 8 Randomized Algorithms .................................................81 Chapter 9 Master Theorem ..............................................................91 Chapter 10 A Note on Empirical Complexity Analysis ....................97 References ......................................................................................... 109 About the Authors .................................................................................... 111 Index ......................................................................................... 113 Preface As there can be more than one algorithm for the same problem, designing and analysing an algorithm becomes important in order to make it efficient and robust as far as possible. This book would serve as a guide to design and analysis of computer algorithms. Chapter 1 gives an overview of different algorithm design techniques and the various applications of the discussed techniques. Brute force approach, divide and conquer design approach, greedy algorithms, dynamic programming, branch and bound technique, backtracking and randomized algorithms are discussed in this chapter. Chapter 2 discusses the divide and conquer strategy and some of the algorithms that employs this technique such as recurrence relation, binary search and merge sort. Chapter 3 gives an insight into the greedy algorithms and some problems that can be solved using the greedy approach like the job sequencing problem with deadline and the Dijkstra algorithm. Chapter 4 discusses in depth the dynamic programming approach. Problems such as the stagecoach problem, optimal binary search tree, 0/1 knapsack problem and the subset sum problem are discussed in this chapter. Chapter 5 deals with the backtracking approach with a solution to the N – Queens problem using this approach. Chapter 6 throws some light on the branch and bound technique. Solution to three famous problems viz. assignment problem, 0/1 knapsack problem and travelling salesman problem are discussed using the branch and bound technique. Chapter 7 introduces the second part of the book – the analysis of algorithms. Two different approaches to the analysis of algorithm viz. the asymptotic analysis and the empirical analysis are discussed in the chapter. Chapter 8 discusses randomized algorithms with an empirical analysis touch. Randomized quick sort and randomized binary search are discussed and analysed empirically. Chapter 9 deals with Master Theorem. Many problems that can be solved using Master Theorem are dealt with in this chapter. Chapter 10 gives a note on the empirical complexity analysis of algorithms. Empirical viii Soubhik Chakraborty, Prashant Pranav, Naghma Khatoon et al. complexity of four prominent sorting algorithms – merge sort, quick sort, bubble sort and selection sort have been discussed in depth in this chapter. The authors thank Nova Science Publishers for accepting the challenge to publish this work in a book form. Soubhik Chakraborty Prashant Pranav Naghma Khatoon Sandip Dutta