Algorithms: Design and Analysis

Algorithms: Design and Analysis of is a textbook designed for the undergraduate and postgraduate students of computer science engineering, information technology, and computer applications. It helps the students to understand the fundamentals and applications of algorithms. The book has been divided into four sections: Algorithm Basics, Data Structures, Design Techniques and Advanced Topics. The first section explains the importance of algorithms, growth of functions, recursion and analysis of algorithms. The second section covers the data structures basics, trees, graphs, sorting in linear and quadratic time. Section three discusses the various design techniques namely, divide and conquer, greedy approach, dynamic approach, backtracking, branch and bound and randomized algorithms used for solving problems in separate chapters. The fourth section includes the advanced topics such as transform and conquer, decrease and conquer, number thoeretics, string matching, computational geometry, complexity classes, approximation algorithms, and parallel algorithms. Finally, the applications of algorithms in Machine Learning and Computational Biology areas are dealt with in the subsequent chapters. This section will be useful for those interested in advanced courses in algorithms. The book also has 10 appendixes which include topics like probability, matrix operations, Red-black tress, linear programming, DFT, scheduling, a reprise of sorting, searching and amortized analysis and problems based on writing algorithms. The concepts and algorithms in the book are explained with the help of examples which are solved using one or more methods for better understanding. The book includes variety of chapter-end pedagogical features such as point-wise summary, glossary, multiple choice questions with answers, review questions, application-based exercises to help readers test their understanding of the learnt concepts.

Table of Contents:
CHAPTER 1 INTRODUCTION TO ALGORITHMS ; CHAPTER 2 GROWTH OF FUNCTIONS ; CHAPTER 3 RECURSION ; CHAPTER 4 ANALYSIS OF ALGORITHMS ; 4.6.1 V IVA PROBLEM ; 4.6.2 MARRIAGE PROBLEM ; CHAPTER 5 BASIC DATA STRUCTURES ; 5.3.1 LINEAR SEARCH ; 5.4.1 ADVANTAGES OF A LINKED LIST ; 5.5.1 STATIC IMPLEMENTATION OF STACK ; 5.6.1 STATIC IMPLEMENTATION ; CHAPTER 6 TREES ; CHAPTER 7 GRAPHS ; CHAPTER 8 SORTING IN LINEAR AND QUADRATIC TIME ; CHAPTER 9 DIVIDE AND CONQUER ; CHAPTER 10 GREEDY ALGORITHMS ; 11.2.1 IMPLEMENTING THE DYNAMIC APPROACH ; 11.7 THE OPTIMAL BINARY SEARCH TREE PROBLEM ; CHAPTER 13 BRANCH AND BOUND ; 13.7.1 OPTIMIZATION ; 14.6.1 THE BOOK PROBLEM ; CHAPTER 17 NUMBER THEORETIC ALGORITHMS ; CHAPTER 18 STRING MATCHING ; CHAPTER 19 COMPLEXITY CLASSES ; CHAPTER 20 AN INTRODUCTION TO PSPACE ; CHAPTER 21 APPROXIMATION ALGORITHMS ; CHAPTER 22 PARALLEL ALGORITHMS ; CHAPTER 23 AN INTRODUCTION TO MACHINE LEARNING APPROACHES ; CHAPTER 24 COMPUTATIONAL BIOLOGY AND BIOINFORMATICS ; APPENDIX A1 AMORTIZED ANALYSIS REVISITED ; APPENDIX A2 2-3-4 AND REDBLACK TREES ; APPENDIX A3 MATRIX OPERATIONS ; APPENDIX A4 LINEAR PROGRAMMING ; APPENDIX A5 COMPLEX NUMBERS AND INTRODUCTION TO DFT ; APPENDIX A6 PROBABILITY ; APPENDIX A7 SCHEDULING ; APPENDIX A8 SEARCHING REPRISE ; APPENDIX A9 ANALYSIS OF SORTING ALGORITHMS ; APPENDIX A10 PROBLEMS