Chapter 1: Introduction: This chapter introduces the basic definitions and notations of algorithms, such as functions, relations, asymptotic notation, recurrence relations, and master theorem. It also discusses the importance and applications of algorithms in various domains.
Chapter 2: Divide and Conquer: This chapter explains the divide and conquer strategy, which is a method of solving complex problems by breaking them into smaller subproblems that can be solved recursively or iteratively. The chapter presents several examples of divide and conquer algorithms, such as binary search, merge sort, quick sort, matrix multiplication, Strassen's algorithm, and Karatsuba's algorithm.
Chapter 3: Greedy Method: This chapter describes the greedy method, which is a technique of making locally optimal choices at each step to find a globally optimal solution. The chapter illustrates the greedy method with examples such as activity selection, fractional knapsack, Huffman coding, minimum spanning tree, Prim's algorithm, Kruskal's algorithm, and Dijkstra's algorithm.
Chapter 4: Dynamic Programming: This chapter introduces the dynamic programming approach, which is a way of solving problems by storing and reusing previously computed results to avoid repeated computations. The chapter demonstrates the dynamic programming technique with examples such as matrix chain multiplication, longest common subsequence, optimal binary search tree, knapsack problem, coin change problem, and Floyd-Warshall algorithm.
Chapter 5: Backtracking: This chapter explores the backtracking method, which is a technique of generating all possible solutions to a problem by trying different choices and undoing them if they lead to a dead end. The chapter shows how to use backtracking for problems such as n-queens problem, Hamiltonian cycle problem, subset sum problem, graph coloring problem, and sudoku puzzle.
Chapter 6: Branch and Bound: This chapter discusses the branch and bound technique, which is a method of finding an optimal solution to a problem by pruning the search space using bounds. The chapter explains how to apply branch and bound for problems such as travelling salesman problem, 0/1 knapsack problem, assignment problem, and n-queens problem.
Chapter 7: String Matching Algorithms: This chapter presents various algorithms for finding occurrences of a pattern in a text. The chapter covers algorithms such as naive algorithm, Rabin-Karp algorithm, finite automata algorithm, Knuth-Morris-Pratt algorithm, Boyer-Moore algorithm, and Karp-Rabin fingerprinting.
Chapter 8: NP-Completeness: This chapter introduces the concept of NP-completeness, which is a way of classifying problems based on their computational complexity. The chapter defines the classes P, NP, NP-hard, and NP-complete, and explains how to prove that a problem is NP-complete using polynomial-time reductions. The chapter also lists some common NP-complete problems such as satisfiability problem (SAT), clique problem, vertex cover problem, subset sum problem, Hamiltonian cycle problem, travelling salesman problem (TSP), and knapsack problem.
Chapter 9: Approximation Algorithms: This chapter deals with approximation algorithms, which are algorithms that find near-optimal solutions to NP-hard problems in polynomial time. The chapter describes some approximation algorithms for problems such as vertex cover problem (2-approximation), travelling salesman problem (2-approximation), set cover problem (log n-approximation), bin packing problem (first fit decreasing algorithm), and load balancing problem (greedy algorithm).
Chapter 10: Randomized Algorithms: This chapter explores randomized algorithms, which are algorithms that use random choices to achieve better performance or simplicity. The chapter explains some randomized algorithms for problems such as quick sort (randomized pivot selection), minimum cut problem (Karger's algorithm), primality testing (Fermat's test and Miller-Rabin test), and hashing (universal hashing and perfect hashing).
Features of the Book
The book has the following features that make it a useful and comprehensive resource for learning algorithms:
The book provides a clear and concise explanation of the concepts and techniques of algorithms, with examples and pseudo code to illustrate the algorithms.
The book covers a wide range of topics and algorithms, from basic to advanced, that are relevant and useful for various applications and domains.
The book includes numerous exercises and problems at the end of each chapter, with hints and solutions, to help the readers test their understanding and practice their skills.
The book also contains laboratory programs in C/C++ language for implementing some of the algorithms discussed in the book, along with sample input and output.
The book is based on the syllabus of various universities and institutes, and is suitable for both classroom teaching and self-study.
Conclusion
"Design and Analysis of Algorithms" by A.A.Puntambekar is a comprehensive and well-organized textbook that covers the theory and practice of algorithms in a simple and straightforward manner. The book is an ideal choice for students and professionals who want to learn the fundamentals and applications of algorithms in computer science and engineering.
For more information about the book, you can visit the following links:
[Google Books]
[Open Library]
a7a7d27f09