Free Algorithms Book

This free book, named Algorithms, contains algorithm topics carefully selected and clustered. Instead of dwelling on formal proofs the authors distilled in each case the crisp mathematical idea that makes the algorithm work. In other words, they emphasized rigor over formalism.

There are four parts to this Algorithms books:

Part I of the book starts at the historical beginning: numbers, primality, and factoring, and also includes the RSA cryptosystem, and divide-and-conquer algorithms for integer multiplication, sorting and median finding, as well as the fast Fourier transform.

Part II, the most traditional section of the book, concentrates on data structures and graphs; the contrast here is between the intricate structure of the underlying problems and the short and crisp pieces of pseudocode that solve them.

Part III deals with the "sledgehammers" of the trade, techniques that are powerful and general: dynamic programming (a novel approach helps clarify this traditional stumbling block for students) and linear programming (a clean and intuitive treatment of the simplex algorithm, duality, and reductions to the basic problem).

Part IV is about ways of dealing with hard problems: NP-completeness, various heuristics, as well as quantum algorithms, perhaps the most advanced and modern topic. As it happens, we end the story exactly where we started it, with Shor's quantum algorithm for factoring.

Each chapter is a pdf file, and the whole book is also available as a pdf.
Algorithms Book

Table of contents

Preface

Chapter 0: Prologue
Chapter 1: Algorithms with numbers
Chapter 2: Divide-and-conquer algorithms
Chapter 3: Decompositions of graphs
Chapter 4: Paths in graphs
Chapter 5: Greedy algorithms
Chapter 6: Dynamic programming
Chapter 7: Linear programming
Chapter 8: NP-complete problems
Chapter 9: Coping with NP-completeness
Chapter 10: Quantum algorithms