A comprehensive update of the leading algorithms text, with new material on matchings in bipartite graphs, online algorithms, machine learning, and other topics.Some books on algorithms are rigorous but incomplete; others cover masses of material but lack rigor. Introduction to Algorithms uniquely combines rigor and comprehensiveness.

It covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers, with self-contained chapters and algorithms in pseudocode. Since the publication of the first edition, Introduction to Algorithms has become the leading algorithms text in universities worldwide as well as the standard reference for professionals.

This fourth edition has been updated throughout.

New for the fourth edition   

•  New chapters on matchings in bipartite graphs, online algorithms, and machine learning

•  New material on topics including solving recurrence equations, hash tables, potential functions, and suffix arrays

•  140 new exercises and 22 new problems

•  Reader feedback–informed improvements to old problems

•  Clearer, more personal, and gender-neutral writing style

•  Color added to improve visual presentation

•  Notes, bibliography, and index updated to reflect developments in the field

•  Website with new supplementary material

Table of Contents

I Foundations

Introduction 

1 The Role of Algorithms in Computing 2 Getting Started 

3 Characterizing Running Times 

4 Divide-and-Conquer 

5 Probabilistic Analysis and Randomized Algorithms 

II Sorting and Order Statistics

Introduction 

6 Heapsort 

7 Quicksort 

8 Sorting in Linear Time 

9 Medians and Order Statistics 

III Data Structures

Introduction 

10 Elementary Data Structures 11 Hash Tables 

12 Binary Search Trees 

13 Red-Black Trees 

IV Advanced Design and Analysis Techniques

Introduction 

14 Dynamic Programming 15 Greedy Algorithms 

15 Greedy Algorithms

16 Amortized Analysis 

V Advanced Data Structures

Introduction

17 Augmenting Data Structures

18 B-Trees

19 Data Structures for Disjoint Sets

VI Graph Algorithms

Introduction

20 Elementary Graph Algorithms

21 Minimum Spanning Trees

22 Single-Source Shortest Paths

23 All-Pairs Shortest Paths

24 Maximum Flow

25 Matchings in Bipartite Graphs

VII Selected Topics

Introduction 

26 Parallel Algorithms 

27 Online Algorithms 

28 Matrix Operations 

29 Linear Programming 

30 Polynomials and the FFT 

31 Number-Theoretic Algorithms 32 String Matching 

33 Machine-Learning Algorithms 34 NP-Completeness 

35 Approximation Algorithms 

VIII Appendix: Mathematical Background

Introduction

A Summations

B Sets, Etc.

C Counting and Probability

D Matrices

About the Authors

Thomas H. Cormen is Emeritus Professor of Computer Science at Dartmouth College.

Charles E. Leiserson is Edwin Sibley Webster Professor in Electrical Engineering and Computer Science at MIT.

Ronald L. Rivest is Institute Professor at MIT.

Clifford Stein is Wai T. Chang Professor of Industrial Engineering and Operations Research, and of Computer Science at Columbia University.