Introduction to algorithms

Some books on algorithms are rigorous but incomplete; others cover masses of material but lack rigor. Introduction to Algorithms uniquely combines rigor and comprehensiveness. The book covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers. Each chapter is relatively self-contained and can be used as a unit of study. The algorithms are described in English and in a pseudocode designed to be readable by anyone who has done a little programming. The explanations have been kept elementary without sacrificing depth of coverage or mathematical rigor. The first edition became a widely used text in universities worldwide as well as the standard reference for professionals. The second edition featured new chapters on the role of algorithms, probabilistic analysis and randomized algorithms, and linear programming. The third edition has been revised and updated throughout. It includes two completely new chapters, on van Emde Boas trees and multithreaded algorithms, and substantial additions to the chapter on recurrences (now called Divide-and-Conquer). It features improved treatment of dynamic programming and greedy algorithms and a new notion of edge-based flow in the material on flow networks. Many new exercises and problems have been added for this editionI Foundations Introduction 3 1 The Role of Algorithms in Computing 5 2 Getting Started 16 3 Growth of Functions 43 4 Divide-and-Conquer 65 5 Probabilistic Analysis and Randomized Algorithms 114 II Sorting and Order Statistics Introduction 147 6 Heapsort 151 7 Quicksort 170 8 Sorting in Linear Time 191 9 Medians and Order Statistics 213 III Data Structures Introduction 229 10 Elementary Data Structures 232 11 Hash Tables 253 12 Binary Search Trees 286 13 Red-Black Trees 308 14 Augmenting Data Structures 339 IV Advanced Design and Analysis Techniques Introduction 357 15 Dynamic Programming 359 16 Greedy Algorithms 414 17 Amortized Analysis 451 V Advanced Data Structures Introduction 481 18 B-Trees 484 19 Fibonacci Heaps 505 20 van Emde Boas Trees 531 21 Data Structures for Disjoint Sets 561 VI Graph Algorithms Introduction 587 22 Elementary Graph Algorithms 589 23 Minimum Spanning Trees 624 24 Single-Source Shortest Paths 643 25 All-Pairs Shortest Paths 684 26 Maximum Flow 708 VII Selected Topics Introduction 769 27 Multithreaded Algorithms 772