Algorithms, Part II

437 Pages·2013·10.67 MB·English

by  Robert Sedgewick

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Algorithms
FOURTH EDITION
PART II
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ptg12441863
Algorithms
FOURTH EDITION
PART II
ptg12441863
Robert Sedgewick
and
Kevin Wayne
Princeton University
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ISBN-13: 978-0-13-379911-8
ISBN-10: 0-13-379911-5
First digital release, February 2014
______________________________
To Adam, Andrew, Brett, Robbie
and especially Linda
______________________________
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___________________
To Jackie and Alex
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CONTENTS
Note: This is an online edition of Chapters 4 through 6 of Algorithms, Fourth Edition, which con-
tains the content covered in our online course Algorithms, Part II.
For more information, see http://algs4.cs.princeton.edu.
Preface ix
Chapters 1 through 3, which correspond to our online course Algorithms, Part I, are available as
Algorithms, Fourth Edition, Part I.
4. Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . .515
4.1 Undirected Graphs 518
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Glossary • Undirected graph type • Adjacency-lists representation •
Depth-first search • Breadth-first search • Connected components •
Degrees of separation
4.2 Directed Graphs 566
Glossary • Digraph data type • Depth-first search • Directed cycle detection •
Precedence-constrained scheduling • Topological sort • Strong connectivity •
Kosaraju-Sharir algorithm • Transitive closure
4.3 Minimum Spanning Trees 604
Cut property • Greedy algorithm • Edge-weighted graph data type •
Prim’s algorithm • Kruskal’s algorithm
4.4 Shortest Paths 638
Properties of shortest paths • Edge-weighted digraph data types • Generic
shortest paths algorithm • Dijkstra’s algorithm • Shortest paths in edge-
weighted DAGs • Critical-path method • Bellman-Ford algorithm •
Negative cycle detection • Arbitrage
5. Strings . . . . . . . . . . . . . . . . . . . . . . . . . . .695
5.1 String Sorts 702
Key-indexed counting • LSD string sort • MSD string sort • 3-way string
quicksort
5.2 Tries 730
String symbol table API • R-way tries • Ternary search tries • Character-
based operations
5.3 Substring Search 758
Brute-force algorithm • Knuth-Morris-Pratt algorithm •
Boyer-Moore algorithm • Rabin-Karp fingerprint algorithm
5.4 Regular Expressions 788
Describing patterns with REs • Applications • Nondeterministic finite-state
automata • Simulating an NFA • Building an NFA corresponding to an RE
5.5 Data Compression 810
Rules of the game • Reading and writing binary data • Limitations •
Run-length coding • Huffman compression • LZW compression
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6. Context . . . . . . . . . . . . . . . . . . . . . . . . . . .853
Event-Driven Simulation 856
Hard-disc model • Collision prediction • Collision resolution
B-trees 866
Cost model • Search and insert
Suffix Arrays 875
Suffix sorting • Longest repeated substring • Keyword in context
Network–Flow Algorithms 886
Maximum flow • Minimum cut • Ford-Fulkerson algorithm
Reduction 903
Sorting • Shortest path • Bipartite matching • Linear programming
Intractability 910
Longest-paths problem • P vs. NP • Boolean satisfiability • NP-completeness
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PREFACE
T
his book is intended to survey the most important computer algorithms in use today,
and to teach fundamental techniques to the growing number of people in need of
knowing them. It is intended for use as a textbook for a second course in computer
science, after students have acquired basic programming skills and familiarity with computer
systems. The book also may be useful for self-study or as a reference for people engaged in
the development of computer systems or applications programs, since it contains implemen- ptg12441863
tations of useful algorithms and detailed information on performance characteristics and
clients. The broad perspective taken makes the book an appropriate introduction to the field.
the study of algorithms and data structures is fundamental to any computer-
science curriculum, but it is not just for programmers and computer-science students. Every-
one who uses a computer wants it to run faster or to solve larger problems. The algorithms
in this book represent a body of knowledge developed over the last 50 years that has become
indispensable. From N-body simulation problems in physics to genetic-sequencing problems
in molecular biology, the basic methods described here have become essential in scientific
research; from architectural modeling systems to aircraft simulation, they have become es-
sential tools in engineering; and from database systems to internet search engines, they have
become essential parts of modern software systems. And these are but a few examples—as the
scope of computer applications continues to grow, so grows the impact of the basic methods
covered here.
In Chapter 1, we develop our fundamental approach to studying algorithms, includ-
ing coverage of data types for stacks, queues, and other low-level abstractions that we use
throughout the book. In Chapters 2 and 3, we survey fundamental algorithms for sorting and
searching; and in Chapters 4 and 5, we cover algorithms for processing graphs and strings.
Chapter 6 is an overview placing the rest of the material in the book in a larger context.
ix