Steven Skiena_The Algorithm Design Manual.pdf

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中文名叫《算法设计手册》
Steven s. skiena Department of Computer science State University of New York Stony brook skiena cs sunysb. edu ISBN:978-1-84800-069-8 e-ⅠSBN:978-1-84800-070-4 DOI:10.1007/978-1-84800-070-4 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2008931136 C Springer-Verlag London Limited 2008 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or trans mitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency Enquiries concerning reproduction outside those terms should be sent to the publishers The use of registered names, trademarks, etc, in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for l The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that be made Printed on acid-free paper Springer science+Business media springer. com P reface Most professional programmers that Ive encountered are not well prepared to tackle algorithm design problems. This is a pity, because the techniques of algorithm design form one of the core practical technologies of computer science. Designing correct, efficient, and implementable algorithms for real-world problems requires access to two distinct bodies of knowledge Techniques- Good algorithm designers understand several fundamental al gorithm design techniques, including data structures, dynamic programming depth-first search, backtracking, and heuristics. Perhaps the single most im- portant design technique is modeling, the art of abstracting a messy real-world application into a clean problem suitable for algorithmic attack Resources- Good algorithm designers stand on the shoulders of giants Rather than laboring from scratch to produce a new algorithm for every tasl they can figure out what is known about a particular problem. Rather than re-implementing popular algorithms from scratch, they seek existing imple mentations to serve as a starting point. They are familiar with many classic algorithmic problems, which provide sufficient source material to model most any application This book is intended as a manual on algorithm design, providing access te combinatorial algorithm technology for both students and computer professionals It is divided into two parts: Techniques and Resources. The former is a general guide to techniques for the design and analysis of computer algorithms. The Re sources section is intended for browsing and reference, and comprises the catalog of algorithmic resources, implementations, and an extensive bibliography PREFACE To the reader I have been gratified by the warm reception the first edition of The Algorithm De sign Manual has received since its initial publication in 1997. It has been recognized as a unique guide to using algorithmic techniques to solve problems that often arise in practice. But much has changed in the world since the The Algorithm Design Manual was first published over ten years ago. Indeed, if we date the origins of modern algorithm design and analysis to about 1970, then roughly 30% of modern algorithmic history has happened since the first coming of The Algorithm Design Manual Three aspects of The Algorithm Design Manual have been particularly beloved (1) the catalog of algorithmic problems,(2)the war stories, and(3) the electronic component of the book. These features have been preserved and strengthened in this edition: o The Catalog of Algorithmic Problems- Since finding out what is known about an algorithmic problem can be a difficult task, I provide a catalog of the 75 most important problems arising in practice. By browsing through this catalog, the student or practitioner can quickly identify what their problem is called, what is known about it, and how they should proceed to solve it. To aid in problem identification, we include a pair of“' before”and“ after” pictures for each problem, illustrating the required input and output specifications. One perceptive reviewer called my book"The Hitchhiker's guide to algorithms on the strength of this catalog The catalog is the most important part of this book. To update the catalog for this edition, I have solicited feedback from the worlds leading experts on each associated problem. Particular attention has been paid to updating the discussion of available software implementations for each problem War Stories-In practice, algorithm problems do not arise at the beginning of a large project. Rather, they typically arise as subproblems when it becomes clear that the programmer does not know how to proceed or that the current solution is inadequate To provide a better perspective on how algorithm problems arise in the real world, we include a collection of "war stories, or tales from our experience with real problems. The moral of these stories is that algorithm design and nalysis is not just theory, but an important tool to be pulled out and used as needed This edition retains all the original war stories(with updates as appropriate) plus additional new war stories covering external sorting, graph algorithms simulated annealing, and other topics Electronic Component- Since the practical person is usually looking for a program more than an algorithm, we provide pointers to solid implementa- tions whenever they are available. We have collected these implementations PREFACE atonecentralwebsitesite(http://www.cs.sunysb.edu/algorith)foreasyre- trieval. We have been the number one"Algorithm" site on Google pretty much since the initial publication of the book Further, we provide recommendations to make it easier to identify the correct code for the job. With these implementations available, the critical issue in algorithm design becomes properly modeling your application, more so than becoming intimate with the details of the actual algorithm. This focus permeates the entire book Equally important is what we do not do in this book. We do not stress the mathematical analysis of algorithms, leaving most of the analysis as informal ar- guments. You will not find a single theorem anywhere in this book. When more details are needed, the reader should study the cited programs or references. The goal of this manual is to get you going in the right direction as quickly as possible To the Instructor This book covers enough material for a standard Introduction to algorithms course We assume the reader has completed the equivalent of a second programming course,typically titled Data Structures or Computer Science In a full set of lecture slides for teaching this course is available online at http:/www.algorist.comFurther,Imakeavailableonlineaudioandvideolectures using these slides to teach a full-semester algorithm course. Let me help teach your course. by the magic of the internet! This book stresses design over analysis. It is suitable for both traditional lecture courses and the new"active learning"method, where the professor does not lecture but instead guides student groups to solve real problems. The"war stories" provide an appropriate introduction to the active learning method I have made several pedagogical improvements throughout the book. Textbook- oriented features include More Leisurely Discussion-The tutorial material in the first part of the book has been doubled over the previous edition. The pages have been devoted to more thorough and careful exposition of fundamental material, instead of adding more specialized topics False starts- Algorithms textbooks generally present important algorithms as a fait accompli, obscuring the ideas involved in designing them and the subtle reasons why other approaches fail. The war stories illustrate such de velopment on certain applied problems, but I have expanded such coverage into classical algorithm design material as well Stop and Think- Here I illustrate my thought process as I solve a topic specific homework problem--false starts and all. I have interspersed such PREFACE problem blocks throughout the text to increase the problem-solving activity of my readers. Answers appear immediately following each problem More and Improved Homework Problems- This edition of The Algorithm Design Manual has twice as many homework exercises as the previous one Exercises that proved confusing or ambiguous have been improved or re- placed. Degree of difficulty ratings(from 1 to 10) have been assigned to all problems Self-Motivating Exam Design-In my algorithms courses, I promise the stu dents that all midterm and final exam questions will be taken directly from homework problems in this book. This provides a"student-motivated exam so students know exactly how to study to do well on the exam. I have carefully picked the quantity, variety, and difficulty of homework exercises to make this work; ensuring there are neither too few or too many candidate problems Take-Home Lessons- Highlighted "take-home lesson boxes scattered throughout the text emphasize the big-picture concepts to be gained from the chapter Links to Programming Challenge Problems- Each chapters exercises will contain links to 3-5 relevant "Programming Challenge" problems from http://wwa.programming-challenges.comThesecanbeusedtoaddapro gramming component to paper-and-pencil algorithms courses More Code, Less Pseudo-code- more algorithms in this book appear as code (written in C) instead of pseudo-code. I believe the concreteness and relia- bility of actual tested implementations provides a big win over less formal presentations for simple algorithms. Full implementations are available for studyathttp://www.algorist.com Chapter Notes- Each tutorial chapter concludes with a brief notes section pointing readers to primary sources and additional references Acknowledgments pdating a book dedication after ten years focuses attention on the effects of time Since the first edition, Renee has become my wife and then the mother of our two children, Bonnie and Abby. My father has left this world, but Mom and my brothers Len and rob remain a vital presence in my life. I dedicate this book to my family, new and old, here and departed I would like to thank several people for their concrete contributions to this new edition. Andrew Gaun and Betson Thomas helped in many ways, particularly inbuildingtheinfrastructureforthenewhttp://www.cs.sunysb.edu/algorithand dealing with a variety of manuscript preparation issues. David gries offered valu- able feedback well beyond the call of duty. Himanshu gupta and Bin Tang bravely PREFACE IX taught courses using a manuscript version of this edition. Thanks also to my Springer-Verlag editors, Wayne Wheeler and Allan Wylde A select group of algorithmic sages reviewed sections of the Hitchhiker's guide sharing their wisdom and alerting me to new developments. Thanks to Ami Amir. Herve Bronnimann. Bernard Chazelle. Chris Chu. Scott Cotton, Yefim Dinitz, Komei Fukuda, Michael Goodrich, Lenny Heath Cihat Imamoglu, Tao Jiang, David Karger, Giuseppe Liotta, Albert Mao, Silvano Martello, Catherine McGeoch, Kurt Mehlhorn, Scott A. Mitchell, Naceur Meskini, Gene Myers, Gonzalo Navarro, Stephen North. Joe o'Rourke. Mike paterson. Theo Pavlidis. Seth Pettie. Michel Pocchiola, Bart Preneel, Tomasz Radzik, Edward Reingold, Frank Ruskey, Peter Sanders, Joao Setubal, Jonathan Shewchuk, Robert Skeel, Jens Stoye, Torsten Suel, Bruce Watson, and Uri Zwick Several exercises were originated by colleagues or inspired by other texts. Re constructing the original sources years later can be challenging, but credits for each problem(to the best of my recollection) appear on the website It would be rude not to thank important contributors to the original edition Ricky Bradley and Dario Vlah built up the substantial infrastructure required for the www site in a logical and extensible manner. Zhong li drew most of the catalog figures using xfig. Richard Crandall, Ron Danielson, Takis Metaxas, Dave Miller, Giri Narasimhan, and Joe Zachary all reviewed preliminary versions of the first edition; their thoughtful feedback helped to shape what you see here Much of what I know about algorithms I learned along with my graduate students. Several of them(Yaw-Ling Lin, Sundaram Gopalakrishnan, Ting Chen Francine Evans, Harald Rau, Ricky Bradley, and Dimitris Margaritis) are the real heroes of the war stories related within. My Stony Brook friends and algorithm colleagues Estie Arkin, Michael Bender, Jie Gao, and Joe Mitchell have always been a pleasure to work and be with. Finally, thanks to Michael Brochstein and the rest of the city contingent for revealing a proper life well beyond Stony Brook Caveat It is traditional for the author to magnanimously accept the blame for whatever deficiencies remain. I dont. Any errors, deficiencies, or problems in this book are somebody else's fault, but I would appreciate knowing about them so as to deter mine who is to blame Steven s. Skiena Department of Computer Science Stony Brook universit Stony Brook, NY 11794-4400 http://www.cs.sunysb.edu/skiena April 2008 Contents I Practical Algorithm Design 1 Introduction to Algorithm Design 1. 1 Robot Tour Optimization 1359 1.2 Selecting the Right Jobs 1.3 Reasoning about Correctness 1.4 Modeling the Problem 1.5 About the War Stories 22 1.6 War Story: Psychic modelin 1.7 Exercises 7 2 Algorithm Analysis 31 2.1 The RAM Model of Computation 31 2.2 The Big Oh Notation 2.3 Growth Rates and dominance relations 37 2.4 Working with the Big Oh 2.5 Reasoning about efficiency 2.6 Logarithms and Their Applications 46 2.7 Properties of logarithms 50 2.8 War Story: Mystery of the Pyramids 51 2.9 Advanced Analysis() 54 2.10 Exercises 57 3 Data structures 65 3.1 Contiguous vs. Linked Data Structures 66 11 CONTENTS 3.2 Stacks and Queues 71 3.3 Dictionaries 72 3.4 Binary Search Trees 3.5 Priority Queues 3.6 War Story: Stripping Triangulations 3.7 Hashing and Strings 89 3.8 Specialized Data Structures 93 3.9 War Story: String em Up 94 3.10 Exercises 98 4 Sorting and searching 103 4.1 Applications of Sorting 104 4.2 Pragmatics of Sorting 107 4.3 Heapsort: Fast Sorting via Data Structures 108 4.4 War Story: Give me a Ticket on an airplane 11 4.5 Mergesort: Sorting by Divide-and-Conquer 4.6 Quicksort Sorting by randomization 123 4.7 Distribution Sort: Sorting via Bucketing 129 4.8 War Story: Skiena for the Defense 131 4.9 Binary Search and Related Algorithms 132 4.10 Divide-and-Conquer 135 4.11 Exercises 5 Graph Traversal 145 5.1 Flavors of graphs 146 5.2 Data Structures for graphs 151 5.3 War Story: I was a Victim of Moore's law 155 5.4 War Story: Getting the Graph 5.5 Traversing a Graph 5.6 Breadth-First Search 162 5.7 Applications of Breadth-First Search 166 5.8 Depth-First Search 169 5.9 Applications of Depth-First Search 5.10 Depth-First Search on Directed graphs 5.11 Exercises 184 6 Weighted Graph algorithms 191 6.1 Minimum Spanning Trees 192 6.2 War Story: Nothing but Nets 202 6.3 Shortest Paths 205 6.4 War Story: Dialing for Documents 212 6.5 Network Flows and Bipartite Matching 217 6.6 Design Graphs, Not algorithms 222 6.7 Exercises 225

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