《算法导论》第三版英文原版——刷题必备

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"算法导论第三版英文原版" 《算法导论》是计算机科学领域的一本经典教材，由Thomas H. Cormen、Charles E. Leiserson、Ronald L. Rivest和Clifford Stein四位作者合作编写。本书的第三版在前两版的基础上进行了更新和扩展，旨在为学生和专业人员提供全面而深入的算法知识，适用于那些准备找工作并需要强化算法技能的人群。这本书涵盖了算法设计、分析和实现的核心概念，包括排序和搜索算法、图算法、动态规划、贪心算法、分治策略、回溯法以及近似算法等。通过阅读此书，读者可以学习如何设计有效的算法来解决各种计算问题，并理解这些算法的时间和空间复杂度。以下是书中的一些关键知识点： 1. 排序与搜索：包括快速排序、归并排序、堆排序、二分查找和哈希表。这些算法在数据处理和信息检索中扮演着重要角色。 2. 图算法：涉及Dijkstra最短路径算法、Floyd-Warshall所有对最短路径算法、Bellman-Ford负权边最短路径算法以及拓扑排序。这些算法在网络路由、社交网络分析等领域有广泛应用。 3. 动态规划：如背包问题、最长公共子序列、矩阵链乘法等问题的解决方案，动态规划是解决具有重叠子问题和最优子结构的优化问题的有效方法。 4. 贪心算法：如霍夫曼编码、Prim最小生成树算法和Kruskal最小生成树算法，这些算法通常用于寻找局部最优解来逼近全局最优解。 5. 分治策略：如归并排序、快速排序、大数乘法（Karatsuba和Toom-Cook）等，分治法将复杂问题分解为较小的子问题，然后逐个解决。 6. 回溯法：用于解决约束满足问题和组合优化问题，如八皇后问题、N-Queens问题、数独求解等。 7. 近似算法：对于NP难问题，如旅行商问题、顶点覆盖问题，近似算法可以找到接近最优解的解决方案。此外，书中还包括了算法的效率评估、算法的复杂性理论、递归分析和摊还分析等基础概念，以及概率算法和随机化方法。书中每个章节都配有丰富的实例、习题和实验，帮助读者加深理解和实践应用。《算法导论》第三版英文原版是一本深度和广度兼具的算法教程，不仅适合计算机科学专业的学生，也对软件工程师、数据科学家和其他信息技术专业人士极具参考价值。通过阅读和学习，读者能够掌握设计、分析和实现高效算法的技巧，提升解决问题的能力。

Preface xv

What are the prerequisites for reading this book?

You shou ld have some p rogram min g ex per ience. In p ar tic ula r, yo u sh ou ld un-

derstand recursive procedures and simple data structures such as arrays and

linked lists.

You shou ld have som e fac ili ty w it h m athem ati cal p ro ofs , and es pe ci al ly pro of s

by mathematical induction. A few portions of the book rely on some knowledge

of elementary calculus. Beyond that, Parts I and VIII of this book teach you all

the mathematical techniques you will need.

We have heard, loud and clear, the call to supply solutions to problems and

exercises. Our Web site, http://mitpress.mit.edu/algorithms/, links to solutions for

afewoftheproblemsandexercises. Feelfreetocheckyoursolutionsagainstours.

We ask, however, that you do not send your solutions to us.

To the professional

The wide range of topics in this book makes it an excellent handbook on algo-

rithms. Because each chapter is relatively self-contained, you can focus in on the

topics that most interest you.

Most of the algorithms we discuss have great practical utility. We therefore

address implementation concerns and other engineering issues. We often provide

practical alternatives to the few algorithms that are primarily of theoretical interest.

If you wish to implement any of the algorithms, you should ﬁnd the transla-

tion of our pseudocode into your favorite programming language to be a fairly

straightforward task. We have designed the pseudocode to present each algorithm

clearly and succinctly. Consequently, we do not address error-handling and other

software-engineering issues that require speciﬁc assumptions about your program-

ming environment. We attempt to present each algorithm simply and directly with-

out allowing the idiosyncrasies of a particular programming language to obscure

its essence.

We understand that if you are using this book outside of a course, then you

might be unable to check your solutions to problems and exercises against solutions

provided by an instructor. Our Web site, http://mitpress.mit.edu/algorithms/, links

to solutions for some of the problems and exercises so that you can check your

work. Please do not send your solutions to us.

To our colleagues

We have supplied an extensive bibliography and pointers to the current literature.

Each chapter ends with a set of chapter notes that give historical details and ref-

erences. The chapter notes do not provide a complete reference to the whole ﬁeld

xvi Preface

of algorithms, however. Though it may be hard to believe for a book of this size,

space constraints prevented us from including many interesting algorithms.

Despite myriad requests from students for solutions to problems and exercises,

we have chosen as a matter of policy not to supply references for problems and

exercises, to remove the temptation for students to look up a solution rather than to

ﬁnd it themselves.

Changes for the third edition

What has changed between the second and third editions of this book? The mag-

nitude of the changes is on a par with the changes between the ﬁrst and second

editions. As we said about the second-edition changes, depending on how you

look at it, the book changed either not much or quite a bit.

Aquicklookatthetableofcontentsshowsthatmostofthesecond-editionchap-

ters and sections appear in the third edition. We removed two chapters and one

section, but we have added three new chapters and two new sections apart from

these new chapters.

We kept the hybrid organization from the ﬁrst two editions. Rather than organiz-

ing chapters by only problem domains or according only to techniques, this book

has elements of both. It contains technique-based chapters on divide-and-conquer,

dynamic programming, greedy algorithms, amortized analysis, NP-Completeness,

and approximation algorithms. But it also has entire parts on sorting, on data

structures for dynamic sets, and on algorithms for graph problems. We ﬁnd that

although you need to know how to apply techniques for designing and analyzing al-

gorithms, problems seldom announce to you which techniques are most amenable

to solving them.

Here is a summary of the most signiﬁcant changes for the third edition:

We added new chapters on van Emde Boas trees and multithreaded algorithms,

and we have broken out material on matrix basics into its own appendix chapter.

We revised the chapter on recurrences to more broadly cover the divide-and-

conquer technique, and its ﬁrst two sections apply divide-and-conquer to solve

two problems. The second section of this chapter presents Strassen’s algorithm

for matrix multiplication, which we have moved from the chapter on matrix

operations.

We removed two chapters that were rarely taught: binomial heaps and sorting

networks. One key idea in the sorting networks chapter, the 0-1 principle, ap-

pears in this edition within Problem 8-7 as the 0-1 sorting lemma for compare-

exchange algorithms. The treatment of Fibonacci heaps no longer relies on

binomial heaps as a precursor.

Preface xvii

We revised our treatment of dynamic programming and greedy algorithms. Dy-

namic programming now leads off with a more interesting problem, rod cutting,

than the assembly-line scheduling problem from the second edition. Further-

more, we emphasize memoization a bit more than we did in the second edition,

and we introduce the notion of the subproblem graph as a way to understand

the running time of a dynamic-programming algorithm. In our opening exam-

ple of greedy algorithms, the activity-selection problem, we get to the greedy

algorithm more directly than we did in the second edition.

The way we delete a node from binary search trees (which includes red-black

trees) now guarantees that the node requested for deletion is the node that is

actually deleted. In the ﬁrst two editions, in certain cases, some other node

would be deleted, with its contents moving into the node passed to the deletion

procedure. With our new way to delete nodes, if other components of a program

maintain pointers to nodes in the tree, they will not mistakenly end up with stale

pointers to nodes that have been deleted.

The material on ﬂow networks now bases ﬂows entirely on edges. This ap-

proach is more intuitive than the net ﬂow used in the ﬁrst two editions.

With the material on matrix basics and Strassen’s algorithm moved to other

chapters, the chapter on matrix operations is smaller than in the second edition.

We have modiﬁed our treatment of the Knuth-Morris-Pratt string-matching al-

gorithm.

We corrected several errors. Most of these errors were posted on our Web site

of second-edition errata, but a few were not.

Based on many requests, we changed the syntax (as it were) of our pseudocode.

We now use “ D”toindicateassignmentand“

”totestforequality,justasC,

C++, Java, and Python do. Likewise, we have eliminated the keywords do and

then and adopted “// ”asourcomment-to-end-of-linesymbol. Wealsonowuse

dot-notation to indicate object attributes. Our pseudocode remains procedural,

rather than object-oriented. In other words, rather than running methods on

objects, we simply call procedures, passing objects as parameters.

We added 100 new exercises and 28 new problems. We also updated many

bibliography entries and added several new ones.

Finally, we went through the entire book and rewrote sentences, paragraphs,

and sections to make the writing clearer and more active.

xviii Preface

Web site

You can use o ur We b sit e, http:// mit pre ss. mit .ed u/alg ori thms /, to obta in sup pl e-

mentary information and to communicate with us. The Web site links to a list of

known errors, solutions to selected exercises and problems, and (of course) a list

explaining the corny professor jokes, as well as other content that we might add.

The Web site also tells you how to report errors or make suggestions.

How we produced this book

Like the second edition, the third edition was produced in L

.Weusedthe

Times font with mathematics typeset using the MathTime Pro 2 fonts. We thank

Michael Spivak from Publish or Perish, Inc., Lance Carnes from Personal TeX,

Inc., and Tim Tregubov from Dartmouth College for technical support. As in the

previous two editions, we compiled the index using Windex, a C program that we

wrote, and the bibliography was produced with B

IBT

X. The PDF ﬁles for this

book were created on a MacBook running OS 10.5.

We drew the illustrations for the third edition using MacDraw Pro, with some

of the mathematical expressions in illustrations laid in with the psfrag package

for L

.Unfortunately,MacDrawProislegacysoftware,havingnotbeen

marketed for over a decade now. Happily, we still have a couple of Macintoshes

that can run the Classic environment under OS 10.4, and hence they can run Mac-

Draw Pro—mostly. Even under the Classic environment, we ﬁnd MacDraw Pro to

be far easier to use than any other drawing software for the types of illustrations

that accompany computer-science text, and it produces beautiful output.

Who

knows how long our pre-Intel Macs will continue to run, so if anyone from Apple

is listening: Please create an OS X-compatible version of MacDraw Pro!

Acknowledgments for the third edition

We have been working with the MIT Press for over two decades now, and what a

terriﬁc relationship it has been! We thank Ellen Faran, Bob Prior, Ada Brunstein,

and Mary Reilly for their help and support.

We were geographically distributed while producing the third edition, working

in the Dartmouth College Department of Computer Science, the MIT Computer

We investigated several drawing programs that run under Mac OS X, but all had signiﬁcant short-

comings compared with MacDraw Pro. We brieﬂy attempted to produce the illustrations for this

book with a different, well known drawing program. We found that it took at least ﬁve times as long

to produce each illustration as it took with MacDraw Pro, and the resulting illustrations did not look

as good. Hence the decision to revert to MacDraw Pro running on older Macintoshes.

Preface xix

Science and Artiﬁcial Intelligence Laboratory, and the Columbia University De-

partment of Industrial Engineering and Operations Research. We thank our re-

spective universities and colleagues for providing such supportive and stimulating

environments.

Julie Sussman, P.P.A., once again bailed us out as the technical copyeditor. Time

and again, we were amazed at the errors that eluded us, but that Julie caught. She

also helped us improve our presentation in several places. If there is a Hall of Fame

for technical copyeditors, Julie is a sure-ﬁre, ﬁrst-ballot inductee. She is nothing

short of phenomenal. Thank you, thank you, thank you, Julie! Priya Natarajan also

found some errors that we were able to correct before this book went to press. Any

errors that remain (and undoubtedly, some do) are the responsibility of the authors

(and probably were inserted after Julie read the material).

The treatment for van Emde Boas trees derives from Erik Demaine’s notes,

which were in turn inﬂuenced by Michael Bender. We also incorporated ideas

from Javed Aslam, Bradley Kuszmaul, and Hui Zha into this edition.

The chapter on multithreading was based on notes originally written jointly with

Harald Prokop. The material was inﬂuenced by several others working on the Cilk

project at MIT, including Bradley Kuszmaul and Matteo Frigo. The design of the

multithreaded pseudocode took its inspiration from the MIT Cilk extensions to C

and by Cilk Arts’s Cilk++ extensions to C++.

We also thank the many readers of the ﬁrst and second editions who reported

errors or submitted suggestions for how to improve this book. We corrected all the

bona ﬁde errors that were reported, and we incorporated as many suggestions as

we could. We rejoice that the number of such contributors has grown so great that

we must regret that it has become impractical to list them all.

Finally, we thank our wives—Nicole Cormen, Wendy Leiserson, Gail Rivest,

and Rebecca Ivry—and our children—Ricky, Will, Debby, and Katie Leiserson;

Alex and Christopher Rivest; and Molly, Noah, and Benjamin Stein—for their love

and support while we prepared this book. The patience and encouragement of our

families made this project possible. We affectionately dedicate this book to them.

HOMAS H. CORMEN Lebanon, New Hampshire

CHARLES E. LEISERSON Cambridge, Massachusetts

RONALD L. RIVEST Cambridge, Massachusetts

CLIFFORD STEIN New York, New York

February 2009

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