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编程与解谜学习算法：实践与探索

Algorithms

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"《通过编程与解谜学习算法》是一本由Alexander Kulikov和Pavel Pevzner合著的教材，于2018年由Leanpub出版。这本书是Coursera上热门数据结构与算法在线专精课程以及edX上的在线微硕士项目的核心资源。自2016年在线课程上线以来，已有数十万学生参与，通过解决书中详尽的编程挑战和算法谜题来深化理解。该书强调实践学习，将理论与实际编程技能相结合，涵盖了包括C、C++、Java、JavaScript、Python、Scala、C#、Haskell、Ruby和Rust（后四种语言仅在Coursera平台上支持）在内的多种编程语言。编程挑战旨在引导读者在这些语言中实现遇到的算法，让学生在实践中掌握和巩固理论知识。此外，书中还设计了算法谜题，以创新的方式激发学生的思维，鼓励他们独立发明算法。这些谜题不仅增加了学习的乐趣，即使在解决过程中遇到困难，也能帮助学生更深入地理解算法的美妙和力量。通过这种方式，学生们可以在自我探索和互动中以适合自己的节奏学习，与其他来自世界各地的优秀学生共同进步。无论是想要提升编程技能还是深入了解算法原理，这本书都是一个理想的工具。它不仅适合初学者，也适合有经验的专业人士进一步深化对算法的理解。参与Coursera或edX的在线课程，结合书中的丰富资源，将极大地推动你在算法学习之旅中的成长。"

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What Lies Ahead xv

What Lies Ahead

Watch for our future editions that will cover the following topics.

Data Structures

Arrays and Lists

Priority Queues

Disjoint Sets

Hash Tables

Binary Search Trees

Algorithms on Graphs

Graphs Decomposition

Shortest Paths in Graphs

Minimum Spanning Trees

Shortest Paths in Real Life

Algorithms on Strings

Pattern Matching

Suﬃx Trees

Suﬃx Arrays

Burrows–Wheeler Transform

Advanced Algorithms and Complexity

Flows in Networks

Linear Programmings

NP-complete Problems

Coping with NP-completeness

Streaming Algorithms

xvi Meet the Authors

Meet the Authors

Alexander S. Kulikov is a senior research fellow

at Steklov Mathematical Institute of the Russian

Academy of Sciences, Saint Petersburg, Russia and

a lecturer at the Department of Computer Science and

Engineering at University of California, San Diego,

USA. He also directs the Computer Science Center in

Saint Petersburg that provides free advanced computer

science courses complementing the standard univer-

sity curricula. Alexander holds a Ph. D. from Steklov

Mathematical Institute. His research interests include

algorithms and complexity theory. He co-authored

online courses “Data Structures and Algorithms” and

“Introduction to Discrete Mathematics for Computer

Science” that are available at Coursera and edX.

Pavel Pevzner is Ronald R. Taylor Professor of Com-

puter Science at the University of California, San

Diego. He holds a Ph. D. from Moscow Institute

of Physics and Technology, Russia and an Honorary

Degree from Simon Fraser University. He is a Howard

Hughes Medical Institute Professor (2006), an As-

sociation for Computing Machinery Fellow (2010),

an International Society for Computational Biology

Fellow (2012), and a Member of the the Academia

Europaea (2016). He has authored the textbooks

Computational Molecular Biology: An Algorithmic

Approach (2000), An Introduction to Bioinformatics

Algorithms (2004) (jointly with Neil Jones), and Bioin-

formatics Algorithms: An Active Learning Approach

(2014) (jointly with Phillip Compeau). He co-authored

online courses “Data Structures and Algorithms”,

“Bioinformatics”, and “Analyze Your Genome!” that

are available at Coursera and edX.

Meet Our Online Co-Instructors xvii

Meet Our Online Co-Instructors

Daniel Kane is an associate professor at the University

of California, San Diego with a joint appointment

between the Department of Computer Science and

Engineering and the Department of Mathematics. He

has diverse interests in mathematics and theoretical

computer science, though most of his work ﬁts into the

broad categories of number theory, complexity theory,

or combinatorics.

Michael Levin is an Associate Professor at the

Computer Science Department of Higher School of

Economics, Moscow, Russia and the Chief Data Sci-

entist at the Yandex.Market, Moscow, Russia. He also

teaches Algorithms and Data Structures at the Yandex

School of Data Analysis.

Neil Rhodes is a lecturer in the Computer Science and

Engineering department at the University of Califor-

nia, San Diego and formerly a staﬀ software engineer

at Google. Neil holds a B.A. and M.S. in Computer

Science from UCSD. He left the Ph.D. program at

UCSD to start a company, Palomar Software, and spent

ﬁfteen years writing software, books on software de-

velopment, and designing and teaching programming

courses for Apple and Palm. He’s taught Algorithms,

Machine Learning, Operating Systems, Discrete Math-

ematics, Automata and Computability Theory, and

Software Engineering at UCSD and Harvey Mudd

College in Claremont, California.

xviii Acknowledgments

Acknowledgments

This book was greatly improved by the eﬀorts of a large number of indi-

viduals, to whom we owe a debt of gratitude.

Our co-instructors and partners in crime Daniel Kane, Michael Levin,

and Neil Rhodes invested countless hours in the development of our on-

line courses at Coursera and edX platforms.

Hundreds of thousands of our online students provided valuable feed-

back that led to many improvements in our MOOCs and this MOOC book.

In particular, we are grateful to the mentors of the Algorithmic Toolbox

class at Coursera: Ayoub Falah, Denys Diachenko, Kishaan Jeeveswaran,

Irina Pinjaeva, Fernando Gonzales Vigil Richter, and Gabrio Secco.

We thank our colleagues who helped us with preparing programming

challenges: Maxim Akhmedov, Roman Andreev, Gleb Evstropov, Niko-

lai Karpov, Sergey Poromov, Sergey Kopeliovich, Ilya Kornakov, Gennady

Korotkevich, Paul Melnichuk, and Alexander Tiunov.

We are grateful to Anton Konev for leading the development of inter-

active puzzles as well as Anton Belyaev and Kirill Banaru for help with

some of the puzzles.

We thank Alexey Kladov and Alexander Smal for help with the “Good

Programming Practices” section of the book.

Randall Christopher brought to life our idea for the textbook cover.

Finally, our families helped us preserve our sanity when we were work-

ing on this MOOC book.

A. K. and P. P.

Saint Petersburg and San Diego

December 2017

Chapter 1: Algorithms and Complexity

This book presents programming challenges that will teach you how to

design and implement algorithms. Solving a programming challenge is

one of the best ways to understand an algorithm’s design as well as to

identify its potential weaknesses and ﬁx them.

1.1 What Is an Algorithm?

Roughly speaking, an algorithm is a sequence of instructions that one

must perform in order to solve a well-formulated problem. We will spec-

ify problems in terms of their inputs and their outputs, and the algorithm

will be the method of translating the inputs into the outputs. A well-

formulated problem is unambiguous and precise, leaving no room for mis-

interpretation.

After you designed an algorithm, two important questions to ask are:

“Does it work correctly?” and “How much time will it take?” Certainly

you would not be satisﬁed with an algorithm that only returned correct

results half the time, or took 1000 years to arrive at an answer.

1.2 Pseudocode

To understand how an algorithm works, we need some way of listing the

steps that the algorithm takes, while being neither too vague nor too for-

mal. We will use pseudocode, a language computer scientists often use

to describe algorithms. Pseudocode ignores many of the details that are

required in a programming language, yet it is more precise and less am-

biguous than, say, a recipe in a cookbook.

1.3 Problem Versus Problem Instance

A problem describes a class of computational tasks. A problem instance is

one particular input from that class. To illustrate the diﬀerence between

a problem and an instance of a problem, consider the following example.

You ﬁnd yourself in a bookstore buying a book for $4.23 which you pay

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