Python算法解析：掌握Python语言基础算法

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"Python Algorithms: Mastering Basic Algorithms in the Python Language" 本书《Python Algorithms》是Magnus Lie Hetland所著，旨在深入浅出地讲解如何使用Python语言进行算法分析和设计。作者以其在《Beginning Python》一书中的经验为基础，为读者提供了古典算法的解析，并确保读者能够掌握基础的算法问题解决技巧。书中以高度教学化和易读的方式处理了一些编程和计算机科学中最重要且最具挑战性的领域。学习目标包括： 1. 学会将新问题转化为已有高效解决方案的经典算法问题，或证明某些问题属于被认为无法有效解决的问题类别。 2. 通过数学工具和基本实验、基准测试对算法和Python程序进行分析。 3. 对Python程序及其底层算法的正确性、最优性或近似误差界限进行证明。 4. 深入理解并能有效地在Python中实现几种经典算法和数据结构。 5. 使用经过时间检验的设计原则和技术设计并实现新算法，解决新问题。 6. 利用Python提供的各种高性能计算工具优化实现。该书适合已经有一定Python编程基础，需要学习算法问题解决或需要复习的程序员。对于计算机科学学生，或是生物信息学等与编程相关的学科的学生，这本书也是一本有价值的参考资料。书中的章节涵盖了： 1. 引言 2. 基础知识 3. 计数基础 4. 归纳与递归...以及减少 5. 遍历：算法学的骨架钥匙 6. 分而治之，组合与征服 7. 贪心策略？证明它！ 8. 环环相扣的依赖与记忆化 9. 从A到B，与Edsger和朋友们一起 10. 匹配、割与流 11. 困难问题与（有限的）容错通过阅读此书，读者不仅可以掌握Python内置的知名算法和数据结构，还能学会自己评估和实现其他算法，从而提升在实际编程项目中的效率和问题解决能力。

■ CONTENTS

xiv

About the Technical Reviewer

■ Alex Martelli was born and grew up in Italy and holds a Laurea in Ingeneria

Elettronica from the Universitá di Bologna. He wrote Python in a Nutshell and

coedited the Python Cookbook. He’s a member of the PSF and won the 2002

Activators’ Choice Award and the 2006 Frank Willison Award for contributions to

the Python community. He currently lives in California and works as senior staff

engineer for Google. His detailed profile is at www.google.com/profiles/aleaxit;

a summary bio is at http://en.wikipedia.org/wiki/Alex_Martelli.

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C H A P T E R 1

■ ■ ■

Introduction

1. Write down the problem.

2. Think real hard.

3. Write down the solution.

“The Feynman Algorithm”

as described by Murray Gell-Mann

Consider the following problem. You are to visit all the cities, towns, and villages of, say, Sweden and

then return to your starting point. This might take a while (there are 24 978 locations to visit, after all), so

you want to minimize your route. You plan on visiting each location exactly once, following the shortest

route possible. As a programmer, you certainly don’t want to plot the route by hand. Rather, you try to

write some code that will plan your trip for you. For some reason, however, you can’t seem to get it right.

A straightforward program works well for a smaller number of towns and cities but seems to run forever

on the actual problem, and improving the program turns out to be surprisingly hard. How come?

Actually, in 2004, a team of five researchers

found such a tour of Sweden, after a number of other

research teams had tried and failed. The five-man team used cutting-edge software with lots of clever

optimizations and tricks of the trade, running on a cluster of 96 Xeon 2.6 GHz workstations. Their

software ran from March 2003 until May 2004, before it finally printed out the optimal solution. Taking

various interruptions into account, the team estimated that the total CPU time spent was about 85 years!

Consider a similar problem: You want to get from Kashgar, in the westernmost regions of China, to

Ningbo, on the east coast, following the shortest route possible. Now, China has 3 583 715 km of

roadways and 77 834 km of railways, with millions of intersections to consider and a virtually

unfathomable number of possible routes to follow. It might seem that this problem is related to the

previous one, yet this shortest path problem is one solved routinely, with no appreciable delay, by GPS

software and online map services. If you give those two cities to your favorite map service, you should

get the shortest route in mere moments. What’s going on here?

You will learn more about both of these problems later in the book; the first one is called the

traveling salesman (or salesrep) problem and is covered in Chapter 11, while so-called shortest path

problems are primarily dealt with in Chapter 9. I also hope you will gain a rather deep insight into why

one problem seems like such a hard nut to crack while the other admits several well-known, efficient

solutions. More importantly, you will learn something about how to deal with algorithmic and

computational problems in general, either solving them efficiently, using one of the several techniques

and algorithms you encounter in this book, or showing that they are too hard and that approximate

solutions may be all you can hope for. This chapter briefly describes what the book is about—what you

David Applegate, Robert Bixby, Vašek Chvátal, William Cook, and Keld Helsgaun

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CHAPTER 1 ■ INTRODUCTION

can expect and what is expected of you. It also outlines the specific contents of the various chapters to

come in case you want to skip around.

What’s All This, Then?

This is a book about algorithmic problem solving for Python programmers. Just like books on, say,

object-oriented patterns, the problems it deals with are of a general nature—as are the solutions. Your

task as an algorist will, in many cases, be more than simply to implement or execute an existing

algorithm, as you would, for example, in solving an algebra problem. Instead, you are expected to come

up with new algorithms—new general solutions to hitherto unseen, general problems. In this book, you

are going to learn principles for constructing such solutions.

This may not be your typical algorithm book, though. Most of the authoritative books on the subject

(such as the Knuth’s classics or the industry-standard textbook by Cormen et al.) have a heavy formal

and theoretical slant, even though some of them (such as the one by Kleinberg and Tardos) lean more in

the direction of readability. Instead of trying to replace any of these excellent books, I’d like to

supplement them. Building on my experience from teaching algorithms, I try to explain as clearly as

possible how the algorithms work and what common principles underlie many of them. For a

programmer, these explanations are probably enough. Chances are you’ll be able to understand why the

algorithms are correct and how to adapt them to new problems you may come to face. If, however, you

need the full depth of the more formalistic and encyclopedic textbooks, I hope the foundation you get in

this book will help you understand the theorems and proofs you encounter there.

There is another genre of algorithm books as well: the “(Data Structures and) Algorithms in blank”

kind, where the blank is the author’s favorite programming language. There are quite a few of these

(especially for blank = Java, it seems), but many of them focus on relatively basic data structures, to the

detriment of the more meaty stuff. This is understandable if the book is designed to be used in a basic

course on data structures, for example, but for a Python programmer, learning about singly and doubly

linked lists may not be all that exciting (although you will hear a bit about those in the next chapter). And

even though techniques such as hashing are highly important, you get hash tables for free in the form of

Python dictionaries; there’s no need to implement them from scratch. Instead, I focus on more high-

level algorithms. Many important concepts that are available as black-box implementations either in the

Python language itself or in the standard library (such as sorting, searching, and hashing) are explained

more briefly, in special “black box” sidebars throughout the text.

There is, of course, another factor that separates this book from those in the “Algorithms in

Java/C/C++/C#” genre, namely, that the blank is Python. This places the book one step closer to the

language-independent books (such as those by Knuth,

Cormen et al., and Kleinberg and Tardos, for

example), which often use pseudocode, the kind of fake programming language that is designed to be

readable rather than executable. One of Python’s distinguishing features is its readability; it is, more or

less, executable pseudocode. Even if you’ve never programmed in Python, you could probably decipher

the meaning of most basic Python programs. The code in this book is designed to be readable exactly in

this fashion—you need not be a Python expert to understand the examples (although you might need to

look up some built-in functions and the like). And if you want to pretend the examples are actually

pseudocode, feel free to do so. To sum up …

Knuth is also well-known for using assembly code for an abstract computer of his own design.

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