Python算法解析：掌握Python语言基础算法

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"Python Algorithms - Wei Zhi.pdf" 是一本深入探讨如何用Python语言进行算法分析和设计的书籍，适合Python专家阅读。本书由Magnus Lie Hetland撰写，旨在教授读者如何利用Python实现经典算法，并设计解决新问题的算法。全书涵盖了Python语言中的基础算法知识，帮助读者提升在编程领域的专业技能。书中可能包含以下关键知识点： 1. **算法基础**：介绍算法的基本概念，包括算法的重要性、定义和特性，以及如何评估算法的效率（如时间复杂度和空间复杂度）。 2. **数据结构**：深入讨论Python中的常见数据结构，如数组、链表、栈、队列、堆、图和树等，以及它们在解决问题中的应用。 3. **排序与搜索**：涵盖经典的排序算法（如冒泡排序、插入排序、选择排序、快速排序、归并排序、堆排序等）和搜索算法（如线性搜索、二分搜索等），并分析它们的效率。 4. **递归与动态规划**：讲解递归的思想，如何构建递归函数，以及动态规划的原理，通过实例展示如何使用这两种方法解决复杂问题。 5. **图算法**：介绍图的基本操作，如遍历（深度优先搜索和广度优先搜索）和最短路径算法（如Dijkstra算法、Floyd-Warshall算法等）。 6. **字符串处理**：讲解如何使用Python处理字符串，包括模式匹配、正则表达式以及文本处理算法。 7. **计算几何与数学算法**：探讨Python在几何计算和数学问题中的应用，如线性代数、矩阵运算、数值求解等。 8. **复杂度分析**：深入理解算法的时间和空间复杂度，学习如何分析和优化算法性能。 9. **设计模式**：介绍软件设计模式，如工厂模式、单例模式、装饰器模式等，以及如何在Python中应用这些模式。 10. **实战应用**：提供实际案例，让读者有机会将所学应用于真实世界的问题解决中，增强实战经验。此外，书中还可能包含习题和实践项目，帮助读者巩固理论知识并提高实际编程能力。对于希望在Python领域深入研究算法的开发者来说，这本书是不可或缺的参考资料。

■ 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.

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

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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