Sedgewick与Wayne的《算法第四版》深度解析

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"Algorithms 4th Edition - Robert Sedgewick 和 Kevin Wayne - Princeton University" 《算法第四版》是由罗伯特·西德威克（Robert Sedgewick）和凯文·韦恩（Kevin Wayne）两位来自普林斯顿大学的专家共同编著的经典教材。这本书深入浅出地讲解了算法设计与分析的核心概念，是学习和掌握算法的必备参考书。它覆盖了广泛的主题，旨在帮助读者理解和应用各种算法，从而解决计算机科学中的实际问题。在本书中，作者们讨论了以下关键知识点： 1. **排序与搜索算法**：包括经典的快速排序、归并排序、堆排序以及二分查找等，这些都是计算机科学中最基础且重要的算法。 2. **图算法**：介绍了图的遍历（深度优先搜索和广度优先搜索）、最短路径算法（如Dijkstra算法和Floyd-Warshall算法）以及最小生成树（Prim算法和Kruskal算法）。 3. **动态规划**：讲解了如何使用动态规划解决背包问题、最长公共子序列问题等复杂问题，强调了状态转移方程和优化技巧。 4. **数据结构**：涵盖了数组、链表、栈、队列、哈希表、树（二叉树、平衡树如AVL和红黑树）等基本数据结构的设计与实现。 5. **递归与分治策略**：阐述了递归的本质，以及如何利用分治法解决如快速傅里叶变换（FFT）和大整数乘法等问题。 6. **字符串处理**：讨论了模式匹配算法，如Knuth-Morris-Pratt(KMP)算法和Boyer-Moore算法，以及文本处理和DNA序列分析的基础知识。 7. **概率和随机化算法**：介绍了如何利用概率分析来评估算法性能，以及如何设计和分析如Monte Carlo和Las Vegas方法的随机化算法。 8. **近似算法和NP完全问题**：探讨了如何处理那些在有限时间内无法找到最优解的问题，如旅行商问题（Traveling Salesman Problem）和网络流问题。 9. **算法设计技巧**：包括回溯、贪心、分治和动态规划的综合运用，以及如何通过这些技巧来构造新算法。 10. **算法分析**：深入讲解了时间复杂度、空间复杂度的概念，以及如何进行渐进分析，帮助读者评估算法的效率。该书不仅提供了理论知识，还包含了大量的实例和练习，帮助读者巩固所学，提升编程能力。此外，书中还可能包含了在线资源，如代码实现和额外练习，以促进读者的动手实践。购买大量此书时，出版社提供优惠，适合批量购买用于课堂教学或企业培训，也可以定制电子版本和封面，以适应特定的业务需求、培训目标、市场定位及品牌建设。

One. Fundamentals
1.1 Basic Programming Model 8
1.2 Data Abstraction 64
1.3 Bags, Queues, and Stacks 120
1.4 Analysis of Algorithms 172
1.5 Case Study: Union-Find 216
The objective of this book is to study a broad variety of important and useful algorithms—methods
for solving problems that are suited for computer implementation. Algorithms go hand in hand with
data structures—schemes for organizing data that leave them amenable to efficient processing by an
algorithm. This chapter introduces the basic tools that we need to study algorithms and data structures.
First, we introduce our basic programming model. All of our programs are implemented using a
small subset of the Java programming language plus a few of our own libraries for input/output and
for statistical calculations. SECTION 1.1 is a summary of language constructs, features, and libraries that
we use in this book.
Next, we emphasize data abstraction, where we define abstract data types (ADTs) in the service of
modular programming. In SECTION 1.2 we introduce the process of implementing an ADT in Java, by
specifying an applications programming interface (API) and then using the Java class mechanism to
develop an implementation for use in client code.
As important and useful examples, we next consider three fundamental ADTs: the bag, the queue, and
the stack. SECTION 1.3 describes APIs and implementations of bags, queues, and stacks using arrays,
resizing arrays, and linked lists that serve as models and starting points for algorithm implementations
throughout the book.
Performance is a central consideration in the study of algorithms. SECTION 1.4 describes our approach
to analyzing algorithm performance. The basis of our approach is the scientific method: we develop
hypotheses about performance, create mathematical models, and run experiments to test them,
repeating the process as necessary.
We conclude with a case study where we consider solutions to a connectivity problem that uses
algorithms and data structures that implement the classic union-find ADT.
Algorithms
When we write a computer program, we are generally implementing a method that has been devised
previously to solve some problem. This method is often independent of the particular programming
language being used—it is likely to be equally appropriate for many computers and many
programming languages. It is the method, rather than the computer program itself, that specifies the
steps that we can take to solve the problem. The term algorithm is used in computer science to
describe a finite, deterministic, and effective problem-solving method suitable for implementation as
a computer program. Algorithms are the stuff of computer science: they are central objects of study in
the field.
We can define an algorithm by describing a procedure for solving a problem in a natural language, or

by writing a computer program that implements the procedure, as shown at right for Euclid’s

algorithm for finding the greatest common divisor of two numbers, a variant of which was devised

over 2,300 years ago. If you are not familiar with Euclid’s algorithm, you are encouraged to work

EXERCISE 1.1.24 and EXERCISE 1.1.25, perhaps after reading SECTION 1.1. In this book, we use computer

programs to describe algorithms. One important reason for doing so is that it makes easier the task of

checking whether they are finite, deterministic, and effective, as required. But it is also important to

recognize that a program in a particular language is just one way to express an algorithm. The fact that

many of the algorithms in this book have been expressed in multiple programming languages over the

past several decades reinforces the idea that each algorithm is a method suitable for implementation

on any computer in any programming language.

Most algorithms of interest involve organizing the data involved in the computation. Such organization

leads to data structures, which also are central objects of study in computer science. Algorithms and

data structures go hand in hand. In this book we take the view that data structures exist as the

byproducts or end products of algorithms and that we must therefore study them in order to understand

the algorithms. Simple algorithms can give rise to complicated data structures and, conversely,

complicated algorithms can use simple data structures. We shall study the properties of many data

structures in this book; indeed, we might well have titled the book Algorithms and Data Structures.

When we use a computer to help us solve a problem, we typically are faced with a number of

possible approaches. For small problems, it hardly matters which approach we use, as long as we

have one that correctly solves the problem. For huge problems (or applications where we need to

solve huge numbers of small problems), however, we quickly become motivated to devise methods

that use time and space efficiently.

The primary reason to learn about algorithms is that this discipline gives us the potential to reap huge

savings, even to the point of enabling us to do tasks that would otherwise be impossible. In an

application where we are processing millions of objects, it is not unusual to be able to make a

program millions of times faster by using a well-designed algorithm. We shall see such examples on

numerous occasions throughout the book. By contrast, investing additional money or time to buy and

install a new computer holds the potential for speeding up a program by perhaps a factor of only 10 or

100. Careful algorithm design is an extremely effective part of the process of solving a huge problem,

whatever the applications area.

When developing a huge or complex computer program, a great deal of effort must go into

understanding and defining the problem to be solved, managing its complexity, and decomposing it

into smaller subtasks that can be implemented easily. Often, many of the algorithms required after the

decomposition are trivial to implement. In most cases, however, there are a few algorithms whose

choice is critical because most of the system resources will be spent running those algorithms. These

are the types of algorithms on which we concentrate in this book. We study fundamental algorithms

that are useful for solving challenging problems in a broad variety of applications areas.

The sharing of programs in computer systems is becoming more widespread, so although we might

expect to be using a large fraction of the algorithms in this book, we also might expect to have to

implement only a small fraction of them. For example, the Java libraries contain implementations of a

host of fundamental algorithms. However, implementing simple versions of basic algorithms helps us

to understand them better and thus to more effectively use and tune advanced versions from a library.

More important, the opportunity to reimplement basic algorithms arises frequently. The primary

reason to do so is that we are faced, all too often, with completely new computing environments

(hardware and software) with new features that old implementations may not use to best advantage. In

this book, we concentrate on the simplest reasonable implementations of the best algorithms. We do

pay careful attention to coding the critical parts of the algorithms, and take pains to note where low-

level optimization effort could be most beneficial.

The choice of the best algorithm for a particular task can be a complicated process, perhaps involving

sophisticated mathematical analysis. The branch of computer science that comprises the study of such

questions is called analysis of algorithms. Many of the algorithms that we study have been shown

through analysis to have excellent theoretical performance; others are simply known to work well

through experience. Our primary goal is to learn reasonable algorithms for important tasks, yet we

shall also pay careful attention to comparative performance of the methods. We should not use an

algorithm without having an idea of what resources it might consume, so we strive to be aware of

how our algorithms might be expected to perform.

Summary of topics

As an overview, we describe the major parts of the book, giving specific topics covered and an

indication of our general orientation toward the material. This set of topics is intended to touch on as

many fundamental algorithms as possible. Some of the areas covered are core computer-science areas

that we study in depth to learn basic algorithms of wide applicability. Other algorithms that we

discuss are from advanced fields of study within computer science and related fields. The algorithms

that we consider are the products of decades of research and development and continue to play an

essential role in the ever-expanding applications of computation.

Fundamentals (CHAPTER 1) in the context of this book are the basic principles and methodology that

we use to implement, analyze, and compare algorithms. We consider our Java programming model,

data abstraction, basic data structures, abstract data types for collections, methods of analyzing

algorithm performance, and a case study.

Sorting algorithms (CHAPTER 2) for rearranging arrays in order are of fundamental importance. We

consider a variety of algorithms in considerable depth, including insertion sort, selection sort,

shellsort, quicksort, mergesort, and heapsort. We also encounter algorithms for several related

problems, including priority queues, selection, and merging. Many of these algorithms will find

application as the basis for other algorithms later in the book.

Searching algorithms (CHAPTER 3) for finding specific items among large collections of items are also

of fundamental importance. We discuss basic and advanced methods for searching, including binary

search trees, balanced search trees, and hashing. We note relationships among these methods and

compare performance.

Graphs (CHAPTER 4) are sets of objects and connections, possibly with weights and orientation.

Graphs are useful models for a vast number of difficult and important problems, and the design of

algorithms for processing graphs is a major field of study. We consider depth-first search, breadth-

first search, connectivity problems, and several algorithms and applications, including Kruskal’s and

Prim’s algorithms for finding minimum spanning tree and Dijkstra’s and the Bellman-Ford algorithms

for solving shortest-paths problems.

Strings (CHAPTER 5) are an essential data type in modern computing applications. We consider a

range of methods for processing sequences of characters. We begin with faster algorithms for sorting

and searching when keys are strings. Then we consider substring search, regular expression pattern

matching, and data-compression algorithms. Again, an introduction to advanced topics is given

through treatment of some elementary problems that are important in their own right.

Context (CHAPTER 6) helps us relate the material in the book to several other advanced fields of study,

including scientific computing, operations research, and the theory of computing. We survey event-

driven simulation, B-trees, suffix arrays, maximum flow, and other advanced topics from an

introductory viewpoint to develop appreciation for the interesting advanced fields of study where

algorithms play a critical role. Finally, we describe search problems, reduction, and NP-

completeness to introduce the theoretical underpinnings of the study of algorithms and relationships to

material in this book.

THE STUDY OF ALGORITHMS IS INTERESTING AND EXCITING because it is a new field (almost all the

algorithms that we study are less than 50 years old, and some were just recently discovered) with a

rich tradition (a few algorithms have been known for hundreds of years). New discoveries are

constantly being made, but few algorithms are completely understood. In this book we shall consider

intricate, complicated, and difficult algorithms as well as elegant, simple, and easy ones. Our

challenge is to understand the former and to appreciate the latter in the context of scientific and

commercial applications. In doing so, we shall explore a variety of useful tools and develop a style of

algorithmic thinking that will serve us well in computational challenges to come.

1.1 Basic Programming Model

OUR STUDY OF ALGORITHMS is based upon implementing them as programs written in the Java

programming language. We do so for several reasons:

• Our programs are concise, elegant, and complete descriptions of algorithms.

• You can run the programs to study properties of the algorithms.

• You can put the algorithms immediately to good use in applications.

These are important and significant advantages over the alternatives of working with English-

language descriptions of algorithms.

A potential downside to this approach is that we have to work with a specific programming language,

possibly making it difficult to separate the idea of the algorithm from the details of its implementation.

Our implementations are designed to mitigate this difficulty, by using programming constructs that are

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