Sedgewick & Wayne's《算法》第四版第1部分：基础与核心算法

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"Algorithms(Addison,4ed,Part I,2014)" 是罗伯特·西德维克（Robert Sedgewick）和凯文·韦恩（Kevin Wayne）编著的《算法》第四版的第一部分，这是一本在世界各地广泛应用于大学和学院的算法教材。该书主要涵盖了第1至第3章的内容，专注于介绍计算机算法的基本概念，数据结构以及排序、搜索、图处理和字符串处理中的关键算法。第四版的特点是提供了新的Java实现，这些实现采用了模块化的编程风格，使得代码对读者完全开放，易于理解和使用。书中的50个算法是每个程序员都应该了解和掌握的基础知识。书的内容旨在让读者能够深入了解和运用这些重要的计算工具。在本书的"Part I"中，我们可以期待学习到以下核心知识点： 1. **算法基础**：这部分可能会介绍算法的定义、分类以及它们在计算机科学中的重要性。它可能会探讨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**：包括数组、链表、栈、队列、树、哈希表等基本数据结构的定义、操作和应用。这些数据结构是实现高效算法的基础。 3. **排序算法**：如冒泡排序、选择排序、插入排序、快速排序、归并排序、堆排序等，以及它们的时间复杂度分析和适用场景。 4. **搜索算法**：包括线性搜索、二分搜索、广度优先搜索（BFS）、深度优先搜索（DFS）等，以及在不同数据结构中的应用。 5. **图处理**：涉及图的表示（邻接矩阵、邻接表）、图的遍历（DFS和BFS）、最短路径算法（Dijkstra、Floyd-Warshall）、最小生成树（Prim和Kruskal算法）等。 6. **字符串处理**：涵盖模式匹配（如KMP算法）、字符串排序、文本处理算法等，这些都是在文本分析和数据挖掘中常见的问题。 7. **模块化编程风格**：书中提供的Java实现强调了代码的可读性和复用性，这对于软件开发来说是非常重要的实践。通过深入学习这本书的内容，读者不仅可以掌握基础的算法知识，还能了解到如何在实际问题中应用这些算法，从而提升编程能力和解决问题的效率。此外，书中可能还会包含练习题和案例研究，以帮助读者巩固所学知识并提高实际操作能力。

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he objective of this book is to study a broad variety of important and useful

algorithms—methods for solving problems that are suited for computer imple-

mentation. Algorithms go hand in hand with data structures—schemes for or-

ganizing data that leave them amenable to efcient 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 imple-

mented 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 dene abstract data types (ADTs) in

the service of modular programming. In Section 1.2 we introduce the process of im-

plementing 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 de-

scribes our approach to analyzing algorithm performance. The basis of our approach is

the scientic 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-nd ADT.

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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 species the steps that we can

take to solve the problem. The term algorithm is used in computer science to describe

a nite, deterministic, and effective problem-solving method suitable for implementa-

tion as a computer program. Algorithms are the stuff of computer science: they are

central objects of study in the eld.

We can dene 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 nding 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 encour-

aged 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 de-

scribe algorithms. One important reason for

doing so is that it makes easier the task of

checking whether they are nite, determin-

istic, 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 al-

gorithms 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 computa-

tion. 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.

Compute the greatest common divisor of

two nonnegative integers p and q

as follows:

If q is 0, the answer is p. If not, divide p by q

and take the remainder r. The answer is the

greatest common divisor of q and r.

public static int gcd(int p, int q)

{

if (q == 0) return p;

int r = p % q;

return gcd(q, r);

}

Euclid’s algorithm

Java-language description

English-language description

4 Chapter 1

Fundamentals

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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 efciently.

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 dening the problem to be solved, managing its complex-

ity, 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 bet-

ter and thus to more effectively use and tune advanced versions from a library. More

important, the opportunity to reimplement basic algorithms arises frequently. The pri-

mary 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 criti-

cal parts of the algorithms, and take pains to note where low-level optimization effort

could be most benecial.

Choosing the best algorithm for a particular task can be a complicated process, per-

haps involving sophisticated mathematical analysis. The branch of computer science

that comprises the study of such questions is called analysis of algorithms. Many of the

5Chapter 1

Fundamentals

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algorithms that we study have been shown through analysis to have excellent theoreti-

cal performance; others are simply known to work well through experience. Our pri-

mary 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, giv-

ing specic 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 elds of study within computer science and related elds. The algo-

rithms 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 in-

sertion sort, selection sort, shellsort, quicksort, mergesort, and heapsort. We also en-

counter algorithms for several related problems, including priority queues, selection,

and merging. Many of these algorithms will nd application as the basis for other algo-

rithms later in the book.

Searching algorithms (Chapter 3) for nding specic 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 difcult and important

problems, and the design of algorithms for processing graphs is a major eld of study.

We consider depth-rst search, breadth-rst search, connectivity problems, and sev-

eral algorithms and applications, including Kruskal’s and Prim’s algorithms for nding

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

shortest-paths problems.

6 Chapter 1

Fundamentals

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