算法导论第四版：面向初学者与专业人士的基础教程

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"Algorithms+4th+Edition" 是一本由Robert Sedgewick和Kevin Wayne合著的关于算法的教科书，适用于初次接触或已有一年或两年大学经验的学生。这本书是基于Sedgewick系列算法书籍的内容，特别是在第一版和第二版的基础上发展起来的，但融入了多年来教学和学习的经验。它被设计成一个学期课程的教材，并且对在职程序员来说也是一个现代基础算法的参考书。与Sedgewick的《Algorithms in C/C++/Java, Third Edition》不同，这本书更注重作为初级或中级读者的入门教程。该书的目标是为学生提供足够的计算机科学背景，以便他们在科学、工程或社会科学领域的任何研究中成功应用计算。内容涵盖了广泛的算法主题，包括排序、搜索、图算法等基础知识，旨在培养学生的算法思维和问题解决能力。书中可能涉及的具体知识点包括但不限于： 1. **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。 2. **搜索算法**：二分查找、线性查找、深度优先搜索（DFS）、广度优先搜索（BFS）等。 3. **数据结构**：数组、链表、栈、队列、树（二叉树、平衡树如AVL和红黑树）、哈希表等的基本操作和应用。 4. **图算法**：Dijkstra算法、Floyd-Warshall算法、Prim算法和Kruskal算法等用于求解最短路径和最小生成树的问题。 5. **动态规划**：解决背包问题、最长公共子序列、最短路径等优化问题的方法。 6. **递归与分治**：递归定义、递归函数的分析，以及如何将问题分解为子问题来解决（如归并排序和快速排序的实现）。 7. **贪心算法**：通过局部最优解寻找全局最优解的策略，如霍夫曼编码和活动安排问题。 8. **随机化算法**：如鸽巢原理、随机化排序算法（如快速选择）和概率分析。此外，书中的内容可能会讨论算法设计技巧、复杂度分析（时间复杂度和空间复杂度）、算法效率比较，以及如何使用伪代码和实际编程语言（如Java）来实现这些算法。它还可能包含练习题和案例研究，以帮助学生加深理解和应用所学知识。对于批量购买或特殊销售，出版社提供了优惠，这可能包括电子版本、自定义封面和针对特定需求定制的内容。这本书不仅适合课堂教学，也适合自学和专业开发使用。

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 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 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 deﬁne 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 scientiﬁc method: we develop hypotheses about performance, create mathematical

models, and run experiments to test them, repeating the process as necessary.

We concl ude w it h a c ase s tudy wh ere we co nsid er solu tion s to a connectivity problem

that uses algorithms and data structures that implement the classic union-ﬁnd ADT.

A l g o r i t h m s 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 implementa-

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

central objects of study in the ﬁeld.

We ca n de ﬁne an al gor ithm by d esc rib ing a pro cedure fo r so lvi ng a prob lem 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 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 ﬁnite, 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

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 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 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 sci-

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

5CHAPTER 1

■

Fundamentals

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, giv-

ing 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 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 ﬁnd application as the basis for other algo-

rithms 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 con side r d epth -ﬁrs t s earch , bre adt h-ﬁr st se arch, co nnec tiv it y p ro ble ms, a nd s ev -

eral 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.

6 CHAPTER 1

■

Fundamentals

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