算法第4版Part I：2014年2月最新修订高清英文PDF

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"算法：第4版(Algorithms, 4th Edition) Part I 2014.2.最新版，由(美)Robert Sedgewick 和 Kevin Wayne 联合编写，是2014年2月发布的修订版，分为Part I 和 Part II，本资源为Part I。" 《算法：第四版》是由著名计算机科学家Robert Sedgewick和Kevin Wayne合作编写的经典算法教材。这本书是算法教学和研究的重要参考资料，旨在帮助读者深入理解算法设计、分析和实现的核心概念。 Part I 部分通常涵盖了算法基础和核心主题，包括以下几个方面： 1. **排序和搜索算法**：这部分会详细介绍经典的排序算法，如冒泡排序、选择排序、插入排序、快速排序、归并排序以及堆排序，以及线性查找、二分查找等搜索算法。这些算法是计算机科学的基础，对理解和优化数据处理至关重要。 2. **递归和分治策略**：递归是算法设计中一个重要的概念，用于解决复杂问题。书中会讲解如何通过递归解决问题，如计算阶乘、斐波那契数列等。同时，分治策略是一种高效解决问题的方法，如在快速排序和归并排序中的应用。 3. **图算法**：在Part I中，可能会介绍图的基本概念，如邻接矩阵和邻接表，以及图的遍历算法，如深度优先搜索（DFS）和广度优先搜索（BFS）。此外，可能还会涉及最短路径算法，如Dijkstra算法和Floyd-Warshall算法。 4. **动态规划**：动态规划是一种强大的解决问题的方法，常用于求解最优解。书中可能会通过解决背包问题、最长公共子序列等问题来介绍动态规划的基本思想和技巧。 5. **数据结构**：除了基本的数据结构如数组、链表、栈和队列，Part I可能会深入讲解树（如二叉树、平衡树AVL和红黑树）和哈希表等高级数据结构，并探讨它们在算法中的应用。 6. **复杂度分析**：书中会讲解如何分析算法的时间复杂度和空间复杂度，帮助读者评估算法的效率，并学会在不同场景下选择合适的算法。 7. **算法设计技巧**：包括贪心算法和回溯法等，这些都是设计和解决问题的有效工具。 8. **实践与实现**：Sedgewick和Wayne的书通常强调实际编程实现，可能包含用Java或其他编程语言实现上述算法的示例代码，帮助读者提高编程技能。通过学习《算法：第四版》Part I的内容，读者可以建立起坚实的算法基础，为后续深入学习更复杂的算法和数据结构打下坚实的基础。此外，这本书对于准备参加编程竞赛、面试或从事软件开发工作的人员来说，都是不可或缺的参考资料。

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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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