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首页算法导论Word版:计算机科学经典读物
算法导论Word版:计算机科学经典读物
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《算法导论(第二版)》是计算机科学领域的一部经典著作,由Thomas H. Cormen、Charles E. Leiserson、Ronald L. Rivest和Clifford Stein四位作者共同编撰,隶属于麻省理工学院电气工程与计算机科学系系列教材。本书由The MIT Press出版,并通过与McGraw-Hill Book Company的合作协议进行分发。 该版本的书籍特别适合在电脑屏幕上阅读,对于想要深入理解算法理论和实践的读者来说,它是一本不可或缺的参考文献。书中详细讲解了算法设计、分析和应用的基本原理,涵盖了排序、图算法、动态规划、数据结构等多个核心主题,帮助读者建立起坚实的算法基础。 《算法导论》不仅阐述了算法的理论概念,还提供了大量实际问题的解决方法和步骤,适合于初学者入门,同时也是高级程序员和研究者提升技能的宝贵资源。书中还强调了算法设计的重要性,鼓励读者通过逻辑思考和实践来理解和掌握这些关键概念。 版权方面,本书享有2001年的版权,首次出版日期为1990年,所有内容未经书面许可不得以任何形式复制或通过电子或机械手段(如复印、录音或信息存储和检索)进行传播。如果你欲购买或获取本书,请根据地区选择相应的订购渠道:北美地区的订单应寄往McGraw-Hill Book Company,而北美以外的订单则需联系The MIT Press 或其当地经销商。 《算法导论(第二版)》是一本全面且深入的算法教材,无论你是想系统学习还是寻求特定问题的解决方案,都将从中受益匪浅。无论是作为学术研究资料,还是技术开发者的工具书,都具有极高的价值。
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strategies we will use throughout this book, and many of the fundamental ideas used in
algorithm analysis. Later parts of this book will build upon this base.
Chapter 1 is an overview of algorithms and their place in modern computing systems.
This
chapter defines what an algorithm is and lists some examples. It also makes a case that
algorithms are a technology, just as are fast hardware, graphical user interfaces,
objectoriented
systems, and networks.
In Chapter 2, we see our first algorithms, which solve the problem of sorting a sequence
of n
numbers. They are written in a pseudocode which, although not directly translatable to
any
conventional programming language, conveys the structure of the algorithm clearly
enough
that a competent programmer can implement it in the language of his choice. The sorting
algorithms we examine are insertion sort, which uses an incremental approach, and merge
sort, which uses a recursive technique known as "divide and conquer." Although the time
each requires increases with the value of n, the rate of increase differs between the two
algorithms. We determine these running times in Chapter 2, and we develop a useful
notation
to express them.
Chapter 3 precisely defines this notation, which we call asymptotic notation. It starts by
defining several asymptotic notations, which we use for bounding algorithm running
times
from above and/or below. The rest of Chapter 3 is primarily a presentation of
mathematical
notation. Its purpose is more to ensure that your use of notation matches that in this book
than
to teach you new mathematical concepts.
Chapter 4 delves further into the divide-and-conquer method introduced in Chapter 2. In
particular, Chapter 4 contains methods for solving recurrences, which are useful for
describing the running times of recursive algorithms. One powerful technique is the
"master
method," which can be used to solve recurrences that arise from divide-and-conquer
algorithms. Much of Chapter 4 is devoted to proving the correctness of the master
method,
though this proof may be skipped without harm.
Chapter 5 introduces probabilistic analysis and randomized algorithms. We typically use
probabilistic analysis to determine the running time of an algorithm in cases in which,
due to
the presence of an inherent probability distribution, the running time may differ on
different
inputs of the same size. In some cases, we assume that the inputs conform to a known
probability distribution, so that we are averaging the running time over all possible
inputs. In
other cases, the probability distribution comes not from the inputs but from random
choices
made during the course of the algorithm. An algorithm whose behavior is determined not
only
by its input but by the values produced by a random-number generator is a randomized
algorithm. We can use randomized algorithms to enforce a probability distribution on the
inputs-thereby ensuring that no particular input always causes poor performance-or even
to
bound the error rate of algorithms that are allowed to produce incorrect results on a
limited
basis.
Appendices A-C contain other mathematical material that you will find helpful as you
read
this book. You are likely to have seen much of the material in the appendix chapters
before
having read this book (although the specific notational conventions we use may differ in
some
cases from what you have seen in the past), and so you should think of the Appendices as
reference material. On the other hand, you probably have not already seen most of the
material in Part I. All the chapters in Part I and the Appendices are written with a tutorial
flavor.
Chapter 1: The Role of Algorithms in
Computing
What are algorithms? Why is the study of algorithms worthwhile? What is the role of
algorithms relative to other technologies used in computers? In this chapter, we will
answer
these questions.
1.1 Algorithms
Informally, an algorithm is any well-defined computational procedure that takes some
value,
or set of values, as input and produces some value, or set of values, as output. An
algorithm is
thus a sequence of computational steps that transform the input into the output.
We can also view an algorithm as a tool for solving a well-specified computational
problem.
The statement of the problem specifies in general terms the desired input/output
relationship.
The algorithm describes a specific computational procedure for achieving that
input/output
relationship.
For example, one might need to sort a sequence of numbers into nondecreasing order.
This
problem arises frequently in practice and provides fertile ground for introducing many
standard design techniques and analysis tools. Here is how we formally define the sorting
problem:
. Input: A sequence of n numbers _a1, a2, ..., an_.
. Output: A permutation (reordering) of the input sequence such that
.
For example, given the input sequence _31, 41, 59, 26, 41, 58_, a sorting algorithm
returns
as output the sequence _26, 31, 41, 41, 58, 59_. Such an input sequence is called an
instance
of the sorting problem. In general, an instance of a problem consists of the input
(satisfying
whatever constraints are imposed in the problem statement) needed to compute a solution
to
the problem.
Sorting is a fundamental operation in computer science (many programs use it as an
intermediate step), and as a result a large number of good sorting algorithms have been
developed. Which algorithm is best for a given application depends on-among other
factorsthe
number of items to be sorted, the extent to which the items are already somewhat sorted,
possible restrictions on the item values, and the kind of storage device to be used: main
memory, disks, or tapes.
An algorithm is said to be correct if, for every input instance, it halts with the correct
output.
We say that a correct algorithm solves the given computational problem. An incorrect
algorithm might not halt at all on some input instances, or it might halt with an answer
other
than the desired one. Contrary to what one might expect, incorrect algorithms can
sometimes
be useful, if their error rate can be controlled. We shall see an example of this in Chapter
31
when we study algorithms for finding large prime numbers. Ordinarily, however, we
shall be
concerned only with correct algorithms.
An algorithm can be specified in English, as a computer program, or even as a hardware
design. The only requirement is that the specification must provide a precise description
of the
computational procedure to be followed.
What kinds of problems are solved by algorithms?
Sorting is by no means the only computational problem for which algorithms have been
developed. (You probably suspected as much when you saw the size of this book.)
Practical
applications of algorithms are ubiquitous and include the following examples:
. The Human Genome Project has the goals of identifying all the 100,000 genes in
human DNA, determining the sequences of the 3 billion chemical base pairs that make
up human DNA, storing this information in databases, and developing tools for data
analysis. Each of these steps requires sophisticated algorithms. While the solutions to
the various problems involved are beyond the scope of this book, ideas from many of
the chapters in this book are used in the solution of these biological problems, thereby
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