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Cormen, Leiserson, Rivest, Stein. Introduction to algorithms (2ed, MIT, 2001)(984s)_CsAl_.pdf |
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Size 11.6Mb Date Sep 1, 2005 |
To the teacher
This book is designed to be both versatile and complete. You will find it useful for a variety of courses, from an undergraduate course in data structures up through a graduate course in algorithms. Because we have provided considerably more material than can fit in a typical one-term course, you should think of the book as a "buffet" or "smorgasbord" from which you can pick and choose the material that best supports the course you wish to teach. You should find it easy to organize your course around just the chapters you need. We have made chapters relatively self-contained, so that you need not worry about an unexpected and unnecessary dependence of one chapter on another. Each chapter presents the easier material first and the more difficult material later, with section boundaries marking natural stopping points. In an undergraduate course, you might use only the earlier sections from a chapter; in a graduate course, you might cover the entire chapter. We have included over 920 exercises and over 140 problems. Each section ends with exercises, and each chapter ends with problems. The exercises are generally short questions that test basic mastery of the material. Some are simple self-check thought exercises, whereas others are more substantial and are suitable as assigned homework. The problems are more elaborate case studies that often introduce new material; they typically consist of several questions that lead the student through the steps required to arrive at a solution. We have starred (⋆) the sections and exercises that are more suitable for graduate students than for undergraduates. A starred section is not necessarily more difficult than an unstarred...
To the professional
The wide range of topics in this book makes it an excellent handbook on algorithms. Because each chapter is relatively self-contained, you can focus in on the topics that most interest you. Most of the algorithms we discuss have great practical utility. We therefore address implementation concerns and other engineering issues. We often provide practical alternatives to the few algorithms that are primarily of theoretical interest. If you wish to implement any of the algorithms, you will find the translation of our pseudocode into your favorite programming language a fairly straightforward task. The pseudocode is designed to present each algorithm clearly and succinctly. Consequently, we do not address error-handling and other software-engineering issues that require specific assumptions about your programming environment. We attempt to present each algorithm simply and directly without allowing the idiosyncrasies of a particular programming language to obscure its essence....
Finally, virtually every section has been edited to correct, simplify, and clarify explanations and proofs....
Acknowledgments for the second edition
When we asked Julie Sussman, P.P.A., to serve as a technical copyeditor for the second edition, we did not know what a good deal we were getting. In addition to copyediting the technical content, Julie enthusiastically edited our prose. It is humbling to think of how many errors Julie found in our earlier drafts, though considering how many errors she found in the first edition (after it was printed, unfortunately), it is not surprising. Moreover, Julie sacrificed her own schedule to accommodate ours-she even brought chapters with her on a trip to the Virgin Islands! Julie, we cannot thank you enough for the amazing job you did....
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....
Input: A sequence of n numbers a1, a2, ..., an . Output: A permutation (reordering) of the input sequence such that ....
that the problem is NP-complete, you can instead spend your time developing an efficient algorithm that gives a good, but not the best possible, solution. As a concrete example, consider a trucking company with a central warehouse. Each day, it loads up the truck at the warehouse and sends it around to several locations to make deliveries. At the end of the day, the truck must end up back at the warehouse so that it is ready to be loaded for the next day. To reduce costs, the company wants to select an order of delivery stops that yields the lowest overall distance traveled by the truck. This problem is the well-known "traveling-salesman problem," and it is NP-complete. It has no known efficient algorithm. Under certain assumptions, however, there are efficient algorithms that give an overall distance that is not too far above the smallest possible. Chapter 35 discusses such "approximation algorithms." Exercises 1.1-1 Give a real-world example in which one of the following computational problems appears: sorting, determining the best order for multiplying matrices, or finding the convex hull....
technology, you can accomplish some tasks without knowing much about algorithms, but with a good background in algorithms, you can do much, much more. Exercises 1.2-1 Give an example of an application that requires algorithmic content at the application level, and discuss the function of the algorithms involved....
Chapter 2: Getting Started
This chapter will familiarize you with the framework we shall use throughout the book to think about the design and analysis of algorithms. It is self-contained, but it does include several references to material that will be introduced in Chapters 3 and 4. (It also contains several summations, which Appendix A shows how to solve.) We begin by examining the insertion sort algorithm to solve the sorting problem introduced in Chapter 1. We define a "pseudocode" that should be familiar to readers who have done computer programming and use it to show how we shall specify our algorithms. Having specified the algorithm, we then argue that it correctly sorts and we analyze its running time. The analysis introduces a notation that focuses on how that time increases with the number of items to be sorted. Following our discussion of insertion sort, we introduce the divide-andconquer approach to the design of algorithms and use it to develop an algorithm called merge sort. We end with an analysis of merge sort's running time....
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