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Cormen, Leiserson, Rivest, Stein. Introduction to algorithms (2ed, MIT, 2001)(984s)_CsAl_.pdf |
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You should have some programming experience. In particular, you should understand recursive procedures and simple data structures such as arrays and linked lists. You should have some facility with proofs by mathematical induction. A few portions of the book rely on some knowledge of elementary calculus. Beyond that, Parts I and VIII of this book teach you all the mathematical techniques you will need....
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....
Introduction
This part will get you started in thinking about designing and analyzing algorithms. It is intended to be a gentle introduction to how we specify algorithms, some of the design 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 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....
which they appear. There are many choices, therefore, for the vertices of the convex hull. Chapter 33 gives two good methods for finding the convex hull. These lists are far from exhaustive (as you again have probably surmised from this book's heft), but exhibit two characteristics that are common to many interesting algorithms. 1. There are many candidate solutions, most of which are not what we want. Finding one that we do want can present quite a challenge. 2. There are practical applications. Of the problems in the above list, shortest paths provides the easiest examples. A transportation firm, such as a trucking or railroad company, has a financial interest in finding shortest paths through a road or rail network because taking shorter paths results in lower labor and fuel costs. Or a routing node on the Internet may need to find the shortest path through the network in order to route a message quickly. Data structures This book also contains several data structures. A data structure is a way to store and organize data in order to facilitate access and modifications. No single data structure works well for all purposes, and so it is important to know the strengths and limitations of several of them. Technique Although you can use this book as a "cookbook" for algorithms, you may someday encounter a problem for which you cannot readily find a published algorithm (many of the exercises and problems in this book, for example!). This book will teach you techniques of algorithm design and analysis so that you can develop algorithms on your own, show that they give the correct answer, and understand their efficiency. Hard problems Most of this book is about efficient algorithms. Our usual measure of efficiency is speed, i.e., how long an algorithm takes to produce its result. There are some problems, however, for which no efficient solution is known. Chapter 34 studies an interesting subset of these problems, which are known as NP-complete. Why are NP-complete problems interesting? First, although no efficient algorithm for an NPcomplete problem has ever been found, nobody has ever proven that an efficient algorithm for one cannot exist. In other words, it is unknown whether or not efficient algorithms exist for NP-complete problems. Second, the set of NP-complete problems has the remarkable property that if an efficient algorithm exists for any one of them, then efficient algorithms exist for all of them. This relationship among the NP-complete problems makes the lack of efficient solutions all the more tantalizing. Third, several NP-complete problems are similar, but not identical, to problems for which we do know of efficient algorithms. A small change to the problem statement can cause a big change to the efficiency of the best known algorithm. It is valuable to know about NP-complete problems because some of them arise surprisingly often in real applications. If you are called upon to produce an efficient algorithm for an NPcomplete problem, you are likely to spend a lot of time in a fruitless search. If you can show...
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