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Cormen, Leiserson, Rivest, Stein. Introduction to algorithms (2ed, MIT, 2001)(984s)_CsAl_.pdf |
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one, but it may require an understanding of more advanced mathematics. Likewise, starred exercises may require an advanced background or more than average creativity....
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....
Changes for the second edition
What has changed between the first and second editions of this book? Depending on how you look at it, either not much or quite a bit. A quick look at the table of contents shows that most of the first-edition chapters and sections appear in the second edition. We removed two chapters and a handful of sections, but we have added three new chapters and four new sections apart from these new chapters. If you were to judge the scope of the changes by the table of contents, you would likely conclude that the changes were modest. The changes go far beyond what shows up in the table of contents, however. In no particular order, here is a summary of the most significant changes for the second edition:
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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....
modularity, and error handling are often ignored in order to convey the essence of the algorithm more concisely. We start with insertion sort, which is an efficient algorithm for sorting a small number of elements. Insertion sort works the way many people sort a hand of playing cards. We start with an empty left hand and the cards face down on the table. We then remove one card at a time from the table and insert it into the correct position in the left hand. To find the correct position for a card, we compare it with each of the cards already in the hand, from right to left, as illustrated in Figure 2.1. At all times, the cards held in the left hand are sorted, and these cards were originally the top cards of the pile on the table....
3 as well. In other words, x and y point to ("are") the same object after the assignment y ← x. Sometimes, a pointer will refer to no object at all. In this case, we give it the special value NIL. 8. Parameters are passed to a procedure by value: the called procedure receives its own copy of the parameters, and if it assigns a value to a parameter, the change is not seen by the calling procedure. When objects are passed, the pointer to the data representing the object is copied, but the object's fields are not. For example, if x is a parameter of a called procedure, the assignment x ← y within the called procedure is not visible to the calling procedure. The assignment f [x] ← 3, however, is visible. 9. The boolean operators "and" and "or" are short circuiting. That is, when we evaluate the expression "x and y" we first evaluate x. If x evaluates to FALSE, then the entire expression cannot evaluate to TRUE, and so we do not evaluate y. If, on the other hand, x evaluates to TRUE, we must evaluate y to determine the value of the entire expression. Similarly, in the expression "x or y" we evaluate the expression y only if x evaluates to FALSE. Short-circuiting operators allow us to write boolean expressions such as "x ≠ NIL and f[x] = y" without worrying about what happens when we try to evaluate f[x] when x is NIL. Exercises 2.1-1 Using Figure 2.2 as a model, illustrate the operation of INSERTION-SORT on the array A = 31, 41, 59, 26, 41, 58 ....
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