## Chapter Contents For the most part, we have organized this text by technique used to solve problems, rather than by application area. We feel that this organization makes the field of algorithm design and analysis appear more coherent. Furthermore, students can more readily establish a repertoire of techniques that they can investigate as possible ways to solve a new problem. The chapter contents are as follows: - [Chapter 1](LiB0008.html#16) is an introduction to the design and analysis of algorithms. It includes both an intuitive and formal introduction to the concept of order. - [Chapter 2](LiB0014.html#141) covers the divide-and-conquer approach to designing algorithms. - [Chapter 3](LiB0024.html#252) presents the dynamic programming design method. We discuss when dynamic programming should be used instead of divide-and-conquer. - [Chapter 4](LiB0032.html#359) discusses the greedy approach and ends with a comparison of the dynamic programming and greedy approaches to solving optimization problems. - [Chapters 5](LiB0039.html#471) and [6](LiB0047.html#565) cover backtracking and branch-and-bound algorithms respectively. - In [Chapter 7](LiB0052.html#627) we switch from analyzing algorithms to computational complexity, which is the analysis of problems. We introduce computation complexity by analyzing the Sorting Problem. We chose that problem because of its importance, because there are such a large variety of sorting algorithms, and, most significantly, because there are sorting algorithms that perform about as well as the lower bound for the Sorting Problem (as far as algorithms that sort only by comparisons of keys). After comparing sorting algorithms, we analyze the problem of sorting by comparisons of keys. The chapter ends with Radix Sort, which is a sorting algorithm that does not sort by comparison keys. - In [Chapter 8](LiB0067.html#759) we further illustrate computational complexity by analyzing the Searching Problem. We analyze both the problem of searching for a key in a list and the Selection Problem, which is the problem of finding the *k*th-smallest key in a list. - [Chapter 9](LiB0074.html#880) is devoted to intractability and the theory of *NP.* To keep our text accessible yet rigorous, we give a more complete discussion of this material than is usually given in an algorithms text. We start out by explicitly drawing the distinction between problems for which polynomial-time algorithms have been found, problems that have been proven to be intractable, and problems that have not been proven to be intractable but for which polynomial-time algorithms have never been found. We then discuss the sets *P* and *NP, NP*-complete problems, and *NP*-equivalent problems. We have found that students are often left confused if they do not explicitly see the relationships among these sets. We end the chapter with a discussion of approximation algorithms. - [Chapter 10](LiB0080.html#989) covers number-theoretic algorithms, including Euclid's algorithm, and the new polynomial-time algorithm for determining whether a number is prime. - [Chapter 11](LiB0089.html#1224) covers an introduction to parallel algorithms, including parallel architectures and the PRAM model. - [Appendix A](LiB0093.html#1281) reviews the mathematics that is necessary for understanding the text. - [Appendix B](LiB0102.html#1369) covers techniques for solving recurrences. The results in [Appendix B](LiB0102.html#1369) are used in our analyses of divide-and-conquer algorithms in [Chapter 2](LiB0014.html#141). - [Appendix C](LiB0108.html#1464) presents a disjoint set data structure that is needed to implement two algorithms in [Chapter 4](LiB0032.html#359).