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算法设计与分析基础 （第3版）（影印版） 
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《算法设计与分析基础 （第3版）（影印版）》在讲述算法设计技术时采用了新的分类方法，在讨论分析方法时条分缕析，形成了连贯有序、耳目一新的风格。为便于学生掌握，本书涵盖算法入门课程的全部内容，更注重对概念(而非形式)的理解。书中通过一些流行的谜题来激发学生的兴趣，帮助他们加强和提高解决算法问题的能力。每章小结、习题提示和详细解答，形成了非常鲜明的教学特色。
历经十年数百所高校教学实践的算法入门经典。算法是思维的艺术，是数学之美的完美体现，是计算机和信息科学的灵魂，更是优秀程序员的安身立命之本。《算法设计与分析基础 (第3版）（影印版）》将算法视为解决问题的工具，通过作者独创的、具有里程碑意义的新型分类法弥补了传统算法设计技术分类法的缺陷，用深入浅出的语言和新颖的实例与谜题，诠释了何为算法、算法的分类、算法幕后的思想、算法的效率，抽丝剥茧、条分缕析地探索了算法设计与分析过程。
Anany Levitin博士，美国维拉诺瓦大学教授，毕业于莫斯科国立大学并获得数学硕士学位。他拥有耶路撒冷希伯来大学数学博士学位和美国肯塔基大学计算机科学硕士学位。他的著作《算法设计与分析基础》已经被翻译为中文、俄文、希腊文和韩文，并被全球数百所高校广泛用作教材。目前，Levitin博士在美国维拉诺瓦大学讲授“算法设计与分析”课程。他的另一本著作《算法谜题》已经于2011年秋出版。
Anany Levitin，美籍犹太人，维拉诺瓦大学（Villanova）计算机科学系教授。他的论文“算法设计技术新途径：弥补传统分类法的缺憾”(A New Road Mpa of Algorithm Design Techniques： Picking Up Where the Traditional Classfication Leaves Off)深受业内好评，并享有广泛的声誉。他提出的这种新分类方法涵盖众多经典算法，开创了传统分类无法以一致方式介绍这些算法的先河。作为通用的问题解决工具，算法设计技术的应用很广，尤其适用于解决“狼，羊，白菜”问题和旅行商问题之类的流行谜题。 因为他对算法教育所做出的杰出贡献，Levitin教授曾多次受邀在SIGCSE(Computer Science Education，计算机教育) 全球大会上发表演讲，此大会每三年才举行一次。 Anany Levitin教授目前的研究课题为“Do We Teach the Right Algorithm Design Techniques ？”
New to the Third Edition xvii
Preface xix 1Introduction 1.1 What Is an Algorithm? Exercises 1.1 1.2 Fundamentals of Algorithmic Problem Solving Understanding the Problem Ascertaining the Capabilities of the Computational Device Choosing between Exact and Approximate Problem Solving Algorithm Design Techniques Designing an Algorithm and Data Structures Methods of Specifying an Algorithm Proving an Algorithm's Correctness Analyzing an Algorithm Coding an Algorithm Exercises 1.2 1.3 Important Problem Types Sorting Searching String Processing Graph Problems Combinatorial Problems Geometric Problems Numerical Problems Exercises 1.3 1.4 Fundamental Data Structures Linear Data Structures Graphs Trees Sets and Dictionaries Exerises 1.4 Summary 2 Fundamentals of the Analysis of Algorithm Efficiency 2.1 The Analysis Framework Measuring an Input's Size Units for Measuring Running Time Orders of Growth Worst-Case, Best-Case, and Average-Case Efficiencies Recapitulation of the Analysis Framework Exercises 2.1 2.2 Asymptotic Notations and Basic Efficiency Classes Informal Introduction O-notation -notation -notation Useful Property Involving the Asymptotic Notations Using Limits for Comparing Orders of Growth Basic Efficiency Classes Exercises 2.2 2.3 Mathematical Analysis of Nonrecursive Algorithms Exercises 2.3 2.4 Mathematical Analysis of Recursive Algorithms Exercises 2.4 2.5 Example: Computing the nth Fibonacci Number Exercises 2.5 2.6 Empirical Analysis of Algorithms Exercises 2.6 2.7 Algorithm Visualization Summary 3 Brute Force and Exhaustive Search 3.1 Selection Sort and Bubble Sort Selection Sort Bubble Sort Exercises 3.1 3.2 Sequential Search and Brute-Force String Matching Sequential Search Brute-Force String Matching Exercises 3.2 3.3 Closest-Pair and Convex-Hull Problems by Brute Force Closest-Pair Problem Convex-Hull Problem Exercises 3.3 3.4 Exhaustive Search Traveling Salesman Problem Knapsack Problem Assignment Problem Exercises 3.4 3.5 Depth-First Search and Breadth-First Search Depth-First Search Breadth-First Search Exercises 3.5 Summary 4 Decrease-and-Conquer 4.1 Insertion Sort Exercises 4.1 4.2 Topological Sorting Exercises 4.2 4.3 Algorithms for Generating Combinatorial Objects Generating Permutations Generating Subsets Exercises 4.3 4.4 Decrease-by-a-Constant-Factor Algorithms Binary Search Fake-Coin Problem Russian Peasant Multiplication Josephus Problem Exercises 4.4 4.5 Variable-Size-Decrease Algorithms Computing a Median and the Selection Problem Interpolation Search Searching and Insertion in a Binary Search Tree The Game of Nim Exercises 4.5 Summary 5 Divide-and-Conquer 5.1 Mergesort Exercises 5.1 5.2 Quicksort Exercises 5.2 5.3 Binary Tree Traversals and Related Properties Exercises 5.3 5.4 Multiplication of Large Integers and Strassen's Matrix Multiplication Multiplication of Large Integers Strassen's Matrix Multiplication Exercises 5.4 5.5 The Closest-Pair and Convex-Hull Problems by Divide-and-Conquer The Closest-Pair Problem Convex-Hull Problem Exercises 5.5 Summary 6 Transform-and-Conquer 6.1 Presorting Exercises 6.1 6.2 Gaussian Elimination LU Decomposition Computing a Matrix Inverse Computing a Determinant Exercises 6.2 6.3 Balanced Search Trees AVL Trees 2-3 Trees Exercises 6.3 6.4 Heaps and Heapsort Notion of the Heap Heapsort Exercises 6.4 6.5 Horner's Rule and Binary Exponentiation Horner's Rule Binary Exponentiation Exercises 6.5 6.6 Problem Reduction Computing the Least Common Multiple Counting Paths in a Graph Reduction of Optimization Problems Linear Programming Reduction to Graph Problems Exercises 6.6 Summary 7 Space and Time Trade-Offs 7.1 Sorting by Counting Exercises 7.1 7.2 Input Enhancement in String Matching Horspool's Algorithm Boyer-Moore Algorithm Exercises 7.2 7.3 Hashing Open Hashing (Separate Chaining) Closed Hashing (Open Addressing) Exercises 7.3 7.4 B-Trees Exercises 7.4 Summary 8 Dynamic Programming 8.1 Three Basic Examples Exercises 8.1 8.2 The Knapsack Problem and Memory Functions Memory Functions Exercises 8.2 8.3 Optimal Binary Search Trees Exercises 8.3 8.4 Warshall's and Floyd's Algorithms Warshall's Algorithm Floyd's Algorithm for the All-Pairs Shortest-Paths Problem Exercises 8.4 Summary 9 Greedy Technique 9.1 Prim's Algorithm Exercises 9.1 9.2 Kruskal's Algorithm Disjoint Subsets and Union-Find Algorithms Exercises 9.2 9.3 Dijkstra's Algorithm Exercises 9.3 9.4 Huffman Trees and Codes Exercises 9.4 Summary 10 Iterative Improvement 10.1 The Simplex Method Geometric Interpretation of Linear Programming An Outline of the Simplex Method Further Notes on the Simplex Method Exercises 10.1 10.2 The Maximum-Flow Problem Exercises 10.2 10.3 Maximum Matching in Bipartite Graphs Exercises 10.3 10.4 The Stable Marriage Problem Exercises 10.4 Summary 11 Limitations of Algorithm Power 11.1 Lower-Bound Arguments Trivial Lower Bounds Information-Theoretic Arguments Adversary Arguments Problem Reduction Exercises 11.1 11.2 Decision Trees Decision Trees for Sorting Decision Trees for Searching a Sorted Array Exercises 11.2 11.3 P, NP, and NP-Complete Problems P and NP Problems NP-Complete Problems Exercises 11.3 11.4 Challenges of Numerical Algorithms Exercises 11.4 Summary 12 Coping with the Limitations of Algorithm Power 12.1 Backtracking n-Queens Problem Hamiltonian Circuit Problem Subset-Sum Problem General Remarks Exercises 12.1 12.2 Branch-and-Bound Assignment Problem Knapsack Problem Traveling Salesman Problem Exercises 12.2 12.3 Approximation Algorithms for NP-Hard Problems Approximation Algorithms for the Traveling Salesman Problem Approximation Algorithms for the Knapsack Problem Exercises 12.3 12.4 Algorithms for Solving Nonlinear Equations Bisection Method Method of False Position Newton's Method Exercises 12.4 Summary Epilogue APPENDIX A Useful Formulas for the Analysis of Algorithms Properties of Logarithms Combinatorics Important Summation Formulas Sum Manipulation Rules Approximation of a Sum by a Definite Integral Floor and Ceiling Formulas Miscellaneous APPENDIX B Short Tutorial on Recurrence Relations Sequences and Recurrence Relations Methods for Solving Recurrence Relations Common Recurrence Types in Algorithm Analysis References Hints to Exercises Index
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