Introduction to Design and Analysis of Algorithms

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Based on a new classification of algorithm design techniques and a clear delineation of analysis methods, "Introduction to the Design and Analysis of Algorithms" presents the subject in a coherent and innovative manner. Written in a student-friendly style, the book emphasizes the understanding of ideas over excessively formal treatment while thoroughly covering the material required in an introductory algorithms course. Popular puzzles are used to motivate students' interest and strengthen their skills in algorithmic problem solving. Other learning-enhancement features include chapter summaries, hints to the exercises, and a detailed solution manual. Features Employs an innovative and more comprehensive taxonomy of algorithm design techniques. Covers mathematical analysis of both nonrecursive and recursive algorithms, as well as empirical analysis and algorithm visualization. Discusses limitations of algorithms and waysto overcome them. Treats algorithms as problem-solving tools and develops algorithmic thinking by using puzzles and games. Contains over 600 exercises with hints for students and detailed solutions for instructors. New chapter! Iterative improvement algorithms: the simplex method, maximum network flows, maximum matching in bipartite graphs, and the stable marriage problem. New! Revised section on approximation algorithms for TSP. Table Of Contents 1.Introduction 1.1 What is an Algorithm? 1.2 Fundamentals of Algorithmic Problem Solving 1.3 Important Problem Types 1.4 Fundamental Data Structures 2. Fundamentals of the Analysis of Algorithm Efficiency 2.1 Analysis Framework 2.2 Asymptotic Notations and Basic Efficiency Classes 2.3 Mathematical Analysis of Nonrecursive Algorithms 2.4 Mathematical Analysis of Recursive Algorithms 2.5 Example: Fibonacci Numbers 2.6 Empirical Analysis of Algorithms 2.7 Algorithm Visualization 3. Brute Force 3.1 Selection Sort and Bubble Sort 3.2 Sequential Search and Brute-Force String Matching 3.3 Closest-Pair and Convex-Hull Problems by Brute Force 3.4 Exhaustive Search 4. Divide-and-Conquer 4.1 Mergesort 4.2 Quicksort 4.3 Binary Search 4.4 Binary Tree Traversals and Related Properties 4.5 Multiplication of Large Integers and Strassen’s Matrix Multiplication 4.6 Closest-Pair and Convex-Hull Problems by Divide-and-Conquer 5. Decrease-and-Conquer 5.1 Insertion Sort 5.2 Depth-First Search and Breadth-First Search 5.3 Topological Sorting 5.4 Algorithms for Generating Combinatorial Objects 5.5 Decrease-by-a-Constant-Factor Algorithms 5.6 Variable-Size-Decrease Algorithms 6. Transform-and-Conquer 6.1 Presorting 6.2 Gaussian Elimination 6.3 Balanced Search Trees 6.4 Heaps and Heapsort 6.5 Horner’s Rule and Binary Exponentiation 6.6 Problem Reduction 7. Space and Time Tradeoffs 7.1 Sorting by Counting 7.2 Input Enhancement in String Matching 7.3 Hashing 7.4 B-Trees 8. Dynamic Programming 8.1 Computing a Binomial Coefficient 8.2 Warshall’s and Floyd’s Algorithms 8.3 Optimal Binary Search Trees 8.4 The Knapsack Problem and Memory Functions 9. Greedy Technique 9.1 Prim’s Algorithm 9.2 Kruskal’s Algorithm 9.3 Dijkstra’s Algorithm 9.4 Huffman Trees 10. Iterative Improvement 10.1 The Simplex Method 10.2 The Maximum-Flow Problem 10.3 Maximum Matching in Bipartite Graphs 10.4 The Stable Marriage Problem 11. Limitations of Algorithm Power 11.1 Lower-Bound Arguments 11.2 Decision Trees 11.3 P, NP, and NP-complete Problems 11.4 Challenges of Numerical Algorithms 12. Coping with the Limitations of Algorithm Power 12.1 Backtracking 12.2 Branch-and-Bound 12.3 Approximation Algorithms for NP-hard Problems 12.4 Algorithms for Solving Nonlinear Equations