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Introduction to the Design and Analysis of Algorithms
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Contents Preface1Introduction1.1 What is an Algorithm?1.2 Fundamentals of Algorithmic Problem Solving1.3 Important Problem Types1.4 Fundamental Data Structures 2 Fundamentals of the Analysis of Algorithm Efficiency2.1 Analysis Framework2.2 Asymptotic Notations and Basic Efficiency Classes2.3 Mathematical Analysis of Nonrecursive Algorithms2.4 Mathematical Analysis of Recursive Algorithms2.5 Example: Fibonacci Numbers2.6 Empirical Analysis of Algorithms2.7 Algorithm Visualization 3 Brute Force3.1 Selection Sort and Bubble Sort3.2 Sequential Search and Brute-Force String Matching3.3 Closest-Pair and Convex-Hull Problems by Brute Force3.4 Exhaustive Search 4 Divide-and-Conquer4.1 Mergesort4.2 Quicksort4.3 Binary Search4.4 Binary Tree Traversals and Related Properties4.5 Multiplication of Large Integers and Strassen's Matrix Multiplication4.6 Closest-Pair and Convex-Hull Problems by Divide-and-Conquer 5 Decrease-and-Conquer5.1 Insertion Sort5.2 Depth-First Search and Breadth-First Search5.3 Topological Sorting5.4 Algorithms for Generating Combinatorial Objects5.5 Decrease-by-a-Constant-Factor Algorithms5.6 Variable-Size-Decrease Algorithms 6 Transform-and-Conquer6.1 Presorting6.2 Gaussian Elimination6.3 Balanced Search Trees 6.4 Heaps and Heapsort 6.5 Horner's Rule and Binary Exponentiation6.6 Problem Reduction 7 Space and Time Tradeoffs7.1 Sorting by Counting7.2 Input Enhancement in String Matching7.3 Hashing7.4 B-Trees 8 Dynamic Programming8.1 Computing a Binomial Coefficient 8.2 Warshall's and Floyd's Algorithms8.3 Optimal Binary Search Trees8.4 The Knapsack Problem and Memory Functions 9 Greedy Technique9.1 Prim's Algorithm 9.2 Kruskal's Algorithm 9.3 Dijkstra's Algorithm 9.4 Huffman Trees 10 Iterative Improvement10.1 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 Power11.1 Lower-Bound Arguments11.2 Decision Trees 11.3 P, NP, and NP-complete Problems 11.4 Challenges of Numerical Algorithms 4 12 Coping with the Limitations of Algorithm Power12.1 Backtracking 12.2 Branch-and-Bound 12.3 Approximation Algorithms for NP-hard Problems 12.4 Algorithms for Solving Nonlinear Equations Epilogue APPENDIX AUseful Formulas for the Analysis of Algorithms APPENDIX BShort Tutorial on Recurrence Relations Bibliography Hints to Exercises Index  