Preface xiii I Foundations Introduction 3 1 The Role of Algorithms in Computing 5 2 Getting Started 17 3 Characterizing Running Times 49 4 Divide-and-Conquer 76 5 Probabilistic Analysis and Randomized Algorithms 126 II Sorting and Order Statistics Introduction 157 6 Heapsort 161 7 Quicksort 182 8 Sorting in Linear Time 205 9 Medians and Order Statistics 227 III Data Structures Introduction 249 10 Elementary Data Structures 252 11 Hash Tables 272 12 Binary Search Trees 312 12 Red-Black Trees 331 IV Advanced Design and Analysis Techniques Introduction 361 14 Dynamic Programming 362 15 Greedy Algorithms 417 16 Amortized Analysis 448 V Advanced Data Structures Introduction 477 17 Augmenting Data Structures 480 18 B-Trees 497 19 Data Structures for Disjoint Sets 520 VI Graph Algorithms Introduction 547 20 Elementary Graph Algorithms 549 21 Minimum Spanning Trees 585 22 Single-Source Shortest Paths 604 23 All-Pairs Shortest Paths 646 24 Maximum Flow 670 25 Matchings in Bipartite Graphs 704 VII Selected Topics Introduction 745 26 Parallel Algorithms 748 27 Online Algorithms 791 28 Matrix Operations 819 29 Linear Programming 850 30 Polynomials and the FFT 877 31 Number-Theoretic Algorithms 903 32 String Matching 957 33 Machine-Learning Algorithms 1003 34 NP-Completeness 1042 35 Approximation Algorithms 1104 VIII Appendix: Mathematical Background Introduction 1139 A Summations 1140 B Sets, Etc. 1153 C Counting and Probability 1178 D Matrices 1214 Bibliography 1227 Index 1251
