Table of Contents
I Fundamental Tools 1 1 Algorithm Analysis 3
1.1 Methodologies for Analyzing Algorithms 5
1.2 Asymptotic Notation 13
1.3 A Quick Mathematical Review 21
1.4 Case Studies in Algorithm Analysis 31
1.5 Amortization 34
1.6 Experimentation 42
1.7 Exercises 47
2 Basic Data Structures 55
2.1 Stack sand Queues 57
2.2 Vectors, Lists, and Sequences 65
2.3 Trees 75
2.4 Priority Queues and Heaps 94
2.5 Dictionaries and Hash Tables 114
2.6 Java Example: Heap 128
2.7 Exercises 131
3 Search Trees and Skip Lists 139
3.1 Ordered Dictionaries and Binary Search Trees 141
3.2 AVL Trees 152
3.3 Bounded-Depth Search Trees 159
3.4 Splay Trees 185
3.5 Sk i p Lists 195
3.6 Java Example: AVL and Red-Black Trees 202
3.7 Exercises 212
4 Sorting, Sets, and Selection 217
4.1 Merge-Sort 219
4.2 The Set Abstract Data Type 225
4.3 Quick -Sort 235
4.4 A Lower Bound on Comparison-Based Sorting 239
4.5 Buck et-Sort and Radix-Sort 241
4.6 Comparison of Sorting Algorithms 244
4.7 Selection 245
4.8 Java Example: In-Place Quick -Sort 248
4.9 Exercises 251
5 Fundamental Techniques 257
5.1 The GreedyMethod 259
5.2 Divide-and-Conquer 263
5.3 Dynamic Programming 274
5.4 Exercises 282
II Graph Algorithms 285
6 Graphs 287
6.1 The Graph Abstract Data Type 289
6.2 Data Structures for Graphs 296
6.3 Graph Traversal 303
6.4 Directed Graphs 316
6.5 Java Example: Depth-First Search 329
6.6 Exercises 335
7 Weighted Graphs 339
7.1 Single-Source Shortest Paths 341
7.2 All-Pairs Shortest Paths 354
7.3 Minimum Spanning Trees 360
7.4 Java Example: Dijk stra’s Algorithm 373
7.5 Exercises 376
8 Network Flow and Matching 381
8.1 Flows and Cuts 383
8.2 Maximum Flow 387
8.3 Maximum BipartiteMatching 396
8.4 Minimum-Cost Flow 398
8.5 Java Example: Minimum-Cost Flow 405
8.6 Exercises 412
III Internet Algorithmics 415
9 Text Processing 417
9.1 Strings and PatternMatching Algorithms 419
9.2 Tries 429
9.3 Text Compression 440
9.4 Text Similarity Testing 443
9.5 Exercises 447
10 Number Theory and Cryptography 451
10.1 Fundamental Algorithms Involving Numbers 453
10.2 Cryptographic Computations 471
10.3 Information Security Algorithms and Protocols 481
10.4 The Fast Fourier Transform 488
10.5 Java Example: FFT 500
10.6 Exercises 508
11 Network Algorithms 511
11.1 ComplexityMeasures and Models 513
11.2 Fundamental Distributed Algorithms 517
11.3 Broadcast and Unicast Routing 530
11.4 Multicast Routing 535
11.5 Exercises 541
IV Additional Topics 545
12 Computational Geometry 547
12.1 Range Trees 549
12.2 Priority Search Trees 556
12.3 Quadtrees and k-D Trees 561
12.4 The Plane Sweep Technique 565
12.5 Convex Hulls 572
12.6 Java Example: Convex Hull 583
12.7 Exercises 587
13 NP-Completeness 591
13.1 P and NP 593
13.2 NP-Completeness 599
13.3 Important NP-Complete Problems 603
13.4 Approximation Algorithms 618
13.5 Back track i ng and Branch-and-Bound 627
13.6 Exercises 638
14 Algorithmic Frameworks 643
14.1 External-Memory Algorithms 645
14.2 Parallel Algorithms 657
14.3 Online Algorithms 667
14.4 Exercises 680
A Useful Mathematical Facts 685
Bibliography 689
Index 698
