vi TABLE OF CONTENTS
4.5. Unordered Sele c tio ns 170
4.6. Orderings With Identical Items 178
4.7. Distribution of Objects to Bins 181
4.8. Combining Counting Rules 184
4.9. Introduction to Probability Theory 187
4.10. Conditional Probability 193
4.11. Probabilistic Reasoning 203
4.12. Expected Value Calculations 212
4.13. Some Programming Applications of Probability 215
4.14. Summary of Chapter 4 220
4.15. Bibliographic Notes for Chapter 4 221
Chapter 5. The Tree Data Model 223
5.1. What This Chapter Is About 223
5.2. Basic Terminolo gy 224
5.3. Data Structures for Trees 231
5.4. Recursions on Trees 239
5.5. Structural Induction 248
5.6. Binary Trees 253
5.7. Binary Search Trees 258
5.8. Efficiency o f Binary Search Tree Operations 268
5.9. Priority Queues and Partially Ordered Trees 271
5.10. Heapsort: Sorting with Bala nce d POTs 280
5.11. Summary of Chapter 5 284
5.12. Bibliographic Notes for Chapter 5 285
Chapter 6. The List Da ta Model 286
6.1. What This Chapter Is About 286
6.2. Basic Terminolo gy 287
6.3. Operations on Lists 291
6.4. The Linked-List Data Str ucture 293
6.5. Array-Based Implementation of L ists 301
6.6. Stacks 306
6.7. Implementing Function Calls Using a Stack 312
6.8. Queues 318
6.9. Longest C ommon Subsequences 321
6.10. Representing Character Strings 327
6.11. Summary of Chapter 6 334
6.12. Bibliographic Notes for Chapter 6 335
Chapter 7. The Set Data Model 337
7.1. What This Chapter Is About 337
7.2. Basic Definitions 338
7.3. Operations on Sets 342
7.4. List Implementation of Sets 351
7.5. Characteristic-Vector Implementation of Sets 357
7.6. Hashing 360
7.7. Relations and Functions 366
7.8. Implementing Functions as Data 373
7.9. Implementing Binary Relations 380
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