Chapter 1 Basic Concepts 1 1.1. Algorithms 　　1 1.2. Mathematical Preliminaries 　　 10 1.2.1. Mathematical Induction 　　11 1.2.2. Numbers, Powers, and Logarithms 　　21 1.2.3. Sums and Products 　　 27 1.2.4. Integer Functions and Elementary Number Theory 　　 39 1.2.5. Permutations and Factorials 　　 45 1.2.6. Binomial Coefficients 　　 52 1.2.7. Harmonic Numbers 　　 75 1.2.8. Fibonacci Numbers 　　 79 1.2.9. Generating Functions 　　87 1.2.10. Analysis of an Algorithm 　　96 *1.2.11. Asymptotic Representations 　　 107 *1.2.11.1. The O-notation . 107 * 1.2.11.2. Euler's summation formula 　　 111 * 1.2.11.3. Some asymptotic calculations 　　 116 1.3. MIX 　　124 1.3.1. Description of MIX 　　 124 1.3.2. The NIX Assembly Language 　　 144 1.3.3. Applications to Permutations 　　164 1.4. Some Fundamental Programming Techniques 　　180 1.4.1. Subroutines 　　 180 1.4.2. Coroutines 　　193 1.4.3. Interpretive Routines 　　 200 1.4.3.1. A NIX simulator 　　202 "1.4.3.2. Trace routines 　　 212 1.4.4. Input and Output 　　 215 1.4.5. History and Bibliography 　　 229 Chapter 2 Information Structures 　　 232 2.1. Introduction 　　 232 2.2. Linear Lists 　　238 2.2.1. Stacks, Queues, and Deques 　　238 2.2.2. Sequential Allocation 　　244 2.2.3. Linked Allocation 　　 254 2.2.4. Circular Lists 　　273 2.2.5. Doubly Linked Lists 　　 280 2.2.6. Arrays and Orthogonal Lists 　　 298 2.3. Trees 308 2.3.1. Traversing Binary Trees 318 2.3.2. Binary Tree Representation of Trees 　　334 2.3.3. Other Representations of Trees 　　 348 2.3.4. Basic Mathematical Properties of Trees 　　362 2.3.4.1. Free trees 　　363 2.3.4.2. Oriented trees 　　372 *2.3.4.3. The "infinity lemma" 　　382 *2.3.4.4. Enumeration of trees 　　386 2.3.4.5. Path length 　　399 *2.3.4.6. History and bibliography 　　406 2.3.5. Lists and Garbage Collection 408 2.4. Multilinked Structures 　　424 2.5. Dynamic Storage Allocation 　　 435 2.6. History and Bibliography 　　 457 Answers to Exercises 　　466 Appendix A Tables of Numerical Quantities 　　 619 1. Fundamental Constants (decimal) 　　 619 2. Fundamental Constants (octal) 　　 620 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers 　　621 Appendix B Index to Notations 　　623 Index and Glossary 　　 628