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¸½Â¼AÊýÖµ±í 619
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CONTENTS

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