文档介绍：TABLE OF CONTENTS v
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✦ Table of Contents
Preface ix
Chapter 1. Computer Science: The Mechanization of Abstraction 1
. What This Book Is About 3
. What This Chapter Is About 6
. Data Models 6
. The C Data Model 13
. Algorithms and the Design of Programs 20
. Some C Conventions Used Throughout the Book 22
. Summary of Chapter 1 23
. Bibliographic Notes for Chapter 1 24
Chapter 2. Iteration, Induction, and Recursion 25
. What This Chapter Is About 27
. Iteration 27
. Inductive Proofs 34
. Complete Induction 44
. Proving Properties of Programs 52
. Recursive Definitions 59
. Recursive Functions 69
. Merge Sort: A Recursive Sorting Algorithm 75
. Proving Properties of Recursive Programs 84
. Summary of Chapter 2 87
. Bibliographic Notes for Chapter 2 88
Chapter 3. The Running Time of Programs 89
. What This Chapter Is About 89
. Choosing an Algorithm 90
. Measuring Running Time 91
. Big-Oh and Approximate Running Time 96
. Simplifying Big-Oh Expressions 101
. Analyzing the Running Time of a Program 109
. A Recursive Rule for Bounding Running Time 116
. Analyzing Programs with Function Calls 127
. Analyzing Recursive Functions 132
. Analysis of Merge Sort 136
. Solving Recurrence Relations 144
. Summary of Chapter 3 154
. Bibliographic Notes for Chapter 3 155
Chapter 4. Combinatorics and Probability 156
. What This Chapter Is About 156
. Counting Assignments 157
. Counting Permutations 160
. Ordered Selections 167
vi TABLE OF CONTENTS
. Unordered Selections 170
. Orderings With Identical Items 178
. Distribution of Objects to Bins 181
. Combining Counting Rules 184
. Introduction to Probability Theory 187
. Conditional Probability 193
. Probabilistic Reasoning 203
. Expected Value Calculations 212
. Some Programming Applic