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Preface
1 Introduction
1.1 What is an Algorithm?
Exercises 1.1
1.2 Fundamentals of Algorithmic Problem Solving
Understanding the Problem
Ascertaining the Capabilities of a Computational Device
Choosing between Exact and Approximate Problem Solving
Deciding on Appropriate Data Structures
Algorithm Design Techniques
Methods of Specifying an Algorithm
Proving an Algorithm's Correctness
Analyzing an Algorithm
Coding an Algorithm
Exercises 1.2
1.3 Important Problem Types
Sorting
Searching
String Processing
Graph Problems
Combinatorial Problems
Geometric Problems
Numerical Problems
Exercises 1.3
1.4 Fundamental Data Structures
Linear Data Structures
Graphs
Trees
Sets and Dictionaries
Exercises 1.4
Summary
2 Fundamentals of the Analysis of Algorithm Efficiency
2.1 Analysis Framework
Measuring an Input's Size
Units for Measuring Running -[]me
Orders of Growth
Worst-Case, Best-Case, and Average-Case Efficlencies
Recapitulation of the Analysis Framework
Exercises 2.1
2.2 Asymptotic Notations and Basic Efficiency Classes
Informal Introduction
O-notation
9-notation
Onotation
Useful Property Involving the Asymptotic Notations
Using Limits for Comparing Orders of Growth
Basic Efficiency Classes
Exercises 2.2
2.3 Mathematical Analysis of Nonrecursive Algorithms
Exercises 2.3
2.4 Mathematical Analysis of Recursive Algorithms
Exercises 2.4
2.5 Example: Fibonacci Numbers
Explicit Formula for the nth Fibonacci Number
Algorithms for Computing Fibonacci Numbers
Exercises 2.5
3 Brute Force
4 Divide-and-Conquer
5 Decrease-and-Conquer
6 Transform-and-Conquer
7 Space and lime Tradeoffs
8 Dynamic Programming
9 Greedy Technique
10 Iterative Improvement
11 Limitations of Algorithm Power
12 Coping with the Limitations of Algorithm Power
Epilogue
APPENDIX A
Useful Formulas for the Analysis of Algorithms
APPENDIX B
Short Tutorial on Recurrence Relations
Bibliography
Hints to Exercises
Index
