(All chapters, except Chapter 3, conclude with a Summary, Exercises and References.)
1. Introduction.
What's the Book About?
Mathematics Review.
Exponents.
Logarithms.
Series.
Modular Arithmetic.
The P word.
A Brief Introduction to Recursion.
2. Algorithm Analysis.
Mathematical Background.
Model.
What to Analyze.
Running Time Calculations.
A Simple Example.
General Rules.
Solutions for the Maximum Subsequence Sum Problem.
Logarithms in the Running Time.
Checking Your Analysis.
A Grain of Salt.
3. Lists, Stacks, and Queues.
Abstract Data Types (ADTs).
The List ADT.
Simple Array Implementation of Lists.
Linked Lists.
Programming Details.
Common Errors.
Doubly Linked Lists.
Circularly Linked Lists.
Examples.
Cursor Implementation of Linked Lists.
The Stack ADT.
Stack Model.
Implementation of Stacks.
Applications.
The Queue ADT.
Queue Model.
Array Implementation of Queues.
Applications of Queues.
4. Trees.
Preliminaries.
Implementation of Trees.
Tree Traversals with an Application.
Binary Trees.
Implementation.
Expression Trees.
The Search Tree ADT--Binary Search Trees.
MakeEmpty.
Find.
FindMin and FindMax.
Insert.
Delete.
Average-Case Analysis.
AVL Trees.
Single Rotation.
Double Rotation.
Splay Trees.
A Simple Idea (That Does Not Work).
Splaying.
Tree Traversals (Revisited).
B-Trees.
5. Hashing.
General Idea.
Hash Function.
Separate Chaining.
Open Addressing.
Linear Probing.
Quadratic Probing.
Double Hashing.
Rehashing.
Extendible Hashing.
6. Priority Queues (Heaps).
Model.
Simple Implementations.
Binary Heaps.
Structure Property.
Heap Order Property.
Basic Heap Operations.
Other Heap Operations.
Applications of Priority Queues.
The Selection Problem.
Event Simulation.
d-Heaps.
Leftist Heaps.
Leftist Heap Property.
Leftist Heap Operations.
Skew Heaps.
Binomial Queues.
Binomial Queue Structure.
Binomial Queue Operations.
Implementations of Binomial Queues.
7. Sorting.
Preliminaries.
Insertion Sort.
The Algorithm.
Analysis of Insertion Sort.
A Lower Bound for Simple Sorting Algorithms.
Shellsort.
Analysis of Insertion Sort.
Heapsort.
Analysis of Heapsort.
Mergesort.
Analysis of Mergesort.
Quicksort.
Picking the Pivot.
Partitioning Strategy.
Small Arrays.
Actual Quicksort Routines.
Analysis of Quicksort.
A Linear-Expected-Time Algorithm for Selection.
Sorting Large Structures.
A General Lower Bound for Sorting.
Decision Trees.
Bucket Sort.
External Sorting.
Why We Need New Algorithms.
Model for External Sorting.
The Simple Algorithm.
Multiway Merge.
Polyphase Merge.
Replacement Selection.
8. The Disjoint Set ADT.
Equivalence Relations.
The Dynamic Equivalence Problem.
Basic Data Structure.
Smart Union Algorithms.
Path Compression.
Worst Case for Union-by-Rank and Path Compression.
Analysis of the Union/Find Algorithm.
An Application.
9. Graph Algorithms.
Definitions.
Representation of Graphs.
Topological Sort.
Shortest-Path Algorithms.
Unweighted Shortest Paths.
Dijkstra's Algorithm.
Graphs with Negative Edge Costs.
Acyclic Graphs.
All-Pairs Shortest Path.
Network Flow Problems.
A Simple Maximum-Flow Algorithm.
Minimum Spanning Tree.
Prim's Algorithm.
Kruskal's Algorithm.
Applications of Depth-First Search.
Undirected Graphs.
Biconnectivity.
Euler Circuits.
Directed Graphs.
Finding Strong Components.
Introduction to the NP-Completeness.
Easy vs. Hard.
The Class NP.
NP-Complete Problems.
10. Algorithm Design Techniques.
Greedy Algorithms.
A Simple Scheduling Problem.
Huffman Codes.
Approximate Bin Packing.
Divide and Conquer.
Running Time of Divide and Conquer Algorithms.
Closest-Points Problem.
The Selection Problem.
Theoretical Improvements for Arithmetic Problems.
Dynamic Programming.
Using a Table Instead of Recursion.
Ordering Matrix Multiplications.
Optimal Binary Search Tree.
All-Pairs Shortest Path.
Randomized Algorithms.
Random Number Generators.
Skip Lists.
Primality Testing.
Backtracking Algorithms.
The Turnpike Reconstruction Problem.
Games.
11. Amortized Analysis.
An Unrelated Puzzle.
Binomial Queues.
Skew Heaps.
Fibonacci Heaps.
Cutting Nodes in Leftist Heaps.
Lazy Merging for Binomial Queues.
The Fibonacci Heap Operations.
Proof of the Time Bound.
Splay Trees.
12. Advanced Data Structures and Implementation.
Top-Down Splay Trees.
Red Black Trees.
Bottom-Up Insertion.
Top-Down Red Black Trees.
Top-Down Deletion.
Deterministic Skip Lists.
AA-Trees.
Treaps.
k-d Trees.
Pairing Heaps.
Index.
