All of the data structures we have seen so far, such as arrays and linked lists, are linear. In a linear structure, there is a first item and a last item. Every item (except the last) has a successor and every item (except the first) has a predecessor.

This chapter introduces trees, which are more general structures for representing branching or hierarchical data. For example, biological classification diagrams, many organizational charts in businesses, and sports playoff brackets are trees. We have seen a few trees already in this book, including class inheritance diagrams like Figure 3-10 and recursion trees like Figure 9-16.

We begin with a discussion of the simplest kind of trees, binary trees. Using the game of Questions as a running example, Section 10.1 introduces tree terminology and discusses the implementation of binary trees. The issue of traversing trees is addressed in Section 10.2. More general trees are covered in Section 10.3, where we use trees to design an intelligent Tic Tac Toe player.

## Binary Trees |

Part I: Object-Oriented Programming

Encapsulation

Polymorphism

Inheritance

- Inheritance
- Extending a Class
- The Object Class
- Packages and Access Levels
- Summary
- Vocabulary
- Problems
- Projects

Part II: Linear Structures

Stacks and Queues

- Stacks and Queues
- The Stack Interface
- The Call Stack
- Exceptions
- The Queue Interface
- Summary
- Vocabulary
- Problems
- Projects

Array-Based Structures

- Array-Based Structures
- Shrinking and Stretching Arrays
- Implementing Stacks and Queues
- The List Interface
- Iterators
- The Java Collections Framework: A First Look
- Summary
- Vocabulary
- Problems
- Projects

Linked Structures

- Linked Structures
- List Nodes
- Stacks and Queues
- The LinkedList Class
- The Java Collections Framework Revisited
- Summary
- Vocabulary
- Problems
- Projects

Part III: Algorithms

Analysis of Algorithms

- Analysis of Algorithms
- Timing
- Asymptotic Notation
- Counting Steps
- Best, Worst, and Average Case
- Amortized Analysis
- Summary
- Vocabulary
- Problems
- Projects

Searching and Sorting

- Searching and Sorting
- Linear Search
- Binary Search
- Insertion Sort
- The Comparable Interface
- Sorting Linked Lists
- Summary
- Vocabulary
- Problems
- Projects

Recursion

- Recursion
- Thinking Recursively
- Analyzing Recursive Algorithms
- Merge Sort
- Quicksort
- Avoiding Recursion
- Summary
- Vocabulary
- Problems
- Projects

Part IV: Trees and Sets

Trees

Sets

- Sets
- The Set Interface
- Ordered Lists
- Binary Search Trees
- Hash Tables
- The Java Collections Framework Again
- Summary
- Vocabulary
- Problems
- Projects

Part V: Advanced Topics

Advanced Linear Structures

- Advanced Linear Structures
- Bit Vectors
- Sparse Arrays
- Contiguous Representation of Multidimensional Arrays
- Advanced Searching and Sorting
- Summary
- Vocabulary
- Problems
- Projects

Strings

Advanced Trees

- Advanced Trees
- Heaps
- Disjoint Set Clusters
- Digital Search Trees
- Red-Black Trees
- Summary
- Vocabulary
- Problems
- Projects

Graphs

- Graphs
- Terminology
- Representation
- Graph Traversal
- Topological Sorting
- Shortest Paths
- Minimum Spanning Trees
- Summary
- Vocabulary
- Problems
- Projects

Memory Management

Out to the Disk

- Out to the Disk
- Interacting with Files
- Compression
- External Sorting
- B-Trees
- Summary
- Vocabulary
- Problems
- Projects

Part VI: Appendices

A. Review of Java

- A. Review of Java
- A.1. The First Program
- A.2. Variables and Types
- A.3. Loops
- A.4. Interacting with the User
- A.5. Branching
- A.6. Methods and Breaking Out
- A.7. Constants
- A.8. Operators
- A.9. Debugging
- A.10. Coding Conventions

B. Unified Modeling Language

C. Summation Formulae

- C. Summation Formulae
- C.1. Sum Notation
- C.2. Sum of Constants
- C.3. Sum of First n Integers
- C.4. Sums of Halves and Doubles
- C.5. Upper Limit on Sum of a Function
- C.6. Constant Factors

D. Further Reading

Index

Data Structures and Algorithms in Java

ISBN: 0131469142

EAN: 2147483647

EAN: 2147483647

Year: 2004

Pages: 216

Pages: 216

Authors: Peter Drake

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