1. Slides by Steve Armstrong LeTourneau University Longview, TX
Tree Implementations
Chapter 26
Slides by Steve Armstrong LeTourneau University Longview, TX
ã 2007, Prentice Hall

2. Chapter Contents The Nodes in a Binary Tree
An Interface for a Node
An implementation of BinaryNode
An Implementation of the ADT Binary Tree
Creating a Basic Binary Tree
The Method privateSetTree
Accessor and Mutator Methods
Computing the Height and Counting Nodes
Traversals
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

3. Chapter Contents An Implementation of an Expression Tree General Trees
A Node for a General Tree
Using a Binary Tree for Represent a General Tree
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

4. Fig. 26-1 A node in a binary tree.
Nodes in a Binary Tree
Fig A node in a binary tree.
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

5. Interface for a Node
View interface for class of nodes suitable for a binary tree
View implementation of BinaryNode
Usually the class that represents a node in a tree is a detail hidden from the client
It is placed within a package
Makes it available
Available to all classes involved in implementation of a tree
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

6. An Implementation of the ADT Binary Tree
Recall interface for class of binary trees from previous chapter
In that interface
TreeInterface specifies basic operations common to all trees
TreeInteratorInterface specifies operations for tree traversal
View implementation of BinaryTree,
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

7. The Method privateSetTree
Problem: previous implementation of privateSetTree not sufficient
Given: treeA.setTree(a, treeB, treeC);
Now treeA shares nodes with treeB, treeC
Changes to treeB also affect treeA (Fig. 26-2)
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

8. The Method privateSetTree
Possible solution
Have privatSetTree copy the nodes in TreeB and TreeC
Now treeA is separate and distinct from treeB and treeC
Changes to either treeB or treeC do NOT affect treeA
Note that copying nodes is expensive
Other solutions are considered
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

9. The Method privateSetTree
Another possible solution for treeA.setTree(a, treeB, treeC);
Have privateSetTree first link the root node of treeA to root nodes of treeB, treeC (Fig. 26-3)
Then set treeB.root, treeC.root to null
This still has some problems
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

10. The Method privateSetTree
View second solution which does the following:
Create root node r for containing the data
If left subtree exists, not empty
Attach root node to r as left child
If right subtree exists, not empty, distinct from left subtree
Attach root node r as right child
If right, left subtrees are the same, attach copy of right subtree to r instead
If left (right) subtree exists, different from the invoking tree object
Set its data field root to null
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

11. Accessor, Mutator Methods
View detail of methods implemented
getRootData
isEmpty
clear
setRootData
setRootNode
getRootNode
BinaryNodeInterface
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

12. Computing Height, Counting Nodes
Within BinaryTree – view methods in context
getHeight()
getNumberOfNodes()
Within BinaryNode – view methods in context
getHeight(BinaryNode node)
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

13. Traversals Make recursive method private
Call from public method with no parameters
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

14. Traversals Fig. 26-4 A binary tree.
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

15. Traversals
Fig Using a stack to perform an inorder traversal of the binary tree
Click to view iterative implementation of inorderTraverse
Click to view inorder traversal as an iterator
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

16. Fig. 26-6 Using a stack to traverse the binary tree in (a) preorder
Traversals
Fig Using a stack to traverse the binary tree in (a) preorder
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

17. Fig. 26-6 Using a stack to traverse the binary tree in (b) postorder.
Traversals
Fig Using a stack to traverse the binary tree in (b) postorder.
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

18. Fig. 26-7 Using a queue to traverse the binary tree in level order.
Traversals
Fig Using a queue to traverse the binary tree in level order.
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

19. Implementation of an Expression Tree
Defining an interface for an expression tree
Extend the interface for a binary tree
Add a declaration for the method evaluate
View ExpressionTreeInterface
An expression tree is a binary tree
Implement evaluate in derived class
Note source code for ExpressionTree
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

20. General Trees Fig. 26-8 A node for a general tree.
Click to view interface for node in general tree
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

21. Using a Binary Tree to Represent a General Tree
Fig (a) A general tree;
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

22. Using a Binary Tree to Represent a General Tree
Fig (b) an equivalent binary tree;
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

23. Using a Binary Tree to Represent a General Tree
Fig (c) a more conventional view of the same binary tree.
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X

24. Traversals Traversals of general tree in 26-9a
Preorder: A B E F C G H I D J
Postorder: E F B G H I C J D A
Level order: A B C D E F G H I J
Traversals of binary tree in 26-9c
Postorder: F E I H G J D C B A
Level order: A B E C F G D H J I
Inorder: E F B G H I C J D A
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved X