Lecture Java methods: Object-oriented programming and data structures (2nd AP edition): Chapter 24 - Maria Litvin, Gary Litvin

Chapter 24 - Binary trees. In this chapter, the learning objectives are: Learn about binary trees; learn how to represent and handle a binary tree using the TreeNode class; learn about binary search trees; review sets and maps, and the java.util classes that implement them.

and Data Structures

Maria Litvin ● Gary Litvin

2nd AP edition with GridWorld

Objectives:

classes that implement them

Some Applications of Trees

Number of levels (equals

5 here)

node

node’s

right subtree

Binary Tree Properties

example, a binary tree with 20 levels can

nodes.

where to proceed, left or right (used in binary search trees).

compared to the total number of nodes.

The TreeNode Class

instead of next has left and right

public class TreeNode

{

Holds a reference to

the left childHolds a reference to the right child

The TreeNode Class (cont’d)

// Constructors:

public TreeNode (Object v)

{ value = v; left = null; right = null; }

public TreeNode (Object v, TreeNode lt, TreeNode rt)

{ value = v; left = lt; right = rt; }

// Methods:

}

Trees and Recursion

the left and right subtrees are smaller trees:

{ // Base case: root == null, // the tree is empty do nothing

if (root != null) // Recursive case {

process (root.getValue ( ));

traverse (root.getLeft ( ));

traverse (root.getRight ( ));

} }

TreeNode Example 2

// returns a reference to a new tree, which is a

// copy of the tree rooted at root

traverse the left and right subtrees.

A/ \

B C / \

D E

A B D E C

process the root, then traverse the right

subtree.

A/ \

B C / \

D E

D B E A C

subtrees, then process the root.

A/ \

B C / \

D E

D E B C A

Traversals (cont’d)

Binary Search Trees (BST)

comparator is supplied).

subtree are smaller than the value in the node and all the values in its right subtree are

larger than the value in the node.

15 / \

8 20 / \

1 12

15 / \

12 20

/ \

1 8

BST (cont’d)

for quick searching and linked lists for

inserting and deleting values.

// root refers to a BST; the nodes hold Strings

{

TreeNode node = root;

while ( node != null )

Find the smallest

node of the right

Link that note in

place of the root and

remove the old root

BST (cont’d)

remove , and contains methods take O(log n)

time, where n is the number of nodes in the

tree.

degenerate into a nearly linear shape

tree balanced.

java.util.TreeSet<E>

• compareTo (or comparator’s compare ) is

methods.

implements inorder traversal.

in ascending order.

java.util.TreeSet<E> (cont’d)

Never mind

java.util.TreeMap<K,V>

• compareTo (or comparator’s compare ) for

remove methods.

• The keySet method returns a TreeSet<K>

java.util.TreeMap<K,V> (cont’d)

Review:

for data retrieval applications?

Review (cont’d):

in a binary tree with 10 levels?

a node in a doubly-linked list?

and postorder traversals of the following tree?

A / \

B C / \

D E

Review (cont’d):

property What is it?

2 3 / \

4 5

4 / \

2 5 / \

1 3