CSC 205 Java Programming II

Lecture 25

Binary Tree

Tree

A tree has a nonlinear structure Represents a

hierarchy Items in a tree do

not form a simple sequence

Allows improved efficiency for retrieving items

A Sample XML File

<?xml version="1.0"?><items> <item> <product> <description>Ink Jet Refill Kit</description> <price>29.95</price> </product> <quantity>8</quantity> </item> <item> <product> <description>4-port Mini Hub</description> <price>19.95</price> </product> <quantity>4</quantity> </item></items>

Sample: A DOM Tree

<items>

<item>

<product> <quantity>

<name> <price>

Ink JetRefill Kit

29.95

8

<item>

<product> <quantity>

<name> <price>

4-PortMini Hub

19.95

4

Basic Concepts

Related concepts Node

• Root• Leaf

Edge and path Descendant & Ancestor Parent & child nodes Sibling Sub-tree

• Left/right subtree

Binary Trees

In a binary tree, each node has up to two child nodes Height (or depth) Depth (or level) of a node

fullcomplete

0 … … …

1 … …

2 …

Level

Example – Binary Decision Tree

Binary decision tree Going down the tree with simple test

• Also known as binary taxonomy tree • Storing certain kind of knowledge

Are you a mammal?

Are you bigger than a cat Do you live underwater?

Kangaroo Mouse Trout Robin

Yes

Yes Yes

No

NoNo

Tree Representation

You would think of reference-based impl. Since we discussed nodes and edges That is definitely an option

If the tree is complete We can also use a simple array-based

implementation Using an array is always the simplest

alternative

Array-Based Representation

– for complete treesA

L G

O R I T

H M S

L G

LL GA O R I T H M S

[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

Using Array Representation

The data from the root always in the [0] component of the array

For any non-root node stored in component [i], its parent is always at location [(i-1)/2] (using integer division)

For any non-leaf node stored in component [i], its left and right child nodes are always at location [2*i+1] and [2*i+2], respectively

Array-Based Representation– for any trees

With three arrays used in parallel, any binary tree can be represented One array (of Objects) to store the items Two arrays of integers to keep track of the

left and right child nodes, respectively. (hierarchical relationship)

• -1 if no child exists

See Fig 10-10 on page 436 in your text

Reference-Based Repres’n

Needs a BTNode class UML class diagram

BTNode

-item:Object-left:BTNode-right:BTNode

+BTNode (item:Object)+BTNode (item:Object,left:BTNode, right:BTNode)+setLeft(left:BTNode)+getLeft():BTNode+isLeaf():boolean

Example – Animal Guess

Are you a mammal?

Are you bigger than a cat Do you live underwater?

Kangaroo Mouse Trout Robin

Yes

Yes Yes

No

NoNo

root