BINARY SEARCH TREE (BST) JAVA

8/3/2019 BINARY SEARCH TREE (BST) JAVA

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BINARY SEARCH TREE (BST)BINARY SEARCH TREE (BST)

.

6.3.1 What is Binary Search Tree?

6.3.2 Advantages

6.3.3 Building Binary Search Tree. .

6.3.5 Binary Search Tree Implementation

6.3.6 Binary Search Tree Application

. . . r m ve a a ype6.3.6.2 Abstract Data Type (ADT)

1Intersession May 2009 UiTMT (MP, EZ, NIK)


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Binary Search TreeBinary Search Tree

What is Binary Search Tree (BST)

.

Value in left sub tree are less than the value in the subsequent parentnode

Value in ri ht sub tree are reater than or e ual the value in that

Example : Binary Search Tree with 9 values

subsequent parent node

67

55 70

46 69

68

90

85 100



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Binary Search Tree (cont)Binary Search Tree (cont)

Advantages of Binary Search Tree (BST)

BST is mostly used as data structure to solve complexproblems.

BST is used to store a lot of data in sorted order.

recurs on a gor m.

BST is efficient in accessing the data.



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Building BSTBuilding BST

BST characteristics :

All nodes in LEFT sub tree are < ROOT node

>=

Usually data is unique (no duplicated data)

INORDER traversal on BST will give data in

ascending order. PREORDER or POSTORDER traversal

will give data in different order.

An t e of data can be stored in BST.



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Building BST (cont)Building BST (cont)

Example (a) :

- -

5

1 6

9

3

42-1

-3 Depth: 4Leaves: 4



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Example (b) :

ata :

M

A

A I

DDepth: 4Leaves: 2



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Example (c) :

a a : ac , ompaq, pp e, amsung, os a, e

Hitachi

Compaq Samsung

Apple ToshibaDell

Depth: 2



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BST TraversalBST Traversal

Example (a) :

Data : 5 6 1 3 7 9 2 -1 0 4 -3

5

1

0 73

942

-1

-

Inorder : -3, -1, 0, 1, 2, 3, 4, 5, 6, 7, 9Preorder: 5, 1, 0, -1, -3, 3, 2, 4, 6, 7, 9

, , , , , , , , , ,



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BST Traversal (cont)BST Traversal (cont)

Example (b) :

Data : M A H A D I

M

A

H

A I

D Inorder: A, A, D, H, I, MPreorder: M, A, H, A, D, I

Postorder: D A I H A M



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BST Traversal (cont)BST Traversal (cont)

Example (c) :

Data : Hitachi, Compaq, Apple, Samsung, Toshiba, Dell

Hitachi

Compaq Samsung

Apple ToshibaDell

Inorder: Apple, Compaq, Dell, Hitachi, Samsung, ToshibaPreorder: Hitachi, Compaq, Apple, Dell, Samsung, Toshiba

Postorder: Apple, Dell, Compaq, Toshiba, Samsung, Hitachi



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BST ImplementationBST Implementation

How to implement BST Data Structure?

uses ynam c storage space.

BST ADT has to be modified to suit the type of data to be

stored.

to locate proper position.

uses recurs on me o ec n que.



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BST Implementation (cont.)BST Implementation (cont.)

How to represent BST?

Each node will contain 3 elements :1. Left node reference/link

.

3. Right node reference/link node

left rightdata



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Tree node Structure

Class : TreeNodeAttributes: leftNode // left node reference/link

data // represent data

rightNode // right node reference/link

Methods :

Constructor() // normal constructor

insert() // insert a TreeNode into a tree



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Binary Search Tree (BST) Structure

Class : BSTree

ttr utes:

root// left node reference

public BSTree() // default constructor

public void insertNode(element)

public int calcSize()private int calcSizeAll(node)

ublic double calcSum()

private void preorderHelper(node)

public void inorderTraversal()

rivate void inorderHel er(node)

private double calcSumAll(node)public int countVal(value)private int countValAll(node, value)

public void postorderTraversal()private void postorderHelper(node)

private void printCatAll(node, category)etc



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Class BST for PDTClass BST for PDT

BST for Primitive Data Type (PDT)

// TreeNode definition

public class TreeNode {TreeNode left; // left node

n a a; a a em

TreeNode right; // right node

node

public TreeNode(int d)

data = d

left=right = null;}



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Class BST for PDT (cont)Class BST for PDT (cont)

public insert (int d)

{ if (d < data)

e t == nu

left = new TreeNode(d);else

.

}

else if (d >= data)==

right = new TreeNode(d);

else

ri ht.insert(d);

}}

}// end TreeNode



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Class BST for PDTClass BST for PDT ((cont)cont)

public class BSTree

{

// Construct an empty Tree of integers

public BSTree( )

{ root = null; }

// Insert a new node in the binary search tree., .

// Otherwise, call the insert method of class TreeNode.

public void insertNode( int d )

{

if ( root == null )root = new TreeNode( d );

else

root.insert d

}



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Class BST for PDTClass BST for PDT (cont.)(cont.)

// Preorder Traversal

public void preorderTraversal()

preor er e per root ;

// Recursive method to perform preorder traversal

{

if ( node == null )

System.out.print( " " + node.data );

reorderHel er( node.left );

preorderHelper( node.right );}



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// Inorder Traversal


nor er e per root ;

// Recursive method to perform inorder traversal

{

if ( node == null )

inorderHelper( node.left );

S stem.out. rint( node.data + " " );

inorderHelper( node.right );}



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// Postorder Traversal

public void postorderTraversal()

{ postorderHelper( root ); }

// Recursive method to perform postorder traversal

private void postorderHelper( TreeNode node )

{

if ( node == null )re urn;

postorderHelper( node.left );

.

System.out.print( node.data + " " );

}



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public int calcSize()

return ca c ze root ;

// Recursive method to perform counting without condition

{

if ( node == null )

return 1 + calcSizeAll( node.left )+calcSizeAll( node.right );

}



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public double calcSum()

{ return calcSumAll( root ); }

// Recursive method to perform calcalution without condition

pr va e ou e ca c um ree o e no e

{

if ( node == null )

return node.data + calcSumAll( node.left ) +

calcSumAll node.ri ht

}



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public int countVal(double val)

,

// Recursive method to perform counting with condition

,

{

if ( node == null )

return 0

if (node.data > v)

return 1 + countValAll( node.left )+

countValAll( node.right );

elsereturn countValAll (node.left) +countValAll(node.right);

}



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public void printcat()

{

System.out.println(Category = 2");int num1 = countcategory(root,2);

System.out.println (num1);

System.out.println(Category = 5");

int num2 = countcategory(root,5);ys em.ou .pr n n num ;

System.out.println(Category = 10");

int num3 = countcategory(root,10);

. .

}



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// Recursive method to perform calcalution with condition

,

{if ( node == null )

if (node.data == num)

return 1+countcategory( node.left,num )+countcategory( node.right,num );

else

return countcategory (node.left,num)+

countcategory(node.right,num);}

}// end of BSTree



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BST Application for PDTBST Application for PDT

Main Application for BST (Primitive Data Type)

public static void main( String args[] ){

=

int intVal;

System.out.println( "Inserting the following values: " );

for ( int i = 1; i


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BST Application for PDT (cont)BST Application for PDT (cont)

System.out.println ("\n Calculation Size Of Tree +

tree.calcSize);

ystem.out.pr nt n n um ree +tree.ca c um ;

System.out.println ("\nNumber of value > 50 is "+tree.countVal(50));

" ". .

tree.preorderTraversal();

System.out.println ( "\n\nInorder traversal" );

System.out.println ( "\n\nPostorder traversal" );

tree.postorderTraversal();

S stem.out. rintln(" nNumber of values with diff cate or ");

tree.printcat();}// end main

}// end BSTTest



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Class BST for ADTClass BST for ADT

class Student

BST for Abstract Data Type (ADT) - Student class

private int id;

private float cgpa;

private double fee;

public Student() {};

public void setData(int i, float c, double f)

{ id = i;cgpa = c;

fee = f;

}

public float rtncgpa() { return cgpa; }

public double rtnfee() { return fee; }



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Class BST forClass BST for ADTADT ((cont.)cont.)

class TreeNode {

TreeNode left; //left nodeStudent data; // data item

// Constructor: initialize data to d and make this a leaf node

public TreeNode( Student d ){

data = d;

left = right = null; // this node has no children

}



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Class BST for ADTClass BST for ADT ((cont)cont)

// Insert a TreeNode into a Tree that contains nodes.

public void insert( Student d )

if d.rtnid < data.rtnid

{ if ( left == null )

left = new TreeNode( d );

else

left.insert( d );

}

else if ( d.rtnid() >= data.rtnid() ){

if ( right == null )

right = new TreeNode( d );

e se

right.insert( d );

}

} // end of TreeNode



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class BSTree {

private TreeNode root;

// Construct an empty Tree of integers

public BSTree() { root = null; }

/ Insert a new node in the binary search tree.

// If the root node is null, create the root node here.

// Otherwise, call the insert method of class TreeNode.pu c vo nser o e u en

{

if ( root == null )

=

elseroot.insert( d );



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// Preorder Traversal

ublic void reorderTraversal

{ preorderHelper( root ); }

// Recursive method to perform preorder traversal

private void preorderHelper( TreeNode node )

{

if ( node == null )return;

System.out.println( "Student's ID: " + node.data.rtnid());

ys em.ou .pr n n u en s : no e. a a.r ncgpa ;

preorderHelper( node.left );

preorderHelper( node.right );



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// Inorder Traversal


{ inorderHelper( root ); }

// Recursive method to perform inorder traversal

private void inorderHelper( TreeNode node )

{

if ( node == null )re urn;

inorderHelper( node.left );

" ' ". . . .

System.out.println( "Student's CGPA: " + node.data.rtncgpa());inorderHelper( node.right );



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// Postorder Traversal

public void postorderTraversal()

postor er e per root ;

// Recursive method to perform postorder traversal

{

if ( node == null )

postorderHelper( node.left );

ostorderHel er( node.ri ht );

System.out.println( "Student's ID: " + node.data.rtnid());System.out.println( "Student's CGPA: " + node.data.rtncgpa());

}



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public int countVal()

return countValAll root

// Recursive method to perform counting with condition

private int countValAll( TreeNode node )

{

if ( node == null )

return 0;if (node.data.rtncgpa() >= 3.5)

return 1 + countValAll( node.left )+ countValAll( node.right );

else

re urn coun a no e. e coun a no e.r g ;

}



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public double calcNewVal()


{

if ( node == null )

return 0;

double lessfee = 0.50 * node.data.rtnfee();

return lessfee + calcNewAll( node.left )+ calcNewAll( node.right );

}



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public void printcat()

System.out.println("Number of students with cgpa >= 2 and < 3");int num1 = countcategory(root,2,3);

. .

System.out.println("Number of students with cgpa >= 3 and < 4");

int num2 = countcategory(root,3,4);

System.out.println("Number of students with cgpa >= 1 and < 2");

int num3 = countcategory(root,1,2);

S stem.out. rintln (num3);

}



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Class BST forClass BST for ADTADT (cont)(cont)


rivate int countcate or TreeNode node int low int hi h

{ if ( node == null )

return 0;

if (node.data.rtncgpa() >= low && node.data.rtncgpa() < high)

return 1+countcategory( node.left,low, high ) +

countcategory( node.right,low,high );

elsereturn countcategory (node.left,low,high) +

countcategory(node.right,low,high);

}

en o ree



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BST Application for ADTBST Application for ADT

public class BSTTestObject {

Main Application for ADT class

pu c stat c vo ma n tr ng args

{ BSTree tree = new BSTree();int id; float cg; double fee;Student stud;

for ( int i = 1; i


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BST Application for ADTBST Application for ADT ((cont)cont)

tree.calcSize();

System.out.println("\nNumber of gpa with different category");

.

System.out.println ("\nAverage of GPA : " +

(tree.calcSum() / tree.calcSize()));

" >= "

System.out.println ("\nTotal fee after 50% discount is RM"+

tree.calcNewVal());

System.out.println ( " n nPreorder traversal" );tree.preorderTraversal();

System.out.println ( "\n\nInorder traversal" );

tree.inorderTraversal();

System.out.println ( " n nPostorder traversal" );tree.postorderTraversal();

}// end main

en c ass


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BINARY SEARCH TREE (BST) JAVA