Understanding Binary Search Trees: Principles of Computer Science Lecture 20

CompSci 105 SS 2005 Principles of Computer Science Lecture 20: Binary Search Trees Lecturer: Santokh Singh

A B C D E F G H I Recurisve Definition A tree is a root node attached to a set of trees

Binary Trees Textbook, p. 423-4

Binary Trees A binary tree is either empty or is a root node storing an item attached to a binary tree called the left subtree and a binary tree called the right subtree Textbook, p. 423-4

Binary Tree Node (Ref based) public class TreeNode { Object item; TreeNode left; TreeNode right; }

Binary Tree ADT TreeNode createBinaryTree( ) Object getRootItem( ) TreeNode getLeft ( ) TreeNode getRight ( ) setLeft ( TreeNode ) setRight ( TreeNode ) setRootItem( Object ) B A C Alternative definition, Textbook, p. 430-431

What is the output? void printTree( TreeNode root) if ( root != null ) println( root.getRootItem()); printTree( getLeft () ); printTree( getRight() ); } A B D G H I

Sorted List ADT 0 1 2 3 4 5 6 7 A B E J N A E N B J head

Binary Search Trees (BSTs) As with a Binary Tree, except Root node has a special data element called a key Nodes in left subtree have keys < the root’s key Nodes in right subtree have keys > the root’s key. K >K <K Textbook, p. 423-4

Searching M B Q J O U

Search( TreeNode root, Key searchKey) { if ( root==null ) // item not found else if ( root.getKey == searchKey ) // item is found! else // search in appropriate subtree if ( searchKey < root.getKey()) // search in left subtree else // search in right subtree } Textbook, p. 459-460

Add as a leaf M B Q J O U

public TreeNode insertItem ( TreeNode root, Object item ) { if ( root==null ) // add to root of tree else { // add to appropriate subtree if ( item.getKey() < root.getKey()) // add to left subtree else // add to right subtree } return root; } Textbook, p. 459-460

Exercises • Draw the BST that results from inserting the values 4, 3, 2, 7, 5, 6 in order. • Draw as many different BST’s as you can think of with values A, B, and C. B C A C B A

// Revision - some important sections about Applets and Assignment 3 import java.awt.*; import java.awt.event.*; import java.applet.*; import structure.BinaryTreeNode; import java.util.*; public class Expression extends Applet implements ActionListener{//discussded 12 days ago!! public void init(){ //set left-aligned flow layout setLayout(new FlowLayout(FlowLayout.LEFT)); /* Initialise the Buttons and TextFields here. …. */ …. }//end of init method public void actionPerformed(ActionEvent e){ …. repaint(); } } public void paint(Graphics g){ /* If the binary tree data structure (BinaryTreeNode - discussed on the day before yesterday) is not null then call the draw method. */ // draw method() - discussed yesterday. } … }

Understanding Binary Search Trees: Principles of Computer Science Lecture 20