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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 tree s. Binary Trees. Textbook, p. 423-4. Binary Trees.
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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. } … }