	CS 635 Advanced Object-Oriented Design & Programming Spring Semester, 2002 Binary Tree Example
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Contents of Doc 4, Binary Tree Example


Doc 4, Binary Tree Example Slide # 2

Exercise

This document contains some uncommented code. While you are reading this document keep a list of places were you wish there were comments. Which comments would you have liked to see in the code?


Doc 4, Binary Tree Example Slide # 3

Binary Tree Example

Here is an example of object recursion and Null Object in a binary tree.

First the Java version then the Smalltalk version

Java Version

Node

public interface Node
   {
   public Object put( int key, Object value);
   public Object get( int key);
   public boolean containsKey(int key );
   }


Doc 4, Binary Tree Example Slide # 4

BinaryNode

public class BinaryNode implements Node
   {
   private int key;
   private Object value;
   private Node left;
   private Node right; 
   
   public BinaryNode(int key, Object value )
      {
      this.key = key;
      this.value = value;
      right = left = new LeafNode(this);
      }
   Object privatePut( int newKey, Object newValue)
      {
      if (newKey > key)
         right = new BinaryNode(newKey, newValue);
      else
         left = new BinaryNode(newKey, newValue);
      return null;
      }
   
   public Object put( int newKey, Object newValue)
      {
      if (this.key == newKey)
         {
         Object oldValue = value;
         value = newValue;
         return oldValue;
         }
      if (newKey > key)
         return right.put(newKey, newValue);
      else
         return left.put(newKey, newValue);
      }
      
Doc 4, Binary Tree Example Slide # 5

BinaryNode Continued

   public Object get( int findKey)
      {
      if (this.key == findKey)
         return value;
      if (findKey > key)
         return right.get(findKey);
      else
         return left.get(findKey);
      }
      
   public boolean containsKey(int findKey )
      {
      if (this.key == findKey)
         return true;
      if (findKey > key)
         return right.containsKey(findKey );
      else
         return left.containsKey(findKey);
      }
   public String toString()
      {
      return "(" + left + key + right + ")";
      }
   }
Doc 4, Binary Tree Example Slide # 6

LeafNode

public class LeafNode implements Node
   {
   private BinaryNode parent; 
   
   public LeafNode(BinaryNode parent )
      {
      this.parent = parent;      
      }
      
   public Object put( int key, Object value)
      {
      return parent.privatePut(key, value);
      }
      
   public Object get( int key)
      {
      return null;
      }
      
   public boolean containsKey(int key )
      {
      return false;
      }
      
   public String toString()
      {
      return "";
      }
   }
Doc 4, Binary Tree Example Slide # 7

TestCases

import junit.framework.TestCase;
public class TestNodes extends TestCase
   {
   public TestNodes (String name )
      {
      super(name);
      }
      
   public void testPut()
      {
      Node root = new BinaryNode(10, "10");
      root.put(5, "5");
      root.put(3, "3");
      root.put(20, "20");
      root.put(6, "6");
      root.put(1, "1");
      root.put(4, "4");
      assert("10", root.containsKey( 10 ));
      assert("5", root.containsKey( 5 ));
      assert("3", root.containsKey( 3 ));
      assert("20", root.containsKey( 20 ));
      assert("6", root.containsKey( 6 ));
      assert("1", root.containsKey( 1 ));
      assert("4", root.containsKey( 4 ));
      assertEquals("Find -1", root.containsKey( -1), false);
      }
   public void testToString()
      {
      Node root = new BinaryNode(10, "10");
      root.put(5, "5");
      root.put(3, "3");
      root.put(20, "20");
      root.put(6, "6");
      root.put(1, "1");
      root.put(4, "4");
      assertEquals("tostring", root.toString(), "((((1)3(4))5(6))10(20))");
      }


Doc 4, Binary Tree Example Slide # 8

   public void testGet()
      {
      Node root = new BinaryNode(10, "10");
      root.put(5, "5");
      root.put(3, "3");
      root.put(20, "20");
      root.put(6, "6");
      root.put(1, "1");
      root.put(4, "4");
      assertEquals("10", root.get( 10 ), "10");
      assertEquals("5", root.get( 5 ), "5");
      assertEquals("3", root.get( 3 ), "3");
      assertEquals("20", root.get( 20 ), "20");
      assertEquals("6", root.get( 6 ), "6");
      assertEquals("1", root.get( 1 ), "1");
      assertEquals("4", root.get( 4 ), "4");
      assertEquals("-1", root.get( -1), null);
      }
   }
Doc 4, Binary Tree Example Slide # 9

Smalltalk Version

BinaryNode

Smalltalk.CS635 defineClass: #BinaryNode
   superclass: #{Core.Object}
   indexedType: #none
   private: false
   instanceVariableNames: 'key value left right '
   classInstanceVariableNames: ''
   imports: ''
   category: 'Assignment-1&2'

CS635.BinaryNode class methods

key: aKey value: anObject
   ^super new 
      setKey: aKey 
      value: anObject

CS635.BinaryNode Instance methods

setKey: aKey value: anObject
   key := aKey.
   value := anObject.
   right := left := LeafNode parent: self. 
   
at: aKey
   aKey = key ifTrue:[^value].
   aKey < key ifTrue: [^left at: aKey].
   aKey > key ifTrue: [^right at: aKey].
   
at: aKey put: anObject 
   | oldValue |
   aKey < key ifTrue: [^left at: aKey put: anObject].
   aKey > key ifTrue: [^right at: aKey put: anObject].
   oldValue := value.
   value := anObject.
   ^oldValue


Doc 4, Binary Tree Example Slide # 10

privateAt: aKey put: anObject 
   aKey < key ifTrue: [left := BinaryNode key: aKey value: anObject].
   aKey > key ifTrue: [right := BinaryNode key: aKey value: anObject].
   ^anObject 
   
printOn: aStream
   aStream
      nextPutAll: '(';
      print: left;
      print: key;
      print: right;
      nextPutAll: ')' 
   
includes: aKey
   aKey = key ifTrue:[^true].
   aKey < key ifTrue:[^left includes: aKey].
   aKey > key ifTrue:[^right includes: aKey].


Doc 4, Binary Tree Example Slide # 11

LeafNode

Smalltalk.CS635 defineClass: #LeafNode
   superclass: #{Core.Object}
   indexedType: #none
   private: false
   instanceVariableNames: 'parent '
   classInstanceVariableNames: ''
   imports: ''
   category: 'Assignment-1&2'

CS635.LeafNode class methods

parent: aNode
   ^super new setParent: aNode 
   
setParent: aNode
   parent := aNode 
   
at: aKey
   self keyNotFoundError: aKey
   
at: aKey put: anObject
   parent privateAt: aKey put: anObject
   
keyNotFoundError: aKey
   
   ^Dictionary keyNotFoundSignal raiseWith: aKey 
   
printOn: aStream 
   
includes: aKey
   ^false 
Doc 4, Binary Tree Example Slide # 12

Tests

Smalltalk.CS635 defineClass: #TestBinaryTree
   superclass: #{XProgramming.SUnit.TestCase}
   indexedType: #none
   private: false
   instanceVariableNames: ''
   classInstanceVariableNames: ''
   imports: ''
   category: 'Assignment-1&2'

testAdd
   | root |
   root := BinaryNode key: 10 value: 10.
   root 
      at: 5 put: 5;
      at: 12 put: 12;
      at: 3 put: 3;
      at: 6 put: 6;
      at: 1 put: 1.
   self
      assert: (root includes: 5);
      assert: (root includes: 12);
      assert: (root includes: 3);
      assert:  (root includes: 6);
      deny: (root includes: -1);
      deny: (root includes: 7);
      deny: (root includes: 200).
   root := BinaryNode key: 10 value: 10.
   self
      assert: (root includes: 10);
      deny: (root includes: 1);
      deny: (root includes: 200).


Doc 4, Binary Tree Example Slide # 13

testAt
   | root |
   root := BinaryNode key: 10 value: '10'.
   root 
      at: 5 put: '5';
      at: 12 put: '12';
      at: 3 put: '3';
      at: 6 put: '6';
      at: 1 put: '1'.
   self
      assert: (root at: 5) = '5';
      assert: (root at: 12) = '12';
      assert: (root at: 3) = '3';
      assert:  (root at: 6) = '6'.
   self
      should: [root at: -1]
      raise: KeyedCollection keyNotFoundSignal. 
Doc 4, Binary Tree Example Slide # 14

Comments

Recursive Implementation
On skinny trees the recursive nature of this code can cause a stack overflow

Unless you have balanced trees (AVL, Red-Black, etc) an iterative solution would avoid the stack overflow

Space Requirements
A complete binary tree with N internal nodes (BinaryNode) has 2N leafs.

The above implementation uses less than 2N LeafNodes by using the same LeafNode object for the left and right subtree of a BinaryNode object. For large N this still may require too much space.

It is possible to use only one LeafNode in a program. The only state in the LeafNode is the parent pointer. One can remove this state by making the parent pointer an argument in the at:put: & put() methods. This requires a different public and private at:put: & put() methods. This can be handled in a BinaryTree class. Doing this makes these methods a bit odd.

In Smalltalk there is a nice trick to using only one LeafNode. Smalltalk have a pseudo variable thisContext that contains information about the sender of a method. This allows a method to determine which object sent the method.

The following shows the changes needed to use a single instance of LeafNode.


Doc 4, Binary Tree Example Slide # 15

Single LeafNode Example

 Smalltalk.CS635 defineClass: #LeafNode
   superclass: #{Core.Object}
   indexedType: #none
   private: false
   instanceVariableNames: ''
   classInstanceVariableNames: 'instance '
   imports: ''
   category: 'Assignment-1&2'

CS635.LeafNode class methodsFor: 'instance creation'

instance
   instance isNil ifTrue:[instance := self new].
   ^instance

CS635.LeafNode methods

at: aKey
   self keyNotFoundError: aKey

at: aKey put: anObject
   | callingMethod parentNode |
   callingMethod := thisContext sender.
   parentNode := callingMethod receiver.
   parentNode privateAt: aKey put: anObject
keyNotFoundError: aKey
   ^Dictionary keyNotFoundSignal raiseWith: aKey

printOn: aStream

includes: aKey
   ^false


Doc 4, Binary Tree Example Slide # 16

Changes to the BinaryNode

setKey: aKey value: anObject
   key := aKey.
   value := anObject.
   right := left := LeafNode instance.

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