An Interface for a Node Adapted from Pearson Education, Inc. - PowerPoint Presentation

Slide1

Tree Implementations(plus briefing about Iterators)

Chapter 24

Adapted from Pearson Education, Inc.

1Slide2

ContentsAdapted from Pearson Education, Inc.

The Nodes in a Binary Tree

An Interface for a NodeAn Implementation of

BinaryNode

An Implementation of the ADT Binary Tree

Creating a Basic Binary Tree

The Method privateSetTreeComputing the Height and Counting NodesTraversals & IteratorsAn Implementation of an Expression TreeGeneral TreesA Node for a General TreeUsing a Binary Tree to Represent a General Tree

2Slide3

ObjectivesAdapted from Pearson Education, Inc.

Describe necessary operations on node within binary tree

Implement class of nodes for binary treeImplement class of binary trees

Implement an expression tree by extending class of binary trees

Describe necessary operations on a node within general tree

Use binary tree to represent general tree

3Slide4

Interfaces…(review from ch

23)

package

TreePackage

;

public interface

TreeInterface < T >{public T getRootData ();public int getHeight ();public

int

getNumberOfNodes

();

public

boolean

isEmpty ();public void clear ();} // end TreeInterface

package TreePackage;import java.util.Iterator;public interface TreeIteratorInterface < T >{public Iterator < T > getPreorderIterator ();public Iterator < T > getPostorderIterator ();public Iterator < T > getInorderIterator ();public Iterator < T > getLevelOrderIterator ();} // end TreeIteratorInterface

package TreePackage;public interface BinaryTreeInterface < T > extends TreeInterface < T > ,TreeIteratorInterface < T >{public void setTree (T rootData);public void setTree (T rootData, BinaryTreeInterface < T > leftTree,BinaryTreeInterface < T > rightTree);} // end BinaryTreeInterface

Adapted from Pearson Education, Inc.

4Slide5

An Interface for a Node

Adapted from Pearson Education, Inc.

5

package

TreePackage

;

interface

BinaryNodeInterface

< T >

{

public

T

getData

();

public void setData (T newData

); public BinaryNodeInterface < T > getLeftChild (); public BinaryNodeInterface < T > getRightChild ();

public

void

setLeftChild

(

BinaryNodeInterface

< T > leftChild); public void setRightChild (BinaryNodeInterface < T > rightChild); public boolean hasLeftChild (); public boolean hasRightChild (); public boolean isLeaf (); /** Counts the nodes in the subtree rooted at this node. @return the number of nodes in the subtree rooted at this node */ public int getNumberOfNodes (); /** Computes the height of the subtree rooted at this node. @return the height of the subtree rooted at this node */ public int getHeight (); public BinaryNodeInterface < T > copy (); } // end BinaryNodeInterface

An implementation of

BinaryNode

,

Listing 24-2Slide6

First draft of the class,

Listing 24-3

Notice private method

privateSetTree

:

private

void

privateSetTree

(T

rootData

,

BinaryTree

< T >

leftTree, BinaryTree < T > rightTree)

{ /* FIRST DRAFT - See Segments 24.5 - 24.8 for improvements. */ root = new BinaryNode < T > (rootData) ;

if

(

leftTree

!=

null) root.setLeftChild (leftTree.root); if (rightTree != null) root.setRightChild (rightTree.root); } // end privateSetTree Result of calling:treeA.setTree(a, treeB, treeC) Implementation of a basic Binary TreeAdapted from Pearson Education, Inc.6Slide7

Problems with

PrivateSetTree

Adapted from Pearson Education, Inc.

Result of calling:

treeA.setTree

(a,

treeB

,

treeB

)

Can be solved as follows:

private void

privateSetTree

(T

rootData

, BinaryTree < T > leftTree, BinaryTree

< T > rightTree) { root = new BinaryNode < T > (rootData); if ((leftTree != null) && !leftTree.isEmpty ())

root.setLeftChild

(

leftTree.root.copy

());

if ((rightTree != null) && !rightTree.isEmpty ()) root.setRightChild (rightTree.root.copy ()); } // end privateSetTree But copy is expensive:public BinaryNodeInterface < T > copy () { BinaryNode < T > newRoot = new BinaryNode < T > (data); if (left != null) newRoot.left = (BinaryNode<T>) left.copy (); if (right!= null) newRoot.right =(BinaryNode<T>) right.copy (); return newRoot; } // end copy 7So what is the solution?Slide8

Recursive In-Order traversal of a BT

Adapted from Pearson Education, Inc.

Inorder traversalPublic method for user, calls private method

8Slide9

Iterators vs regular traversal

Adapted from Pearson Education, Inc.

What if I want to do something at each node?I need to be able to stop at each nodeI need to be able to control when to go to the next node

Iterators have these methods: (see

ch.

15)

public boolean hasNext ();

public T

next

();

public void

remove

(); // Optional method

Iterators allow you to step through a structure, one step at a time.

See complete interface Iterator, Listing 15-19Slide10

Using iterators (ch

15)

ListWithIteratorInterface

<String>

nameList

= new

ArrayListWithIterator <String>();

nameList.add

(“

Maha

”);

nameList.add

(“Nadia”);

nameList.add

(“Rehab”);

Iterator < String > nameIterator = nameList.getIterator();

nameIterator.remove();if(nameIterator.hasNext()) nameIterator.next();System.out.println (nameIterator.next

());

nameIterator.remove

();

nameList

nameIterator

MahaNadiaRehab

IllegalStateException

Adapted from Pearson Education, Inc.

10

Print “Nadia”Slide11

Using iterators (ch 15)

ListWithIteratorInterface

<String>

nameList

= new

LinkedListWithIterator

<String>();

nameList.add

(“

Maha

”);

nameList.add

(“Nadia”);

nameList.add

(“Rehab”);

Iterator < String > nameIterator = nameList.getIterator();

if(nameIterator.hasNext()) nameIterator.next();System.out.println (nameIterator.next());

nameIterator.remove();

nameList

nameIterator

Maha

Rehab

Adapted from Pearson Education, Inc.11Slide12

Iterative In-Order Traversal of a BT

Adapted from Pearson Education, Inc.

public void

inorderTraverse

()

{

StackInterface

<

BinaryNodeInterface

<T>>

nodeStack

=

new

LinkedStack

<BinaryNodeInterface<T>> ();

BinaryNodeInterface < T > currentNode = root; while

(!

nodeStack.isEmpty

() || (

currentNode

!= null))

{ // find leftmost node with no left child while (currentNode != null) { nodeStack.push (currentNode); currentNode = currentNode.getLeftChild (); } // end while // visit leftmost node, then traverse its right subtree if (!nodeStack.isEmpty ()) { BinaryNodeInterface < T > nextNode = nodeStack.pop (); System.out.println (nextNode.getData ());

currentNode = nextNode.getRightChild ();

}

// end if

}

// end while

}

// end

inorderTraverse

12Slide13

In-Order Traversal with an Iterator

Adapted from Pearson Education, Inc.

private class

InorderIterator

implements Iterator < T >

{

private

StackInterface

<

BinaryNodeInterface

< T >>

nodeStack

; private

BinaryNodeInterface

< T >

currentNode; public InorderIterator

() { nodeStack = new LinkedStack < BinaryNodeInterface < T >> ();

currentNode

= root;

} // end default constructor public boolean hasNext () { return ( !nodeStack.isEmpty () || (currentNode != null) ); } // end hasNext13Slide14

In-Order Traversal with an Iterator

Adapted from Pearson Education, Inc.

public T

next

()

{

BinaryNodeInterface

< T >

nextNode

= null;

//

find leftmost node with no left child

while (currentNode != null)

{ nodeStack.push (currentNode); currentNode = currentNode.getLeftChild ();

}

// end while

//

get leftmost node, then move to its right subtree if (!nodeStack.isEmpty ()) { nextNode = nodeStack.pop (); currentNode = nextNode.getRightChild (); } else throw new NoSuchElementException (); return nextNode.getData (); } // end next public void remove () { throw new UnsupportedOperationException (); } // end remove } // end InorderIterator14Slide15

Tracing of inorderTraverse

()

Adapted from Pearson Education, Inc.

15Slide16

Using a stack to do a pre-order traversal

Adapted from Pearson Education, Inc.

16Slide17

Using a stack to do a post-order traversal

Adapted from Pearson Education, Inc.

17Slide18

Using a queue to do a level-order

traversal

Adapted from Pearson Education, Inc.

c d

X

c

d e

X

c

18Slide19

Implementation of an Expression Tree

Adapted from Pearson Education, Inc.

Note interface, Listing 24-5

Derive from

BinaryTree

,

Listing 24-6

19Slide20

Node for a General TreeAdapted from Pearson Education, Inc.

Figure 24-8 A node for a general tree

20Slide21

Node for a General TreeAdapted from Pearson Education, Inc.

Interface,

Listing 24-7

21Slide22

Using a Binary Tree to Represent a General Tree

Adapted from Pearson Education, Inc.

Figure 24-9 (a) A general tree; (b) an equivalent binary tree;

22Slide23

EndChapter 24

Adapted from Pearson Education, Inc.

23