1. Tree Implementations (plus briefing about Iterators)
Chapter 24
Adapted from Pearson Education, Inc.

2. Contents The Nodes in a Binary Tree
An Interface for a Node
An Implementation of BinaryNode
An Implementation of the ADT Binary Tree
Creating a Basic Binary Tree
The Method privateSetTree
Computing the Height and Counting Nodes
Traversals & Iterators
An Implementation of an Expression Tree
General Trees
A Node for a General Tree
Using a Binary Tree to Represent a General Tree
Adapted from Pearson Education, Inc.

3. Objectives Describe necessary operations on node within binary tree
Implement class of nodes for binary tree
Implement 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
Adapted from Pearson Education, Inc.

4. 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.

5. An Interface for a Node An implementation of BinaryNode, Listing 24-2
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 the number of nodes in the subtree rooted at this node */ public int getNumberOfNodes (); /** Computes the height of the subtree rooted at this the height of the subtree rooted at this node */ public int getHeight (); public BinaryNodeInterface < T > copy (); } // end BinaryNodeInterface
An implementation of BinaryNode, Listing 24-2
Adapted from Pearson Education, Inc.

6. Implementation of a basic Binary Tree
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 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)
Adapted from Pearson Education, Inc.

7. Problems with PrivateSetTree
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
So what is the solution?
Adapted from Pearson Education, Inc.

8. Recursive In-Order traversal of a BT
Public method for user, calls private method
Adapted from Pearson Education, Inc.

9. Iterators vs regular traversal
What if I want to do something at each node?
I need to be able to stop at each node
I 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 15-1
Adapted from Pearson Education, Inc.

10. Adapted from Pearson Education, Inc.
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());
nameList
nameIterator
Maha
Nadia
Rehab
IllegalStateException
Print “Nadia”
As we go through this example, ask the students to look at the interface for iterators.
Q - At the first remove, ask students they can predict what will happen.
A - exception
Q - Then ask them why it happened
A - we did not call next() yet.
At the second remove statement, point out that a call to next should give us “Rehab”, we have to make sure in our implementation that that will be the case.
Ask the students where they think the arrow will be after removal? Only then click for next slide!!
Adapted from Pearson Education, Inc.

11. Adapted from Pearson Education, Inc.
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.

12. Iterative In-Order Traversal of a BT
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 inorderTraverse
Adapted from Pearson Education, Inc.

13. In-Order Traversal with an Iterator
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 hasNext
Adapted from Pearson Education, Inc.

14. In-Order Traversal with an Iterator
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 InorderIterator
Adapted from Pearson Education, Inc.

15. Tracing of inorderTraverse()
Adapted from Pearson Education, Inc.

16. Using a stack to do a pre-order traversal
Adapted from Pearson Education, Inc.

17. Using a stack to do a post-order traversal
Adapted from Pearson Education, Inc.

18. Using a queue to do a level-order traversal
c d X
c d e c
Adapted from Pearson Education, Inc.

19. Implementation of an Expression Tree
Note interface, Listing 24-5
Derive from BinaryTree, Listing 24-6
Adapted from Pearson Education, Inc.

20. Figure 24-8 A node for a general tree
Adapted from Pearson Education, Inc.

21. Node for a General Tree Interface, Listing 24-7
Adapted from Pearson Education, Inc.

22. Using a Binary Tree to Represent a General Tree
Figure 24-9 (a) A general tree; (b) an equivalent binary tree;
Adapted from Pearson Education, Inc.

23. End
Chapter 24
Adapted from Pearson Education, Inc.