Binary Trees (8.1)

















Draw an example of a binary tree on the board.

		 A
	       /   \
	      B	    C
	     / \   /
	    D   E F
	       /   \ 
	      G     H
	       \
	        I


What's a Binary Tree?

	a tree where each node has at most two children???


How many different binary trees are there with exactly 2 nodes?


Binary trees are recursive

	a binary tree is a root node
	connected to a left subtree and a right subtree

















What are some applications of binary trees?

	binary search trees
	expression trees
	priority queues


How can you represent an expression as a binary tree?
How do you use the tree to evaluate the expression?

	(2 * (5-3)) + -4

	        +
	       / \
	      *   -
	     / \   \
	    2   -   4
	       / \
	      5   3

















Binary Tree Implementation (8.3)


What's stored in each binary tree node object?


Show the code for binary tree nodes.

















Binary Tree Traversal (8.2)


Classwork
You may work with a partner.

List the nodes of the tree in preorder.
Write the code for a preorder traversal.

		 A
	       /   \
	      B	    C
	     / \   /
	    D   E F
	       /   \ 
	      G     H
	       \
	        I

















Classwork
You may work with a partner.

List the nodes of the tree in postorder.
Write the code for a postorder traversal.

		 A
	       /   \
	      B	    C
	     / \   /
	    D   E F
	       /   \ 
	      G     H
	       \
	        I

















What's an inorder traversal?

List the nodes of the tree in inorder.
Write the code for an inorder traversal.

		 A
	       /   \
	      B	    C
	     / \   /
	    D   E F
	       /   \ 
	      G     H
	       \
	        I

















Write a recursive method that finds the size of a binary tree.

















Classwork
You may work with a partner.

Write a recursive method that finds the height of a binary tree.

















Binary Tree Iterators



How can you traverse a tree without using recursion?


Write a preorder Iterator for a binary tree.


Write a level-order Iterator for a binary tree.