Trees (8.1)

















Draw an example of a tree on the board.


		 A
	       /   \
	      B	    C
	     /|\   /|\
	    D E F G H I
	    |  / \  |
	    J K   L M
	      |
	      N

















What's a Tree?

	a nonlinear or hierarchical structure made from
	a set of nodes and
	a set of directed links (links connect pairs of nodes)
	one node is the root


What's the key defining characteristic of a Tree?

	every node (except the root) has exactly one parent


What are some applications of trees?

	family trees
	XML documents (DOM)
	file folders


Trees are recursive

	a tree is a root node connected to
	zero or more subtrees

















Classwork
You may work with a partner.
Answer the questions about the tree.

		 A
	       /   \
	      B	    C
	     /|\   /|\
	    D E F G H I
	    |  / \  |
	    J K   L M
	      |
	      N

What's the root node?
What are the leaf nodes?

What's the parent of node K?
What are the children of node C?
What are the siblings of node E?

What are the ancestors of node G?
What are the descendants of node F?

















Classwork
You may work with a partner.
Answer the questions about the tree.

		 A
	       /   \
	      B	    C
	     /|\   /|\
	    D E F G H I
	    |  / \  |
	    J K   L M
	      |
	      N

What's the depth of node K?
What's the depth of node C?
What's the depth of the root?

What's the height of node H?
What's the height of node B?
What's the height of a leaf node?
What's the height of the tree?

















Classwork
You may work with a partner.
Answer the questions about the tree.

		 A
	       /   \
	      B	    C
	     /|\   /|\
	    D E F G H I
	    |  / \  |
	    J K   L M
	      |
	      N

What's the size of the subtree rooted at node C?
What's the size of the tree?

How many nodes are there in the tree?
How many edges are there in the tree?
How many edges are there in a tree with N nodes?

















Tree Implementation


What's stored in each tree node object?


How do you store the links to the children?


Draw the tree with first-child/next-sibling links.

	 A
	 |
	 B-------C
	 |       |
	 D-E-F   G-H-I
	 |   |     |
	 J   K-L   M
	     |
	     N


Show the code for a first-child/next-sibling tree.

















Tree Traversal (8.2)


What's a preorder traversal?

List the nodes of the tree in preorder.

		 A
	       /   \
	      B	    C
	     /|\   /|\
	    D E F G H I
	    |  / \  |
	    J K   L M
	      |
	      N


Write the code for a preorder traversal.

















What's a postorder traversal?



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
	    |  / \  |
	    J K   L M
	      |
	      N

















Classwork
You may work with a partner.

Write a recursive method that computes the size of a tree.

















Write a recursive method that computes the height of a tree.