1. CS223 Advanced Data Structures and Algorithms
Trees Neil Tang 01/26/2010
CS223 Advanced Data Structures and Algorithms

2. CS223 Advanced Data Structures and Algorithms
Class Overview
Basics
Binary Tree
Binary Tree Traversal
General Tree
CS223 Advanced Data Structures and Algorithms

3. CS223 Advanced Data Structures and Algorithms
Basics
Tree: A tree consists of a distinguished node r (root) and zero or more nonempty subtrees T1, T2, …Tk, each of whose roots are connected by a direct edge from r.
Child, parent, leaf, sibling
Path and path length
Depth of a node, depth of a tree
Height of a node, height of a tree
Ancestor, descendant
CS223 Advanced Data Structures and Algorithms

4. CS223 Advanced Data Structures and Algorithms
An Example
CS223 Advanced Data Structures and Algorithms

5. CS223 Advanced Data Structures and Algorithms
Properties
No cycle.
There only exists a unique path between a pair of nodes on a tree.
The height of a tree = the depth of that tree.
CS223 Advanced Data Structures and Algorithms

6. CS223 Advanced Data Structures and Algorithms
Binary Tree
Binary tree: A binary tree is a tree in which no node can have more than two children.
Implementation
The depth of a worst-case binary tree: N-1
CS223 Advanced Data Structures and Algorithms

7. CS223 Advanced Data Structures and Algorithms
Binary Tree Traversal
Inorder-Tree-Traversal(t)
if t  null then
Inorder-Tree-Traversal(t.left)
print(t.element)
Inorder-Tree-Traversal(t.right)
Preorder-Tree-Traversal(t)
Preorder-Tree-Traversal(t.left)
Preorder-Tree-Traversal(t.right)
How about Postorder-Tree-Traversal?
CS223 Advanced Data Structures and Algorithms

8. CS223 Advanced Data Structures and Algorithms
An Example
Inorder:
x*a*b+c
Preorder:
*x+*abc
Postorder:
xab*c+*
CS223 Advanced Data Structures and Algorithms

9. CS223 Advanced Data Structures and Algorithms
General Tree
Implementation
CS223 Advanced Data Structures and Algorithms

10. General Tree Traversal
Preorder
What is the first node visted? Last?
CS223 Advanced Data Structures and Algorithms

11. General Tree Traversal
Postorder
What is the first node visited? Last?
CS223 Advanced Data Structures and Algorithms