1. CS2005
Week 8 Lectures
Maps & Binary Trees

2. Aims Describe and specify the Map Data Type
CS2005
Aims
Describe and specify the Map Data Type
Describe java.util.HashMap and java.util.TreeMap
Describe the Binary Tree Data Structure
Define basic Binary Tree terminology
Describe ways of traversing a Binary Tree
Java implementation of a Binary Tree

3. Learning Outcomes describe and use a Map ADT
CS2005
Learning Outcomes
describe and use a Map ADT
describe the structure of a Binary Tree
implement a simple Binary Tree in Java
write Java code to perform simple operations using Binary Trees
recall main points of Watt & Brown chs 10 & 11

4. Map equivalent to table
CS2005
Map equivalent to table

5. CS2005
Map equivalent to set

6. Map ADT Essential Operations create:  Map
CS2005
Map ADT
Essential Operations
create:  Map
put: Key  Value  Map  Map
containsKey: Key  Map  Boolean
get: Key  Map  Value
remove: Key  Map  Map
isEmpty: Map  Boolean

7. Java.util classes TreeMap HashMap complexity O(log n)
CS2005
Java.util classes
TreeMap
complexity O(log n)
iterator over set of keys is sorted
HashMap
complexity O(1)
iterator over set of keys ‘random’

8. CS2005
Binary Tree Structure
Terminology: node, branch, root node, leaf node, parent, child, ancestor, descendant, subtree, null tree, depth

9. Balanced Binary Trees M = abs(Size(left stree) - Size(right stree))
CS2005
Balanced Binary Trees
M = abs(Size(left stree) - Size(right stree))
Tree balanced if
M <= 1 for itself and all its subtrees
Measure if ill-balance
largest value of M for tree and all subtrees
Degree of ill-balance
0 (for trees of size 0 or 1)
(Measure if ill-balance)/(size-1) otherwise

10. Tree Traversals Breadth First Depth First visit root node
CS2005
Tree Traversals
Breadth First
visit root node
then all nodes depth 1
then all nodes depth 2, etc
Depth First
visit all nodes in one subtree before another
same rule applies to all subtrees

11. Breadth First Traversal
CS2005
Breadth First Traversal
If tree empty then return
Make empty queue Q
Append root node to Q
Loop until Q is empty
remove node from Q
process node
append child nodes to Q
Return

12. Depth First Traversal (pre- order)
CS2005
Depth First Traversal (pre- order)
If tree empty then return
Make empty stack S
Push root node on S
Loop until S is empty
pop node from S
process node
push child nodes on S
Return

13. Depth First Traversal (recursive)
CS2005
Depth First Traversal (recursive)
If tree is empty then return
Process the root node
Recursively traverse left subtree
Recursively traverse right subtree
Return
Order of middle steps can be changed

14. Java Implementation Public class BTNode { protected Object element;
CS2005
Java Implementation
Public class BTNode {
protected Object element;
protected BTNode left, right;
protected BTNode(Object elem,
BTNode lt, BTNode rt) {
element = elem;
left = lt;
right = rt; }

15. CS2005
Sample Code
Html document
Binary tree code
test program

16. Example - equals method
CS2005
Example - equals method
public static boolean equals(CharTree t1, CharTree t2) {
if (t1==t2) return true;
if (t1==null || t2==null) return false;
return ((t1.element == t2.element) &&
(CharTree.equals(t1.left,t2.left)) &&
(CharTree.equals(t1.right,t2.right))); }