1. Graphs & Trees

2. Graphs
Nodes connected by Edges

3. Directed Graphs
Directed Graph : Edges are one way

4. Trees Trees: A trunk from the roots Divides into branches
Ends in leaves

5. Tree Strucures Directed graph with: Single root node with no parent
Edge
Node

6. Tree Strucures Directed graph with: Single root node (no parent)
Parent nodes point to 1+ child nodes

7. Trees…
Categorizations

8. Trees…
Brackets

9. Trees…
HTML documents

10. Trees…
Image recognition

11. Expression Tree
Represents mathematical expression
(15 – 1) / 7

12. Expression Tree

13. Expression Tree

14. Traversal
Most operations involve complete traversal

15. Traversal BinaryOp toString: Handle left child Handle self
Handle right child

16. Traversal BinaryOp toString: Handleing may involve recursion
Handle left child
Handle self
Handle right child
Handleing may involve recursion

17. Traversal BinaryOp toString: Handle left child Handle self
Handle right child

18. Traversal BinaryOp toString: Handle left child Handle self
Handle right child

19. Traversal BinaryOp toString: Handle left child Handle self
Handle right child

20. Traversal BinaryOp toString: Handle left child Handle self
Handle right child

21. Traversal BinaryOp toString: Handle left child Handle self
Handle right child

22. Traversal BinaryOp toString: Handle left child Handle self
Handle right child

23. Traversal BinaryOp toString: Handle left child Handle self
Handle right child

24. Traversal
BinaryOp toString code
Puts ( ) around node’s output

25. Traversal Most operations involve complete traversal
Relative order of Left Self Right depends on job

26. Traversal Evaluate: Evaluate left Evaluate right
Do math using left & right

27. Traversal Evaluate: Evaluate left Evaluate right
Do math using left & right

28. Traversal
Evaluate code