1. Trees

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

3. Tree Strucures Collection of nodes connected by edges – Single root node with no parent Node Edge

4. Tree Strucures Collection of nodes connected by edges – Single root node (no parent) – Parent nodes point to 1+ child nodes – Children of a parent are siblings – Every non-root node has 1 parent

5. Trees? Which is a tree? A B C

6. Trees? Which is a tree? A B C

7. Tree Strucures Parents are interior nodes

8. Tree Strucures Nonparents are leaves

9. Tree Strucures Every node can be root of a subtree

10. Tree Strucures Single path from root to any node – Length = number of edges

11. Tree Strucures Single path from root to any node – Length = number of edges Node's depth = distance to root 3 2 1 0

12. Tree Strucures Single path from root to any node – Length = number of edges Node's height = longest path starting from it – Leaf = 0 height 0 1 2 3

13. Tree Strucures Tree as a whole: – Height = Depth = root's height = max depth of all leaves

14. Trees… Categorizations

15. Trees… Brackets

16. Trees… File systems

17. Trees… Image recognition

18. Trees… HTML documents Natural language Math expressions…

19. Expression Tree

20. Tree Traversal Inorder Traversal Traverse(Node) If Null, return Traverse(Left) Print Self Traverse(Right)

21. Tree Traversal Inorder Traversal Traverse(Node) If Null, return Traverse(Left) Print Self Traverse(Right)

22. Tree Traversal Inorder Traversal Traverse(Node) If Null, return Traverse(Left) Print Self Traverse(Right)

23. Tree Traversal Inorder Traversal Traverse(Node) If Null, return Traverse(Left) Print Self Traverse(Right) 15

24. Tree Traversal Inorder Traversal Traverse(Node) If Null, return Traverse(Left) Print Self Traverse(Right) 15 –

25. Tree Traversal Inorder Traversal Traverse(Node) If Null, return Traverse(Left) Print Self Traverse(Right) 15 – 1

26. Tree Traversal Inorder Traversal Traverse(Node) If Null, return Traverse(Left) Print Self Traverse(Right) 15 – 1

27. Tree Traversal Inorder Traversal Traverse(Node) If Null, return Traverse(Left) Print Self Traverse(Right) 15 – 1 /

28. Tree Traversal Inorder Traversal Traverse(Node) If Null, return Traverse(Left) Print Self Traverse(Right) 15 – 1 /

29. Tree Traversal Inorder Traversal Traverse(Node) If Null, return Traverse(Left) Print Self Traverse(Right) 15 – 1 / 7

30. Tree Traversal PostOrder Traversal Traverse(Node) If Null, return Traverse(Left) Traverse(Right) Print Self

31. Tree Traversal PostOrder Traversal Traverse(Node) If Null, return Traverse(Left) Traverse(Right) Print Self

32. Tree Traversal PostOrder Traversal Traverse(Node) If Null, return Traverse(Left) Traverse(Right) Print Self 15

33. Tree Traversal PostOrder Traversal Traverse(Node) If Null, return Traverse(Left) Traverse(Right) Print Self 15 1

34. Tree Traversal PostOrder Traversal Traverse(Node) If Null, return Traverse(Left) Traverse(Right) Print Self 15 1 -

35. Tree Traversal PostOrder Traversal Traverse(Node) If Null, return Traverse(Left) Traverse(Right) Print Self 15 1 -

36. Tree Traversal PostOrder Traversal Traverse(Node) If Null, return Traverse(Left) Traverse(Right) Print Self 15 1 - 7

37. Tree Traversal PostOrder Traversal Traverse(Node) If Null, return Traverse(Left) Traverse(Right) Print Self 15 1 – 7 /

38. Tree Traversal PreOrder Traversal Traverse(Node) If Null, return Print Self Traverse(Left) Traverse(Right) /

39. Tree Traversal PreOrder Traversal Traverse(Node) If Null, return Print Self Traverse(Left) Traverse(Right) / -

40. Tree Traversal PreOrder Traversal Traverse(Node) If Null, return Print Self Traverse(Left) Traverse(Right) / - 15

41. Tree Traversal PreOrder Traversal Traverse(Node) If Null, return Print Self Traverse(Left) Traverse(Right) / - 15 1

42. Tree Traversal PreOrder Traversal Traverse(Node) If Null, return Print Self Traverse(Left) Traverse(Right) / - 15 1

43. Tree Traversal PreOrder Traversal Traverse(Node) If Null, return Print Self Traverse(Left) Traverse(Right) / - 15 1

44. Tree Traversal PreOrder Traversal Traverse(Node) If Null, return Print Self Traverse(Left) Traverse(Right) / - 15 1 7

45. Tree Traversal PreOrder Traversal Traverse(Node) If Null, return Print Self Traverse(Left) Traverse(Right) / - 15 1 7

46. Tree Traversal PreOrder Traversal Traverse(Node) If Null, return Print Self Traverse(Left) Traverse(Right) / - 15 1 7