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Tree Definitions and Operations: AVL, Binary Search Trees, Splay Trees, Optimal BST

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  1. Topic 10 Trees

  2. Tree Definitions

  3. Tree Definitions

  4. Tree Definitions

  5. Binary Search Tree

  6. Traversal • Operations tree

  7. Announcements • Participation 4 is up • Homework 3 grading • Homework 4 grading

  8. Search

  9. Insertion

  10. Deletion • Need • Min/max • Successor/predecessor

  11. Pseudocode

  12. Pseudocode

  13. AVL

  14. Height of AVL Tree

  15. Proof

  16. Insertion

  17. Example

  18. Single Right

  19. Left-Right

  20. Four cases

  21. Deletions

  22. Example

  23. Announcements • Test in 2 weeks • Participation due tomorrow • Clarification

  24. Splay Trees

  25. Amortized Running Time • Runtime:

  26. Basic Operations

  27. When to Splay

  28. Zig

  29. Zig-Zag

  30. Zig-zig

  31. Example

  32. Deletion

  33. Optimal BST

  34. Notation

  35. Example

  36. Example

  37. More Notation • (i,j) • (j+1, j)

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