1. Final Review
Dr. Yingwu Zhu

2. Goals Use appropriate data structures to solve real-world problems
E.g., use stack to implement non-recursive BST traversal,
use queue to implement BST level traversal,
use stack to implement non-recursive quicksort
Use appropriate algorithms to slove real-world problems
Search algorithms
Sorting algorithms

3. Goals Use Big-Oh notation to evaluate algorithm efficiency
Understand ADTs including BST, Heap, Priority Queue, AVL trees
Understand hashing
Understand sorting algorithms

4. ADTs
Tree terminologies
BST
AVL Trees
Heap
Priority Queue

5. Trees
Binary trees
Complete trees
Balanced trees
Level
Height

6. BST Definition Recursive ADT
Implementing a BST (recursive and non-recursive)
Search
Traversals (in-order, pre-order, post-order)
Insertion
Deletion
Other operations: height, level, …

7. BST
T(n) = ?
Is BST balanced?
Lopsidedness problem!
BST  AVL trees

8. AVL Trees Definition Four rotation techniques
Single rotations
Double rotations
Key to perform rotation: identify the nearest ancestor with BF of +2 or -2 for the inserted item
Two steps in double rotations
Rotate child and grandchild nodes of the ancestor
Rotate the ancestor and the new child node

9. Heap Defintion Recusive data structure Semiheap
What data structures are good to implement a heap? Why?
Parent-child relationships

10. Heap Implementation Two basic operations Insertion Deletion removeMax
Other operations?
Two basic operations
Percolate down
Percolate up

11. Priority Queue Definition
Using different ADTs to implement priority queue
Unsorted lists
Sorted lists
BST
Heap
Why heap is a good choice?

12. Hashing Why need hashing? Definition of hash function?
Problem of hashing: collision

13. Hashing Collision resolution techniques Open addressing Chaining
Linear probing
Quadratic probing
Double hashing
Chaining

14. Hashing Three strategies to improve hashing performance
Increase hash table capacity
Use a good hash function (how to evaluate a hash function?)
Use a good collision resolution technique

15. Algorithm Efficiency Big-Oh notation definition T(n)
Non-recursive algorithms
The most executed instruction
Recursive algorithms: telescoping principal
Anchor case
Inductive step

16. Sort Selection sort, insertion sort, bubble sort Heapsort Quicksort
Mergesort

17. Selection Sort
How does it work?
T(n) = ?

18. Insertion Sort How does it work? T(n) = ?
Recursive and Non-recursive algorithms

19. Bubble Sort How does it work?
How does it detect partially sort sublist to improve performance
T(n) = ?
Best case performance
Worst case performance
Two-way bubble sort in Exam 2

20. Quicksort How does it work? Basic operation
Devide and conquer
Basic operation
Split based on pivot
T(n) = ? , best case and worst case?

21. Quicksort How to improve performance
Median-of-three rule in pivot choice
Short sublists are handle first in recursive alg.
Non-recursive
Other solutions

22. Mergesort Internal and external algorithm
Basic operation: split and merge
Binary mergesort
Natural mergesort
How does natural merge sort work?
Exploit partially sort sublists in split and merge
T(n) = ?

23. Heapsort Heapify process How does heapsort work?
Exploits heap property
T(n) = ?

24. Other Basics Iterators and vectors in STL
Function templates and class templates
Overloading operators
Overloading functions
Copy constructors

25. About Final Exam Must >= 75 to pass Multiple choices Short answers
Coding
Reminder: do not loose points in basic concept questions!
Good luck!