Final Review

Dr. Yingwu Zhu

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 heaps to do heapsort, and priority queues

• Use appropriate algorithms to slove real-world problems– Search algorithms– Sorting algorithms

Goals

• Use Big-Oh notation to evaluate algorithm efficiency

• Understand ADTs including BST, Heap, Priority Queue, AVL trees

• Understand hashing • Understand sorting algorithms

ADTs

• Tree terminologies

• BST

• AVL Trees

• Heap

• Priority Queue

Trees

• Binary trees

• Complete trees

• Balanced trees

• Level

• Height

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, …

BST

• T(n) = ?• Is BST balanced?• Lopsidedness problem!• BST AVL trees

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

Heap

• Defintion

• Recusive data structure

• Semiheap

• What data structures are good to implement a heap? Why?

• Parent-child relationships

Heap

• Implementation– Insertion– Deletion– removeMax– Other operations?

• Two basic operations– Percolate down– Percolate up

Priority Queue

• Definition

• Using different ADTs to implement priority queue– Unsorted lists– Sorted lists– BST– Heap

• Why heap is a good choice?

Hashing

• Why need hashing?

• Definition of hash function?

• Problem of hashing: collision

Hashing

• Collision resolution techniques– Open addressing

• Linear probing• Quadratic probing• Double hashing

– Chaining

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

Algorithm Efficiency

• Big-Oh notation definition T(n)

• Non-recursive algorithms– The most executed instruction

• Recursive algorithms: telescoping principal– Anchor case– Inductive step

Sort

• Selection sort, insertion sort, bubble sort

• Heapsort

• Quicksort

• Mergesort

Selection Sort

• How does it work?

• T(n) = ?

Insertion Sort

• How does it work?

• T(n) = ?

• Recursive and Non-recursive algorithms

Bubble Sort

• How does it work?

• How does it detect partially sort sublist to improve performance

• T(n) = ?

• Best case performance

• Worst case performance

Quicksort

• How does it work?– Devide and conquer

• Basic operation– Split based on pivot

• T(n) = ? best case and worst case?

Quicksort

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

Mergesort

• Internal and external algorithm

• Basic operation: split and merge

• Divide-and-conquer

• T(n) = ?

Heapsort

• Heapify process

• How does heapsort work?– Exploits heap property– T(n) = ?

About Final Exam

• Must >= 75 to pass

• Multiple choices

• Short answers

• Coding

• Reminder: do not loose points in basic concept questions!

• Good luck!