Final Review

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Final Review

• Dr. Yingwu Zhu

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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

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Goals

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

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ADTs

• Tree terminologies
• BST
• AVL Trees
• Heap
• Priority Queue

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Trees

• Binary trees
• Complete trees
• Balanced trees
• Level
• Height

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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,

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BST

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

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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

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Heap

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

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Heap

• Implementation
• Insertion
• Deletion
• removeMax
• Other operations?
• Two basic operations
• Percolate down
• Percolate up

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Priority Queue

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

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Hashing

• Why need hashing?
• Definition of hash function?
• Problem of hashing collision

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Hashing

• Collision resolution techniques
• Open addressing
• Linear probing
• Quadratic probing
• Double hashing
• Chaining

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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

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Algorithm Efficiency

• Big-Oh notation definition T(n)
• Non-recursive algorithms
• The most executed instruction
• Recursive algorithms telescoping principal
• Anchor case
• Inductive step

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Sort

• Selection sort, insertion sort, bubble sort
• Heapsort
• Quicksort
• Mergesort

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Selection Sort

• How does it work?
• T(n) ?

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Insertion Sort

• How does it work?
• T(n) ?
• Recursive and Non-recursive algorithms

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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

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Quicksort

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

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Quicksort

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

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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) ?

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Heapsort

• Heapify process
• How does heapsort work?
• Exploits heap property
• T(n) ?

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Other Basics

• Iterators and vectors in STL
• Function templates and class templates
• Overloading operators
• Overloading functions
• Copy constructors

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About Final Exam

• Must gt 75 to pass
• Multiple choices
• Short answers
• Coding
• Reminder do not loose points in basic concept
  questions!
• Good luck!