Class Notes

Notes:

• Review of Basic Data Structures
  • Static Arrays
  • Lists
  • Dynamic Arrays
  • Stacks and Queues
  • Example code for this section.
• Chapter 1
  • Intro to Chapter 1
  • Stable Matching Examples
  • The Gale-Shapley Algorithm
  • Proof of the Gale-Shapley Algorithm
  • Some Observations on the Gale-Shapley Algorithm
  • A quick overview of graphs
  • Some Example Problems
• Chapter 2 Basics of Algorithm Analysis
  • Intro to Chapter 2
  • Asympotitc Notation
  • More on Asympotitc Notation
  • A Little More on Asympotitc Notation
  • A Survey of Common Running Times Part I
  • A Survey of Common Running Times Part II
  • Intro to Priority Queue
  • The Heap
• Chapter 3, Graphs
  • Graphs
  • Connectivity and Paths
  • Graph Representation
  • DFS
  • Some Example Graphs
• Divide Conquer, Combine Sorting
  • Intro
  • Analysis of Mergesort
  • Quicksort
  • A lower bound on comparison based sorting.
  • Sorting Properties
  • Heapsort
  • Counting Sort
  • Bucket Sort
  • Example code for this section.
• Chapter 4, Greedy Techniques
  • Interval Scheduling
  • Shortest Path
  • Kruskal's and Prim's
  • Union Find Data Structure
• Complexity
  • Introduction
  • NP-Complete
  • Further NP-Complete Problems
  • Heuristic Algorithms
• Hash Tables
  • Introduction
• A quick intro to Computational Geometry
  • Intro, Cross and Dot products
  • Convex Hull, Graham's Scan
  • Convex Hull Demo

Course outline

1. Mathematical Techniques
   1. Review of Selected Topics in Mathematics ✓
   2. Recurrence Relations ✓
   3. Review of Proof Methods ✓
2. Analysis of Algorithms and Data Structures
   1. Asymptotic Notation ✓
   2. Complexity ✓
      1. Space
      2. Time
   3. Algorithm Correctness ✓
   4. Program Efficiency
3. Algorithm Design Methods
   1. Brute Force ✓
   2. Divide, Conquer, and Combine ✓
   3. Greedy ✓
   4. Analogy ✓
4. Elementary Data Structures ✓
   1. Implementation ✓
   2. Performance Analysis ✓
   3. Application ✓
   4. Data Structures Covered ✓
      1. Arrays ✓
      2. Lists ✓
      3. Stacks ✓
      4. Queues ✓
5. Additional Data Structures
   1. Trees
      1. Terminology ✓
      2. Representations ✓
      3. Binary Trees
      4. Tree Algorithms
   2. Graphs ✓
      1. Terminology ✓
      2. Representations ✓
      3. Graph Algorithms ✓
6. Algorithms
   1. Searching ✓
   2. Sorting ✓
      1. Properties of Sorting Algorithms ✓
      2. Comparison Based Sorts ✓
      3. Non-Comparison Based Sorts ✓
7. Limits of Computation
   1. The Classes P and NP
   2. NP-complete Problems
   3. Intractable Problems
8. Additional Topics
   1. Other Algorithms
      1. Computational Geometry
      2. Pattern Matching
      3. Numeric Algorithms
   2. Additional Data Structures
      1. Maps
      2. Hash Tables