Sect 3. Algorithms

CONCEPTS

  Algorithm
  Recursion
  Complexity: big O, Omega, Theta
  Euclidean Algorithm: division theorem, prime, factorization, GCD
  Affine encryption: modular arithmetic, 3 theorems
  Topological sort

NOTATION

SKILLS
  
  1. Identify concepts in a context
     E.g., what are c and n0 in the Big Oh notation
  2. Understand recursive algorithms
     E.g., tell output of a recursive function for some input
     E.g., find recursive formulation of a given function
  3. Understand Big Oh (Omega, Theta) notation
     E.g., tell whether a function is Big Oh (Omega, Theta) of another
  4. Understand GCD
     E.g., compute GCD of two numbers
  5. Manipulate Affine Ciphers
     E.g., tell whether a function is an encryption
     E.g., determine the decryption function
     E.g., find fixpoints of an encryption
  6. Understand topological sort
     E.g., sort a poset
  
Sources

  *** Recommended ***
  Youtube: Recursion
  https://www.youtube.com/watch?v=Mv9NEXX1VHc

  Wikibooks: Programming Concepts: Recursive Techniques
  https://en.wikibooks.org/wiki/A-level_Computing/AQA/Paper_1/Fundamentals_of_programming/Recursion

  Wikibooks: Big Oh 
  https://en.wikibooks.org/wiki/Algorithms/Mathematical_Background
  (Not yet "Algorithm Analysis: Solving Recurrence Equations")

  Tutorialspoint: Data Structures - Algorithms Basics
  https://www.tutorialspoint.com/data_structures_algorithms/algorithms_basics.htm
  *** Recommended ***
  Tutorialspoint: Data Structures - Asymptotic Analysis
  https://www.tutorialspoint.com/data_structures_algorithms/asymptotic_analysis.htm

  Wikipedia: GCD visual
  https://en.wikipedia.org/wiki/Algorithm

  *** Recommended ***
  https://en.wikipedia.org/wiki/Affine_cipher

  Youtube: affine cipher
  https://www.youtube.com/watch?v=EVOIAvQ7_JY
  https://www.youtube.com/watch?v=03Gv0YAMWmo
  https://www.youtube.com/watch?v=J8hp4k40YOM

  *** Recommended ***
  Youtube: Topological Sort by IDeserve
  https://www.youtube.com/watch?v=71eHuQvSwc0 (simplest algorithm)

  Youtube: Topological Sort by EducateYourself
  https://www.youtube.com/watch?v=yYW6lQ1ajx4 (precised, detailed)

  Youtube: Topological Sort by GeeksforGeeks
  https://www.youtube.com/watch?v=Q9PIxaNGnig (efficient algorithm)

  *** Recommended ***   
  Lerma, sect 3.1-3.2

  Smid, sect 4.1 (lots of exerceise at the end of the section)

  ADS, sect 8.1-8.2 (lots of examples and exercises)