CS252 Algorithms
Wednesday, 14 September 2022

+ Revisiting reading responses

+ Mathematical definitions of efficiency
- O, Ω, ϴ
    (and exactness vs. sloppiness)
    (log2 vs. ln vs. log10...)
- worst-case analysis
- average-case analysis

+ Notation (and Jeff's anxiety)
- Is there a difference between f and f(n)?
- What kind of object is O(f(n))?
- is, =, ∈

+ A brief digression regarding n^2, log(n), and intuition

+ The definitions and proofs

-   Let f(n) = 3 n^2 + n + 60
    Let g(n) = n^2
    Prove f = O(g)
    Prove f = Ω(g)

- What does O(1) mean? (walk through the definition)

+ Examples: named or otherwise familiar algorithms for each
  O(1)
  O(log n)
  O(n log n)
  O(n)
  O(n^2)

  O(n^3)
  O(sqrt(n))
  O(log log n)
  O(2^n)

+ Quick look at this week's assignment
- Check-in submission
- Final submission
- Karma Questions
- The plan for Friday's class
    - 11:10-12:20!
    - Go through the problem-solving and solution-writing
        process on an example
    - Some talk about LaTeX
- The questions themselves