CS252 Algorithms
Friday, 30 September 2022

+ Problem set #3
- Quick spin through problem 1. This is pictorial, intended to
    be pretty simple, and hopefully fun.
    Goal: get you practice thinking about graph vocabulary.

- Words: connected, cycle, path, shortest path, weights, diameter

- Problem 2: if the best you can do is something that feels
brute force, write it up! Don't violate the preprocessing constraints,
but a well-described and well-analyzed non-optimal algorithm will get
most or all of the points.


+ Grading in general
- First problem set will come back tomorrow;
    Second hopefully late next week
- Not 90/80/70/60: we'll talk more once I return the exam
- This is to a large degree a writing class--some subjectivity no matter what


+ The exam, 10/7

- My philosophy of in-class exams

- Topics to be prepared for
    - O, Ω, ϴ
    - Stable matching
        - what does stable mean?
        - the Gale-Shapley proof
    - Graph vocabulary
    - BFS, DFS, Topological Sort
    - Interval scheduling

- Types of questions
    - short answer (definitions, etc.)
    - O, Ω proofs
        - I promise problem 1 will be a simple polynomial O argument
        - hey, what about ϴ?
    - Run algorithm X on scenario Y
        - Gale-Shapley
        - BFS, DFS
        - Topological sort
        - Interval scheduling
    - Examples of "why X is not true"
        (i.e. counterexamples of X)
    - Short arguments from the correctness proofs of the
        various algorithms
    - Short arguments from the running time proofs
    - ??

- No sophisticated writing expectations

- No tricks

- Class Wednesday 10/5: wide open for questions

======

+ Greedy algorithms generally
- Local vs. global optimization
- Shortest paths in graphs: what exactly is the problem?

+ Interval scheduling

- What's this problem?
    # intervals vs. total coverage vs. ...?

- What greedy strategies are available?
    can we show that any in particular fail?

- What I do when I meet a new algorithm
    - read it to get the rough idea
    - run it by hand on a couple examples
    - while reading the proof, keep an example,
        the algorithm, and the proof visible
        together; try to adjust the example to
        break the proof

- Let's try it!