CS252 Algorithms
Friday, 14 October 2022

+ Misc
- PS 3 grading nearly done, will be done by Monday
- Test grading underway, will be done by Wednesday
- Second test (10/28) will be in class
- Third test will be takehome, due 11/11
- Final will be a (team) project about an algorithm of your choice

+ Recap (Jeff's brain-dump)
- LaTeX
- Writing proofs
- Definitions of O, Ω, Θ
- Stable matching, Gale-Shapley
    - Why this problem?
        Easy to describe the general problem
        Non-trivial to define the right concepts
            to actually solve the problem
        Enormously rich in follow-up questions
        Foreshadowing of proof techniques
        etc.
- Graphs intro
    - definitions; lots of definitions
    - implementation strategies
    - traversal: BFS and DFS
        the act of visiting + spanning trees
        connectivity & conected components
    - topological sort
- Greedy algorithms
    - in general
    - interval scheduling, round 1 (optimize # of non-overlapping intervals)
        - greedy sometimes works
        - greedy sometimes doesn't work
        - proof technique #1: show optimal solution & actual solution
           have the same value of the objective function
           (here, |𝒪| = |A|)

    [Current work]
    - all shortest paths from start node in directed graphs (Dijkstra)
    - minimum spanning tree in weighted undirected graphs (Kruskal, Prim, "reverse-delete")

+ What's next?
- More algorithmic paradigms
    dynamic programming, divide-and-conquer, network flows
- More algorithms: practice, practice, practice
- One big theorem
- Some cool applications (e.g., internet routing / packet switching)
- A fun final project: pick an algorithm, make us a movie about it

+ Recap of O and Ω proofs
- the document I posted yesterday
- key ideas
- proofs that flow from assumptions towards conclusions
    (how does this idea apply to proof by contradiction?)

+ Your questions about homework

+ #reading8
- d(v') = min_{e=(u,v)...}...
- negative edges
- 3 greedy approaches for 1 problem! (is this common?)
- how does Kruskal work? how do you detect cycles?
    - Prim vs. Kruskal (Prim special case of Kruskal?) (no)
- exchange argument round 2: MSTs
- how do they come up with this stuff??
- can we use these complexity results later? (yes!)
- weights: time instead of distance?

+ Meeting a new algorithm: what do you do?
- Read the problem we're trying to solve
    what are the inputs?
    what is the hoped-for output, and its properties?
- Look for examples that fail ("set it up for failure")
- Do a really simple example by hand
- implement it
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