CS252 Algorithms
Monday, 31 October 2022 (Boo!)

+ Homework/testing plan
- Topics left: dynamic programming & network flows
- Tools for giving you practice
    - problem sets
    - takehome exam
    - in-class exam
    - final project (study algorithm of your choice, make
        a video, implement, write a paper...)
- 3 weeks to end of finals
- Option 1
    - PS on dynamic programming
    - PS on network flows
    - Takehome final (comprehensive) 
- Option 2
    - PS on DP & NF
    - Project (pick and algorithm, report, & implement)
    - No exam

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Wire-cutting (often called "rod-cutting")

Given
- A price p[j] you can charge for a piece of
    wire of length j, for j = 1,...,m

Goal
- Maximum revenue you can earn by cutting up
    (or not) a piece of wire of length n <= m
- (Secondary goal: where should I make the cuts?)

Play around
- Do a small example
- Mess with the small example and boundary cases
- What does brute-force look like?

Decompose recursively
- Does it work?
- Complexity?

Build up subproblem solutions
- Top-down (memoized)
- Bottom-up (dynamic programming)
- Complexity?

Backtracing
- Retrieving the cuts that maximize revenue
- (Dijkstra: get the paths, not just the distances)
- (BFS: get the paths, don't just visit everybody)
- (...)