CS252 Algorithms
Wednesday, 2 November 2022

+ Plan
- Notes on "search space" for optimization problems
    also: objective function, constraints
- General structure of DP problem solving
- Apply it to wire-cutting
- Apply it to knapsack
- Apply it to others

+ Optimization problems, etc.
- Given: a search space S and an objective function P:S -> R
- Goal: find s in S such that P(s) is as large as possible
- Short-term goal: just find the biggest P(s)

+ General DP plan
- State the problem. What are we selecting, what
    are we optimizing, what are our constraints,
    input/output, etc.
- Preliminaries
    - Get an example to work with
    - Think about brute force and the size of the search space
- Define a parameterized subproblem that will
    support (1) computing the problem's final answer;
    (2) recursive decomposition of the subproblem?
- Show recursive decomposition of that subproblem
- Iteratively build the subproblem solutions from the
    bottom up
- Get your answer

- Want the item in your search space that gave the optimal result?
    - various kinds of backtracing