DP Solve

Run only when explicitly invoked. Work on the supplied problem as semantic text; do not inspect or change a codebase unless separately authorized outside this skill.

1. Define the target state or answer and its boundaries.
2. Decompose it into subproblems.
3. Identify overlapping subproblems and the minimal state needed to answer each once.
4. Order dependencies and solve base cases first.
5. Record the reusable answers in a memo table.
6. Synthesize the target answer from the memoized results.
7. Check that no conclusion depends on an unstated subproblem.

Prefer a smaller reusable state graph to artificial formalism.