Problem Solving Project and Carry-Forward

Bounded project: a defensible coin solver

Budget 12–18 hours, included in this module. Reuse the lab implementation. Support unlimited positive denominations with a minimum witness or no solution. Publish a precise contract, a last-coin recurrence proof, an independent small oracle, witness validation and one rejected greedy hypothesis.

1. Freeze domain, invalid-input behavior and resource limits. Predict one failure of greedy before running your experiment.
2. Implement and test, preserving original failures. Measure operation counts on a declared amount range; if timing, record environment and repeated runs.
3. Change to at most one of each denomination. Explain the state change and implement a bounded comparison on small inputs; do not silently reuse the old solver.
4. Deliver a one-page handoff with accepted claims, evidence links and limits.

The review requires feasibility and optimality arguments, reproducible commands, a changed-case result and an assistance record. Do not claim production fitness from a small test domain. A reviewer asks you to trace one unseen case and explain why budget exhaustion would be unknown rather than unreachable.

For the semester project, reuse this contract-and-evidence structure on a graph investigation. Keep your plan revision, minimal failure, and changed-model note for later algorithm design and the final capstone.