Algorithm Selection, Correctness Proofs, and Stress Testing

Derive a feasible time-complexity target from input bounds and the total size across test cases.

Use constraints and input structure to shortlist plausible algorithm families before coding.

Distinguish necessary conditions from sufficient conditions when deriving a solution criterion.

Construct a minimal counterexample that disproves an incorrect algorithmic idea.

State an invariant that explains why an iterative or constructive algorithm remains correct.

Use induction to prove the correctness of a recursive or recurrence-based algorithm.

Build a brute-force oracle for checking an optimized solution on small inputs.

Use randomized stress testing to isolate a mismatch between an oracle and an optimized solution.