Tried brute force first and got redirected.
First, restate the problem and identify the key variables and constraints. Then, derive the mathematical condition (e.g., invariant, inequality, or monotonicity) that characterizes an optimal solution, and prove it rigorously. Finally, implement the algorithm based on that condition, ensuring efficiency.
Pro tip: Verbalize your thought process clearly and connect the math to the code; interviewers value structured reasoning over a rushed solution. If stuck, simplify the problem to a smaller case to uncover the pattern.
Clarify the problem, inputs, outputs, and constraints. Restate it in your own words to ensure alignment.
Examine small examples to identify patterns or invariants. Form a hypothesis about the mathematical constraint that enables optimality.
Formally derive the constraint (e.g., using induction, exchange argument, or contradiction) and prove it guarantees an optimal solution.
Translate the proven constraint into an algorithm, choosing appropriate data structures and analyzing time/space complexity.
Write clean code, then test with edge cases and validate against the derived constraint.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.