One Hard DSA Problem

Turn ambiguity into a contract

A difficulty label is not a problem statement. Ask for input size, operation sequence, output, update/query requirements, guarantees, and examples. Restate the problem, including whether values repeat, data is mutable, and answers need exact or modulo arithmetic. For a hard problem, this discovery step prevents choosing a technique that optimizes the wrong dimension.

Propose a direct baseline that is obviously correct, calculate its bottleneck, and only then introduce the appropriate tool: state DP for overlapping subproblems, monotonic structures for nearest constraints, divide-and-conquer for ordered ranges, or graph algorithms for relationships. State the invariant or recurrence and test adversarial boundaries, not just happy paths. Give Big-O in the confirmed variables and mention memory. Never fill missing facts with a random hard problem; an interviewer can supply the intended prompt and will value the disciplined transition from specification to proof.

Complexity: For the confirmed hard DSA problem, state the actual state or edge count; for example, a graph traversal is O(V + E) time and O(V) space.