DSA

Start by clarifying the exact contract for DSA: input representation, mutation rules, duplicate behavior, and what should happen on invalid or empty input. The core idea is selecting a structure from workload rather than a memorized pattern. Work a tiny example aloud and name the invariant after each step, because that is the proof that the approach stays correct as the input grows.

A dependable implementation plan is to clarify operations and limits; compare candidate structures; choose one invariant; analyze expected and worst cases; test mutations. A broad subject label is not enough for a specific algorithm. Keep the code aligned with that invariant instead of adding special cases that silently change the contract. Test the smallest input, a normal case, duplicates or ties where relevant, an adversarial boundary, and a case that exercises the failure path. The expected complexity is depends on operations; common map lookup is expected O(1). Explain both time and auxiliary memory, including recursion or helper structures; do not hide sorting, copying, or repeated scans. If the title omits critical constraints, say what you need to know before committing to a more specialized solution.