algorithm-designlisted

# Algorithm Design ## Overview Use this skill to produce an implementable algorithm decision with explicit correctness reasoning and tradeoff analysis. ## Scope Boundaries - Use this skill when the task matches the trigger condition described in `description`. - Do not use this skill when the primary task falls outside this skill's domain. ## Inputs To Gather - Objective, required outputs, and correctness conditions. - Input constraints (size ranges, distribution, adversarial cases, update/query patterns). - Resource budgets (latency, throughput, memory) and operational constraints. - Mutation/concurrency requirements and ordering guarantees. ## Deliverables - Problem model with assumptions, invariants, and edge-case catalog. - Candidate strategy comparison (pros/cons and applicability bounds). - Selected algorithm and data-structure decision with correctness argument. - Risk list and follow-up verification plan. ## Quality Standard - Assumptions are explicit, measurable, and linked to requirement context. - Correctness argument includes invariant/termination reasoning or equivalent proof sketch. - Selected and rejected options include complexity and operability tradeoffs. - Data-structure choices are justified by access/mutation patterns. - Edge cases and failure modes are identified before implementation. ## Workflow 1. Formalize the problem, constraints, and success criteria. 2. Enumerate candidate strategies at the same abstraction level. 3. Evaluate correctness ris