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
- Formalize the problem, constraints, and success criteria.
- Enumerate candidate strategies at the same abstraction level.
- Evaluate correctness risk, complexity, and implementation/operational tradeoffs.
- Select algorithm and data structures with explicit rationale.
- Define edge-case tests and evidence needed to validate the decision.
Failure Conditions
- Stop when constraints are unknown or contradictory.
- Stop when no candidate has a defensible correctness argument.
- Escalate when feasible options conflict with mandatory resource budgets.