algorithm-complexity-analysislisted

# Algorithm Complexity Analysis ## Overview Use this skill to quantify whether candidate approaches can meet performance and resource constraints at expected scale. ## 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 - Candidate algorithms and dominant operations. - Input-scale assumptions (current, expected, and stress ranges). - Resource budgets (latency targets, throughput targets, memory limits). - Runtime context (I/O patterns, cache behavior, concurrency contention). ## Deliverables - Complexity report with worst-case, average-case, and amortized bounds (as applicable). - Memory and auxiliary-space analysis, including peak usage assumptions. - Budget-fit assessment and scalability breakpoints. - Recommendation with residual risk and monitoring triggers. ## Quality Standard - Complexity claims are tied to explicit assumptions and units. - Dominant operations and constants relevant at target scale are identified. - CPU, memory, I/O, and contention effects are addressed where applicable. - Analysis states confidence level and uncertainty sources. - Decision includes conditions that would invalidate the current choice. ## Workflow 1. Define workload model, scale assumptions, and performance budgets. 2. Derive formal bounds for each candidate's critical operations. 3. Evaluate real-world cost drivers (constants, I