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/O, cache, contention).
4. Compare candidates against budgets and identify breakpoints.
5. Publish recommendation, residual risks, and re-evaluation triggers.

Failure Conditions

• Stop when workload/scale assumptions are missing.
• Stop when dominant cost drivers are unmodeled.
• Escalate when no candidate can satisfy mandatory budgets.