algorithmic_analysis

Time complexity analysis evaluates how an algorithm's runtime grows with input size. Establish lower bounds (Ω) first, then enumerate 5-8 candidate approaches with trade-offs documented against canonical references like CLRS and Knuth TAOCP to determine whether your algorithm meets theoretical limits.

Formal proof of correctness documents assumptions, invariants, and termination conditions across diverse computational models. This Skill generates phase-specific reports with cited proof structures grounded in literature, comparison tables, and formal reasoning to establish both correctness and space complexity suitability.

Lower-bound analysis precedes candidate selection to establish the theoretical minimum complexity achievable. Apply rigorous analysis first to determine Ω bounds, then evaluate multiple data structures and algorithms against these bounds to avoid selecting suboptimal approaches for your problem constraints.

Candidate exploration generates structured comparison tables across 5-8 approaches, documenting time and space complexity, correctness status, and trade-offs. Each candidate is evaluated against established lower bounds and cited against authoritative sources to support informed selection.

Output artifacts include phase-specific reports detailing complexity derivations, formal proofs with proof structures, comparison matrices of candidate algorithms, and citations to canonical references. This documentation supports both immediate decisions and future auditing of algorithmic choices.

Yes. This Skill applies rigorous complexity and correctness analysis across diverse computational models, supporting problems requiring multiple candidate evaluations, lower-bound proofs, and literature-grounded comparisons with formal output including phase reports and structured proof artifacts.