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From role-algorithms
Analyzes computational complexity: P vs NP classification, NP-completeness proofs/reductions, approximation algorithms (PTAS/FPTAS), parameterized complexity (FPT/kernelization), randomized algorithms (Las Vegas/Monte Carlo), and heuristics. Use for hardness classification, reductions, algorithm selection.
npx claudepluginhub rnavarych/alpha-engineer --plugin role-algorithmsHow this skill is triggered — by the user, by Claude, or both
Slash command
/role-algorithms:computational-complexityThis skill is limited to the following tools:
The summary Claude sees in its skill listing — used to decide when to auto-load this skill
- Classifying a problem as P, NP-complete, or NP-hard before choosing an algorithm
Designs algorithms with formal analysis including Big-O/Theta/Omega, amortized analysis, recurrences (Master theorem), correctness proofs (invariants, induction), and paradigms (greedy, divide-and-conquer, DP, backtracking). Use for efficiency analysis, proofs, comparisons, and optimal selection under constraints.
Activates approximate and advanced mathematical algorithms (Bloom, HyperLogLog, Count-Min, MinHash/LSH, FFT, JL projection) when classical O(n log n) is insufficient for large-scale data (n ≥ 10⁶).
Big O notation, time/space complexity analysis, and choosing efficient algorithms.
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references/complexity-classes.md — P, NP, NP-complete, NP-hard, PSPACE definitions; common NPC problems; reduction technique step-by-step; recognizing NP-hard problems in practicereferences/approximation-and-fpt.md — approximation ratios, classic results table, PTAS/FPTAS definitions, inapproximability bounds, FPT algorithms, kernelization, treewidth parameterreferences/randomized-and-heuristics.md — Las Vegas vs Monte Carlo, amplification, MCMC, local search, simulated annealing, genetic algorithms, when-to-use decision table