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algorithms-complexity-guide

Analyze algorithm complexity and computational efficiency for research

skills/domains/cs/algorithms-complexity-guide/SKILL.md

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# Algorithms and Complexity Guide

A skill for analyzing algorithm complexity and computational efficiency in research contexts. Covers asymptotic notation, common complexity classes, NP-completeness, amortized analysis, and strategies for presenting algorithmic contributions in papers.

## Asymptotic Notation

### Big-O, Omega, and Theta

```
O(f(n))   -- Upper bound (worst case, "at most")
            T(n) is O(f(n)) if T(n) <= c * f(n) for large n

Omega(f(n)) -- Lower bound (best case, "at least")
               T(n) is Omega(f(n)) if T(n) >= c * f(n) for large n