complexity

What I do

• Analyze time and space complexity of algorithms
• Classify problems by complexity classes (P, NP, PSPACE)
• Prove NP-completeness and NP-hardness
• Apply asymptotic notation (Big-O, Ω, Θ)
• Design approximation algorithms
• Analyze randomized algorithm complexity

When to use me

When optimizing algorithms, proving computational limits, or classifying problem difficulty.

Key Concepts

• Big-O: f = O(g) if ∃c,n₀: f(n) ≤ cg(n) for n ≥ n₀
• P: Problems solvable in polynomial time
• NP: Problems verifiable in polynomial time
• NP-Complete: Hardest problems in NP, polynomial-time reduction
• Space Complexity: Memory requirements vs input size
• Polynomial-Time Reduction: Transform one problem to another preserving complexity