Computational complexity analysis
Reason about resource growth as inputs scale
Complexity analysis derives how time, space or other resources grow with input size under a specified computation model. Worst-case, average-case, expected and amortised bounds answer different questions. Big O supplies an upper bound, while Theta states a tight asymptotic order. Mathematical analysis complements implementation benchmarks by separating scaling claims from hardware-specific timings.
Choose it when the question concerns scalability, algorithmic feasibility or guarantees over classes of inputs, and the algorithm, cost model and relevant input size parameters can be defined precisely.
Strengths
- Provides guarantees beyond tested input sizes
- Separates algorithmic growth from a particular machine
Limitations
- Asymptotic bounds can hide substantial constants
- Average-case claims depend on an input distribution
Know the boundary
Fast benchmark timings do not prove a complexity bound, and a better asymptotic bound need not be faster at small sizes.