Chapter 2: The Profiling Mindset

"Big-O tells you how it scales. Profiling tells you how it runs."

🏛️ The Academic View

We teach that \(O(1)\) is always better than \(O(N)\). We ignore constants (\(C\)) and hardware constraints.

🏗️ The Engineering Reality

A complex \(O(1)\) hash lookup can be slower than a simple \(O(N)\) loop for small \(N\) due to CPU caching and hash collision overhead.

In this chapter, we build the ArpraxProfiler: * Measuring Wall-Clock Time vs. CPU Time. * Tracing memory allocation (Heap pressure). * Visualizing the "Crossover Point" where asymptotic complexity matters.