Act as a senior software engineer with 10+ years of experience in optimizing code performance. Explain how to implement memoization in [LANGUAGE] for [FUNCTION_TYPE] functions, specifically focusing on [USE_CASE]. Provide a step-by-step guide, including: 1) The basic concept of memoization, 2) How to identify functions that would benefit from memoization, 3) A code example showing before/after implementation, 4) Common pitfalls to avoid (e.g., cache size management, stale data), and 5) How to test the performance improvement. Tailor your explanation for [AUDIENCE_TYPE] developers who are familiar with [RELATED_CONCEPT] but new to optimization techniques.