Binary search is O(log n), but that's not the whole story

Everyone learns binary search as the textbook example of O(log n) efficiency. Halve the search space, halve it again, find your answer in logarithmic time. Clean. Elegant. Fast. That framing isn't wrong. It's just incomplete, and the parts it omits are exactly what bite you in production. The Big-O notation tells you how the algorithm scales. It says nothing about when it's the wrong tool entirely, or why a "slower" algorithm sometimes wins in practice. Let me walk through what's actually happen