I failed my first algorithm interview because I said "it depends" when asked about the time complexity of a search function. The interviewer wanted O(log n). I knew it was a binary search. I even knew it was logarithmic. But I panicked and started rambling about cache lines and branch prediction and whether the array fit in L1. The interviewer's eyes glazed over. "It depends" is technically correct and practically useless when someone wants to know if your solution will still work when the input grows from 1,000 to 1,000,000. That interview taught me something that took years to fully internalize: Big O notation isn't about precision. It's about the shape of growth. It tells you how an algorithm behaves as the input gets large; not the exact number of operations, not the wall-clock time, but the curve. And once you see the curves, everything clicks. Why Big O matters outside of interviews Let me be direct: most working programmers I know learned Big O for interviews and promptly forgot it. That's a mistake.…