Big-O Notation Explained for Java Fresher Interviews

Big-O notation describes how the running time or memory of an algorithm grows as the input size, n, gets larger. The important word is grows. It's not telling me how many seconds something takes; it's telling me the shape of the curve as the input scales up. When I write Big-O, I deliberately drop constants and lower-order terms, because as n gets large those stop mattering. So two n plus five is just O of n, and n squared plus n is just O of n squared, because next to n squared the plain n is negligible. Big-O usually refers to the worst case, an upper bound on the work, which is what I care about in production because that's the scenario I have to survive. The reason it matters so much in interviews is that it's a shared, hardware-independent language for comparing solutions. If I say my approach is O of n instead of O of n squared, the interviewer immediately knows it scales, regardless of how fast my machine is. For perspective, a quadratic algorithm on a thousand elements is about a million operations, while a linear one is a thousand, and a logarithmic one is around ten. The one nuance I'd add is that Big-O ignores constant factors, so for small inputs an algorithm with a better Big-O can actually be slower in practice. But as the data grows, the growth rate is what dominates, and that's exactly what Big-O captures.