Big-O Notation

Big-O answers one question: as the input grows, how fast does the work grow? It ignores constants and small stuff and keeps only the term that dominates for large inputs. Imagine looking for a name in a phone book. Reading every page one by one is O(n): double the pages, double the work. Flipping to the middle and halving the search each time is O(log n): double the pages, add just one more step. A nested loop that compares every item to every other item is O(n^2): 10 items -> 100 checks, 100 items -> 10,000 checks. That's why O(n^2) code feels fine on your laptop and dies in production. Rule of thumb: O(1) < O(log n) < O(n) < O(n log n) < O(n^2). Aim to move left.