📜 WAYPOINT LESSON

Growth, not stopwatches

⭐ beginner⏳ 13 min read📍 Lesson 78 of 85

Big-O describes how work grows with input size — counting operations beats timing a machine.

Counting, not timing

A stopwatch measures a machine; growth describes an algorithm. Count how the work grows as input size n grows:

| Shape | Example | n = 10 | n = 10,000 | | --- | --- | --- | --- | | O(1) | dictionary lookup | 1 | 1 | | O(log n) | binary search | ~3 | ~14 | | O(n) | one loop | 10 | 10,000 | | O(n²) | nested loops | 100 | 100,000,000 |

Nested loops multiply: an outer loop over n with an inner loop over n is n × n. That last row is why "it works on my test data" is not a performance argument — a fix that turns 100,000,000 steps into 10,000 is the difference between a feature and a freeze.