Why does an O(n²) algorithm feel instant for 10 items but crawl for a million? Watch each complexity class grow, and see how long each would really take at one operation per nanosecond — the numbers get absurd fast.
Big-O ignores constants and describes how the work scales with input size n. The chart plots log₁₀(operations) vs n, so a straight line that climbs steeply means exponential growth. The table converts operations to wall-clock time at 1 ns each: n! for n=30 already exceeds the age of the universe (~1.4×10¹⁰ years) — which is why "try every permutation" only works for tiny inputs.