Amortized

Monthly rent is cheap. Once a year the boiler dies and it’s expensive. Amortized is the per-month cost once you spread the boiler bill back across the year.

A hash table insert is O(1) most of the time. Once in a while, it triggers a full rehash costing O(n). Spread across all the cheap inserts that came before, the average is still O(1). That’s “amortized O(1).”

Different from “average case”. Amortized is a worst-case guarantee on a sequence of operations, not a probabilistic claim about one.