VietMX Staff asked 3 years ago
If you do an operation say a million times, you don’t really care about the worst-case or the best-case of that operation – what you care about is how much time is taken in total when you repeat the operation a million times. Essentially amortised time means “average time taken per operation, if you do many operations”. Amortised time doesn’t have to be constant; you can have linear and logarithmic amortised time or whatever else.
A common example is the dynamic array. If we have already allocated memory for a new entry, adding it will be O(1). If we haven’t allocated it we will do so by allocating, say, twice the current amount. This particular insertion will not be O(1), but rather something else.
What is important is that the algorithm guarantees that after a sequence of operations the expensive operations will be amortised and thereby rendering the entire operation O(1).
