The answer
Because 99% of insertions take O(1) time, but occasionally the array runs out of space and must perform an O(N) resize. Amortized analysis proves the average cost remains O(1).
Amortized Time Complexity: What it Means and When to Use it
Why do dynamic arrays need amortized analysis?
More FAQs in Amortized Time Complexity: What it Means and When to Use it
It is the average time taken per operation over a large sequence of operations, smoothing out the cost of rare, expensive worst-case events.
No. Pure O(1) guarantees every single operation is instant. Amortized O(1) means it is instant *most* of the time, but you will occasionally experience a slow operation.
Yes. Inserting into a Hash Map is amortized O(1). Like dynamic arrays, Hash Maps occasionally must rehash and resize their internal buckets, which takes O(N) time.
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