Question

I have a set of n consecutive operations which each one runs in O(1) amortized complexity.
Can I say that the whole set runs in O(n) worst case time complexity?
How do I prove it ?

Answer 1

You didn’t give a code sample so I consider n consecutive operations as an algorithmic for-loop. So the task is to estimate worst case complexity of

for(int i=1; i<n; i++)
{
   f(x) // O(f(x)) = O(1)
}

In other words

Sum(1,n) 1 = O(1) + O(1) + ... O(1) //n-times

or

O(1) + O(1) + ... O(1) = O(n)O(1) = O(n)