Constant Amortized Time

Question

What is meant by \"Constant Amortized Time\" when talking about time complexity of an algorithm?

Answer 1

To develop an intuitive way of thinking about it, consider insertion of elements in dynamic array (for example std::vector in C++). Let's plot a graph, that shows dependency of number of operations (Y) needed to insert N elements in array:

Vertical parts of black graph corresponds to reallocations of memory in order to expand an array. Here we can see that this dependency can be roughly represented as a line. And this line equation is Y=C*N + b (C is constant, b = 0 in our case). Therefore we can say that we need to spend C*N operations on average to add N elements to array, or C*1 operations to add one element (amortized constant time).