Why is append to a dynamic array amortized O(1)?

Answer

Most appends write into free capacity in O(1). Occasionally the array resizes and copies O(n) elements; spread over many appends, the average cost per append stays O(1) (amortized).

let capacity = 4;
let size = 0;

function append(x: number) {
  if (size === capacity) {
    capacity *= 2; // resize + copy O(n)
  }
  size++;
}