How is the time complexity determined when adding an element to an ArrayList?

The amortized time complexity of adding an element to an ArrayList is usually O(1). This is because:

• If the internal array of the ArrayList has free space, the new element is simply written to the next position — this operation takes constant time O(1).
• If the internal array is full, it is expanded: a new larger array is created, and all elements are copied there. This operation takes O(n), where n is the current size of the list.

However, expansion does not occur with every addition, but only periodically, so the average (amortized) complexity of adding remains O(1).

Example:

ArrayList<Integer> list = new ArrayList<>();
list.add(10); // Amortized O(1)