时间复杂度和列表中的add（）

Question

Here's an algorithm. Since it's just a for loop I would see it as O(N), but I've been told it's O(N2). I've been told that it's because of list.add, but that doesn't change N? So why the change in time complexity?

public static void mystery3(List<String> list) {
        for (int i = 0; i < list.size() - 1; i += 2) {
            String first = list.remove(i);
            list.add(i + 1, first);
        }
    }

Answer 1

If you are using an array (Arraylist), remove(i) takes O(n) and the add(...) takes O(n). That's because finding element at index i takes O(1) but resizing takes O(n).

If you use an linked list, remove(i) takes O(n) and `add(...) takes O(n). That's because finding element at index i takes O(n) and removing takes O(1).

Since you a calling the methods n/2 times, its whole runtime is O(n^2).