What is the worst-case time complexity of inserting n2 elements into an AVL tree with n elements initially?

The worst-case time complexity of inserting an element into an AVL tree is O(log n). This is because an AVL tree is a self-balancing binary search tree, and the heights of the two child subtrees of any node differ by at most one. Therefore, lookup, insertion, and deletion all take O(log n) time in both the average and worst cases.

If we are inserting n^2 elements into an AVL tree with n elements initially, we would perform the insertion operation n^2 times. Since each operation has a time complexity of O(log n), the total time complexity would be O(n^2 log n).