In Exercise 14.12, assume the representation from Exercise 14.11.
In Exercise 14.13, what is the complexity if the tree is height balanced?
In the balancing algorithm for quadtrees, which runs in O(dn),
where n is the size of the tree,
the O(d)-part is due to searches for neighbor nodes
to check if they are more finely divided than the current node.
Here, d denotes the height of the quadtree.
Consider maintaining a constant amount of extra information
in the internal nodes of a quadtree such that this information
can be obtained in constant time, thereby reducing the time
complexity of the balancing algorithm to O(n).