Use the PR quadtree to implement an efficient solution to Problem 6.5. That is, store the set of points in a PR quadtree. For each point, the PR quadtree is used to find those points within distance D that should be equivalenced.

What is the asymptotic complexity of this solution?

Data from in Problem 6.5.

Implement a city database using the k-d tree. Each database record contains the name of the city (a string of arbitrary length) and the coordinates of the city expressed as integer x- and y-coordinates. Your database should allow records to be inserted, deleted by name or coordinate, and searched by name or coordinate. You should also support region queries, that is, a request to print all records within a given distance of a specified point.