Given n ≤ 106 points with integer coordinates on a 2D plane, for each point compute the number of points with coordinates greater than those of the current one.
I can only think of a solution in which sorts the points using x coordinate, and then for every point count the number of points after it with greater y coordinate. That can be done by using Fenwick tree or segment tree.
Can we do better than that? Can we do something simpler without using a segment tree or Fenwick tree?