Problem Statement

Provide a function to find the closest two points among a set of given points in two dimensions,   i.e. to solve the   Closest pair of points problem   in the   planar   case. The straightforward solution is a   O(n2)   algorithm   (which we can call brute-force algorithm);   the pseudo-code (using indexes) could be simply: A better algorithm is based on the recursive divide&conquer approach,   as explained also at   Wikipedia's Closest pair of points problem,   which is   O(n log n);   a pseudo-code could be:

Let's start with the solution: