Solving Riddle: Find Closest 2 Points on a Plane in O(N)

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Here's a riddle I'm having trouble solving:
There are N points on a plane. Find the two points that are closest, in time better than O(N^2).

Any idea?
Thanks :)
 
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randomly pick point p. then choose point P+1... :-P
 
Nice problem. Are you sure there is a solution? I'll think on it some more if you know that it can be solved (well, I'll think on it anyways).
 
I know there's a so-called "simple" solution that requires O(N * log^2(N)), and a more complex one that requires O(N * log(N)).
 
Here's a hint:

If the problem was "Given an arbitrary function f(P, Q) of two points, find the pair of points that minimizes f(P, Q)", can you prove that the best algorithm is Θ(n²)?
 

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