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N Points on a Plane

  1. Aug 26, 2005 #1
    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 :)
     
  2. jcsd
  3. Aug 26, 2005 #2
    randomly pick point p. then choose point P+1.... :-p
     
  4. Aug 26, 2005 #3

    AKG

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    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).
     
  5. Aug 26, 2005 #4
    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)).
     
  6. Aug 26, 2005 #5

    Hurkyl

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    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)?
     
  7. Aug 27, 2005 #6
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