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Asked: 2026-06-15T17:55:35+00:00

Given n points , no three of them are collinear. i and j ,

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Given n points , no three of them are collinear.
i and j , 2 points are friends if the circle formed with i &j as diameter does not contain any of the other points.
Give all such points in O(nlogn)

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1 Answer

  1. Editorial Team

    You are trying to compute what is known as the relative neighborhood graph in the literature. The lune determined by the two points must be empty. There is quite a bit of literature on this topic. You could start with the Wikipedia article.
    As user tmyklebu says, it is a subset of the Delaunay triangulation.

          Lune

    Correction. I misread the conditions, as Asiri kindly explained. The relevant graph is instead the Gabriel Graph, which also has a considerable literature:

          enter image description here

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