Problem

We are given a set P = p1, p2, .. ., pN of N points in a plane. A Voronoi diagram is a par...

We are given a set P = p1, p2, .. ., pN of N points in a plane. A Voronoi diagram is a partition of the plane into N regions Ri such that all points in Ri are closer to pi than any other point in P. Figure 1 shows a sample Voronoi diagram for seven (nicely arranged) points. Give an O(N logN) algorithm to construct the Voronoi diagram.

Figure: Voronoi diagram

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