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I know QuickHull algorithm runs in Theta(n), if convex hull is triangular or it has constant size.

What's this means?

I'm not sure about the shape (if it looks a triangle), because the algorithm uses 4 extreme points.

Thanks

Nelson A. Morais
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1 Answers1

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If the number of vertices of the convex hull, let H, is a constant (doesn't depend on N), then QuickHull takes a time proportional to N (more precisely c1.N < T < c2.N for two constants c1 and c2).

When H=3, the hull is a triangle. Regardless the way the algorithm works, it has to return this triangle. Careful implementations should even work for H=2 (a line segment) or H=1 (a single point).