Triangle partitioning

Question

This was a problem in the 2010 Pacific ACM-ICPC contest. The gist of it is trying to find a way to partition a set of points inside a triangle into three subtriangles such that

Answer 1

I think there is a linear time algorithm. See the last paragraph of the paper "Illumination by floodlights- by Steiger and Streinu". Their algorithm works for any k1, k2, k3 that sum up to n. Therefore, k1=k2=k3=n/3 is a special case.

Here is the link where you can find the article. http://www.sciencedirect.com/science/article/pii/S0925772197000278 a CiteSeerX link is http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.4634