Nice answer. But since I studied a lot of optimization, I saw my linear programming answer first. On an interview, typically want to give the first correct an

Nice answer. But since I studied a lot of optimization, I saw my linear programming answer first. On an interview, typically want to give the first correct answer do find. My answer is more general, and that is goodness. Indeed, you mentioned that your answer solves a more general question than intended in the OP. So, you seem to like the generality of your answer but not the generality of mine. The generality of my answer applies to convex polytopes, convex hulls, in any finite dimension, and dimension 3 should be of interest in some cases, e.g., see if two objects intersect. That might be of interest in some of robotics. If the polytopes are determined by points, then my answer solves the problem and we are looking for a separating hyper plane. If each polytope is determined by the intersection of half spaces determined by hyperplanes, then we are looking for a point in common, and again we can use linear programming. So, given points we are looking for a separating hyper plane, and given hyper planes we are looking for a point. Smells like a nice case of duality. Farkas lemma, a special case of my solution, is central to the Kuhn-Tucker conditions in nonlinear optimization. Since the ML people are interested in optimization, they might welcome Farkas lemma and my more general solution. And, again, my answer really is part of "algorithms and data structures" which was the focus of the questions. So, now we are into what is commonly called computational geometry, commonly regarded as part of computer science, and heavily about algorithms. E.g., doing nearest neighbor searches via k-D trees (in Sedgwick) and cutting planes is part of computer science, computational geometry, trees, data structures, and algorithms. For the linear programming, just call a subroutine, e.g., IBM's old OSL (optimization subroutine library). My more general answer indicates that I would be a good person to work with. The question is a separation problem. Well, so as to have readers be more comfortable, I did omit mention of the Hahn-Banach theorem. For curious readers, there are lots of applications of that classic result in D. Luenberger, Optimization by Vector Space Methods. "Hard to work with ...". How 'bout hard to please?