One problem states:
Given two sets $A_1$ and $A_2$ with $n_1$ and $n_2$ points respectively, design an algorithm to compute (if it exists) a disk containing all the points in $A_1$ and none in $A_2$.
My idea is to calculate the minimum spanning circle of both sets (that takes linear time) and see if they intersect (I don't know the running time of this. Maybe you can draw a segment between both centers and see which circle comes first if you see it form the left). If they do, we don't have a solution.
Is this idea correct? If so, it is the best one? If not, how can I do it?