What is an algorithm that solves this problem: Given N circles (defined by center coords and radius), what is the maximum vector sum of points, choosing one point from each circle. Note that the circles may have different radii, may overlap, may be the same or different, etc.
For example, given circles c=(-10,0)r=1 and c=(10,0)r=1, the answer is 2 (choosing the point closest to the origin from one circle, and furthest on the other - summing them yields a vector with abs val 2). Choosing the furthest on each circle would cancel each other out.
Intuitively, I suspect the answer could be: 1. Take the vector sum of the centers of all the circles = V1. This vector is in the same direction as the desired result vector. 2. For each circle, choose the point that is in that direction from its center. I.e. choose the point (center + radius * normalized(V1)) 3. Sum these points to yield the answer
But I am in no way certain and unsure how to prove it's correct (if it is correct)
(This is my first question on this site, please be gentle - let me know how I can improve this question)