I have some questions regarding two similar problems.
We are given ONE set of points in 2D (the plane), and we want to find the closest pair of points within this set. I know the divide and conquer algorithm, but I have seen various sources make different arguments for the number of points one needs to check (3, 5, or 7). Which is actually correct and most optimal? A brief proof of correction for the most optimal solution will be appreciated.
We are given TWO sets of points A and B in 2D (the plane), and we want to find the closest pair (a,b) such that $$$a \in A$$$ and $$$b \in B$$$. How can we solve this? Is this a variant of the above problem with only ONE set of points, or does it require something else?
