The irony is that his solution has an unnecessary log(n) term, because it's finding each point independently instead of taking advantage of the fact that the input points are also a dense grid. ;) so it can probably run 2-10x faster than the optimized version, assuming that the function call to bin search is probably a lot more expensive than filling in the grid, which R can do internally.

(You don't have to binary search each time, you have a known starting point from the previous point. So you binary search once to find the top-left point and the rest is just checking if you moved into the next global grid cell.)