All the problems are now completed.
I wasn't expecting there to be no second part, but welcome it nonetheless.
For the first part of the problem, I started by building the constellations as I receive the stars, but that always gave me numbers too high as the link between two parts of a constellations could come later in the input. So I added a phase to merge constellations that could fit together and that gave me the correct answer.
This is the end of the problems, so the posts will end here. I will post a conclusion in a couple of days with some things I learned, stuff I would do again, stuff I wouldn't do again, etc.