digital plumber

approach

each line is parsed into a program id and the ids it talks to, and every pair is unioned in a small union-find (UFS) with path compression.

part 1 counts the ids whose root matches the root of 0. part 2 tallies the ids by root and returns how many distinct roots there are, which is the number of groups.

the trick

connected components come straight out of union-find: one union per pipe, then count roots.

def _root(self, a):
    if self.parents[a] == a:
        return a
    ra = self._root(self.parents[a])
    self.parents[a] = ra
    return ra