// roads is edge-list. mst is reduced edge-list

sort(roads.begin(), roads.end(), [](Road *r1, Road *r2) {
  return r1->cost < r2->cost;
});

vector<Road*> mst;
for (auto road : roads) { // fills in MST (or forest)
  if (! (road->c1->built && road->c1->built)) {
    road->c1->reachable = true;
    road->c2->reachable = true;
    mst.push_back(road);
  }
  cout << road->c1->id << " " << road->c2->id << " " << road->cost << endl;
}