public Iterable<String> certificateOfElimination(
     String team) { // subset R of teams that eliminates given team; null if not eliminated
   solve(getTeamFromName(team));
   return eliminators.get(team);
 }
 public boolean isEliminated(String team) { // is given team eliminated?
   solve(getTeamFromName(team));
   return (eliminators.containsKey(team));
 }