Case 1: 1
Case 2: 2
Case 1: There is only one room, so the police can catch the thief on the first day.
Case 2: There are two rooms. The police can check room 1 on the first day. The worst case is that the thief is in room 2, but in this case the police
can check room 1 on the second day and will catch the thief for sure.