Given a collection of rooms where Alibada is in one and moves one room a day to an adjacent room, write a program to determine if you can find Alibada with the given list of rooms.

This problem involves tracking the possible locations of Alibada over time. Alibada starts in one room and moves to an adjacent room each day. We are given a strategy of rooms to search. The core idea is to maintain a set of possible rooms Alibada could be in. Initially, all rooms are possible. As we search a room, we eliminate it as a possibility for Alibada's current location. Then, we update the possible locations for the next day by considering that Alibada must have moved to an adjacent room from one of the previously possible locations. If at any point there are no possible rooms left for Alibada to be in, it means our search strategy has failed to find Alibada. The goal is to determine if the given search strategy guarantees finding Alibada.