Today’s invention is a variant on the domestic robot vacuum cleaner.
This starts by performing the usual random sweeps within a room, but over time, it monitors how much dirt has been collected from which part of the room (its movements could be recorded with reasonable precision using eg crude ultrasound reflections from walls and furniture).
Once the cleaner realises that most crud is collected from beside the front door and under the table, it subsequently reprograms its movements so as to emphasise any such regions.
Its attention would thus come to be paid to areas in proportion to the history of dirt collected there.