Moving out of your apartment

After having successfully completed the AI course, you get a job in another town (as an AI expert of course), and you have to move out of your apartment. You have already packed all your belongings in nine moving boxes, scattered around the apartment, now all you have left to do is to move these boxes into the moving truck, which is parked just outside of the apartment. The boxes are too big to carry, so you have to push them between the rooms. The following graph shows the four rooms in the apartment, the truck, how many boxes are initially in which rooms, and how the rooms are connected:

On each turn, you can either move or push a box into an adjacent location, in any direction: north, south, east, west. When this story begins, you have just parked the truck.

Implement the given scenario & Formulate this problem as a search problem, i.e.:

Design suitable representation of the search states?
Design a method of initial state
Set goal state
Calculate path cost at each step.

livingroom
2 boxes
bedroom
3 boxes
kitchen
hall
truck
3 boxes
1 box
boxes
no

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