Answer:
- Graph: see attached
- Path: FABFCADFEBDE
Explanation:
Given a floor plan with rooms labeled A to F, you want a graph with edges representing the connections between rooms, and a path through every door once.
Graph
The graph will have a node assigned to each room. Node F represents the outside area. An edge will connect nodes that have a doorway between the corresponding rooms.
A graph is shown in the attachment.
Path
A path through all doors once will exist if there are 0 or 1 nodes of odd degree. (An odd number of edges connect to the node.) Node E is of degree 3, and node F is of degree 5. All the others have an even number of edges connected, so the desired path can exist. It must begin on one of nodes E or F and end on the other one.
The path can be found by starting at node F (or E) and following any edge that hasn't been followed before. The end node must be E (or F). You don't really need to be too concerned about getting stuck somewhere.
One possible path through all the doors is ...
FABFCADFEBDE
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