4 In Paris, there is a park where there are statues of famous people; there are many visitors each day to this park. Lighting is to be installed at nine places, \(A , B , \ldots , I\), in the park. The places have to be connected either directly or indirectly by cabling, to be laid alongside the paths, as shown in the diagram. The diagram shows the length of each path, in metres, connecting adjacent places.
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1. 1. Use Prim's algorithm, starting from \(A\), to find the minimum length of cabling required.
   2. State this minimum length.
   3. Draw the minimum spanning tree.
2. A security guard walks along all the paths before returning to his starting place. Find the length of an optimal Chinese postman route for the guard.