6 A mountain ridge separates two populated areas. Networks representing roads connecting the villages in each area are shown below. The numbers on the arcs represent distances in kilometres.
\includegraphics[max width=\textwidth, alt={}, center]{e88abde1-8769-4a3c-b115-031cea08d9a6-7_524_1429_340_319} There is also a mountain road of length 15 kilometres connecting C to Z .

1. A national bus company needs a route from A to X .
   1. Use Dijkstra's algorithm on the complete network, including CZ, to find the shortest route from A to X . Give the route and its corresponding distance.
   2. Would it need fewer computations to use Dijkstra's algorithm on the network for villages A to F to find the shortest route from A to C, and then use Dijkstra's algorithm on the network for villages U to Z to find the shortest route from Z to X? Give a brief justification for your answer.
2. The local council needs to discover which roads it should keep clear of snow during the winter to keep all the villages connected, and the corresponding total length of road.
   1. Use Kruskal's algorithm on the network for villages A to F to find a minimum connector for \(\{ \mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D } , \mathrm { E } , \mathrm { F } \}\). Show your use of the algorithm. Draw your minimum connector.
   2. Use Prim's algorithm on the network for villages U to Z to find a minimum connector for \(\{ \mathrm { U } , \mathrm { V } , \mathrm { W } , \mathrm { X } , \mathrm { Y } , \mathrm { Z } \}\), starting at U . Show your use of the algorithm. Draw your minimum connector.
   3. What is the total length of road that the council must keep clear of snow?