5 The network below represents a single-track railway system. The vertices represent stations, the arcs represent railway tracks and the weights show distances in km. The total length of the arcs shown is 60 km .
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1. Apply Dijkstra's algorithm to the network, starting at \(G\), to find the shortest distance (in km ) from \(G\) to \(N\) and write down the route of this shortest path. Greg wants to travel from the station represented by vertex \(G\) to the station represented by vertex \(N\). He especially wants to include the track \(K L\) (in either direction) in his journey.
2. Show how to use your working from part (i) to find the shortest journey that Greg can make that fulfils his requirements. Write down his route. Percy Li needs to check each track to see if any maintenance is required. He wants to start and end at the station represented by vertex \(G\) and travel in one continuous route that passes along each track at least once. The direction of travel along the tracks does not matter.
3. Apply the route inspection algorithm, showing your working, to find the minimum distance that Percy will need to travel. Write down those arcs that Percy will need to repeat. If he travels this minimum distance, how many times will Percy travel through the station represented by vertex \(L\) ?