6 [Answer part (i) of this question on the insert provided.]
The diagram shows a simplified version of an orienteering course. The vertices represent checkpoints and the weights on the arcs show the travel times between checkpoints, in minutes.
\includegraphics[max width=\textwidth, alt={}, center]{b1227633-913e-41a9-8bf8-1f064056963e-4_483_931_461_630}

1. Use Dijkstra's algorithm, starting from checkpoint \(\boldsymbol { A }\), to find the least travel time from \(A\) to \(D\). You must show your working, including temporary labels, permanent labels and the order in which permanent labels were assigned. Give the route that takes the least time from \(A\) to \(D\).
2. By using an appropriate algorithm, find the least time needed to travel every arc in the diagram starting and ending at \(A\). You should show your method clearly.
3. Starting from \(A\), apply the nearest neighbour algorithm to the diagram to find a cycle that visits every checkpoint. Use your solution to find a path that visits every checkpoint, starting from \(A\) and finishing at \(D\).