4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d3f5dcb4-3e23-4d78-965a-a1acaac13819-05_712_1433_223_315}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Dijkstra's algorithm has been applied to the network in Figure 2.
A working value has only been replaced at a node if the new working value is smaller.
- State the length of the shortest path from A to G .
- Complete the table in the answer book giving the weight of each arc listed. (Note that arc CE and arc EF are not in the table.)
- State the shortest path from A to G.
It is now given that
- when Prim's algorithm, starting from A, is applied to the network, the order in which the arcs are added to the tree is \(\mathrm { AB } , \mathrm { BC } , \mathrm { CD } , \mathrm { CE } , \mathrm { EF }\) and FG
- the weight of the corresponding minimum spanning tree is 80
- the shortest path from A to F via E has weight 67
- Determine the weight of arc CE and the weight of arc EF , making your reasoning clear.