3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ca57c64b-0b33-4179-be7f-684bd6ea2162-06_764_1547_314_355}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
[The total weight of the network is \(139 + x + y\) ]
- Explain what is meant by the term "tree".
Figure 3 represents a network of walkways in a warehouse.
The arcs represent the walkways and the nodes represent junctions between them.
The number on each arc represents the length, in metres, of the corresponding walkway.
The values \(x\) and \(y\) are unknown, however it is known that \(x\) and \(y\) are integers and that
$$9 < x < y < 14$$ - Use Dijkstra's algorithm to find the shortest route from A to M.
- State an expression for the length of the shortest route from A to M .
The warehouse manager wants to check that all of the walkways are in good condition.
Their inspection route starts at B and finishes at C .
The inspection route must traverse each walkway at least once and be as short as possible.
- State the arcs that are traversed twice.
- State the number of times that H appears in the inspection route.
The warehouse manager finds that the total length of the inspection route is 172 metres.
- Determine the value of \(x\) and the value of \(y\)