6 The table shows the distances in miles, where direct rail connections are possible, between 11 cities in a country. The government is proposing to construct a high-speed rail network to connect the cities.
| P | S | F | Ln | Br | Nr | Bm | Ld | Nc | Lv | M |
| P | - | 150 | - | 240 | 125 | - | - | - | - | - | - |
| S | 150 | - | 150 | 80 | 105 | - | 135 | - | - | - | - |
| F | - | 150 | - | 80 | - | - | - | - | - | - | - |
| Ln | 240 | 80 | 80 | - | 120 | 115 | 120 | - | - | - | - |
| Br | 125 | 105 | - | 120 | - | 230 | 90 | - | - | - | - |
| Nr | - | - | - | 115 | 230 | - | 160 | 175 | 255 | - | - |
| Bm | - | 135 | - | 120 | 90 | 160 | - | 120 | - | - | 90 |
| Ld | - | - | - | - | - | 175 | 120 | - | 210 | 100 | 90 |
| Nc | - | - | - | - | - | 255 | - | 210 | - | 175 | - |
| Lv | - | - | - | - | - | - | - | 100 | 175 | - | 35 |
| M | - | - | - | - | - | - | 90 | 90 | - | 35 | - |
- Use the tabular form of Prim's algorithm, starting at vertex P , to find a minimum connector for the network. Draw your minimum connector and give its total length.
- Give one advantage and two disadvantages of constructing a rail network using only the arcs of a minimum connector.
- Use Dijkstra's algorithm on the diagram in the Printed Answer Book, to find the shortest route and distance from P to Nr in the original network.
- Give the shortest distance from P to Nr using only arcs in your minimum connector.