2.
| S | A | B | C | D | E | F | G |
| S | - | 150 | 225 | 275 | 135 | 200 | 280 | 255 |
| A | 150 | - | 265 | 300 | 185 | 170 | 385 | 315 |
| B | 225 | 265 | - | 245 | 190 | 155 | 215 | 300 |
| C | 275 | 300 | 245 | - | 250 | 310 | 280 | 275 |
| D | 135 | 185 | 190 | 250 | - | 145 | 205 | 270 |
| E | 200 | 170 | 155 | 310 | 145 | - | 220 | 380 |
| F | 280 | 385 | 215 | 280 | 205 | 220 | - | 250 |
| G | 255 | 315 | 300 | 275 | 270 | 380 | 250 | - |
The table shows the costs, in pounds, of connecting seven computer terminals, \(\mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D } , \mathrm { E } , \mathrm { F }\) and G, to a server, S.
- Use Prim's algorithm, starting at S , to find the minimum spanning tree for this table of costs. You must clearly state the order in which you select the edges of your tree.
(3) - Draw the minimum spanning tree using the vertices given in Diagram 1 in the answer book. State the minimum cost, in pounds, of connecting the seven computer terminals to the server.
- Explain why it is not necessary to check for cycles when using Prim's algorithm.