2. (i) Use the binary search algorithm to try to locate the name SABINE in the following alphabetical list. Explain each step of the algorithm.
- ABLE
- BROWN
- COOKE
- DANIEL
- DOUBLE
- FEW
- OSBORNE
- PAUL
- SWIFT
- TURNER
(ii) Find the maximum number of iterations of the binary search algorithm needed to locate a name in a list of 1000 names.
| A | \(B\) | C | \(D\) | \(E\) | \(F\) |
| A | - | 10 | 12 | 13 | 20 | 9 |
| B | 10 | - | 7 | 15 | 11 | 7 |
| C | 12 | 7 | - | 11 | 18 | 3 |
| D | 13 | 15 | 11 | - | 27 | 8 |
| E | 20 | 11 | 18 | 27 | - | 18 |
| \(F\) | 9 | 7 | 3 | 8 | 18 | - |
The table shows the distances, in metres, between six nodes \(A , B , C , D , E\), and \(F\) of a network.
- Use Prim's algorithm, starting at \(A\), to solve the minimum connector problem for this table of distances. Explain your method and indicate the order in which you selected the edges.
- Draw your minimum spanning tree and find its total length.
- State whether your minimum spanning tree is unique. Justify your answer.
(ii) A connected network \(N\) has seven vertices.