1) Trace the Prim MST algorithm to determine a minimum spanning tree with V. as the root. The adjacency lists for G are given below. The weights are in parentheses.
a) the order in which the edges are added to the tree &
b) the fringe list after each new vertex is added to the tree. Assume that the fringe list is maintained as an unordered linked list with insertions made ar the head
0: 2(12) -> 3(15) -> 4(7) -> 6(8)
1: 2(11) -> 3(2)
2: 0(12) -> 1(11) -> 4(9) -> 7(8)
3: 0(15) -> 1(2) -> 5(3)
4: 0(7) -> 2(9) -> 5(8) -> 8(5)
5: 3(3) 4(8)
6: 0(8) -> 7(6) -> 8(R)
7: 2(8) -> 6(6)
8: 4(5) -> 6(8)

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Prim's algorithm is a greedy algorithm, which always pick the available edge with the less weight. A common implementation is to assign a key to each vertex, set all the keys to infinite except the root, which is set to 0. Put the root into an empty list where the tree will be contained. Update the connected vertices keys to the connecting edges weigths. Choose the minimum weight edge, and put the connected vertex into...

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