1. The network below shows the paths to success from L (log cabin) to W (White House). The first number is the cost of building a freeway along the edge and the second is the number of trees (in thousands) that would have to be cut down. 8,4 8,5 8,41 i 12,4 7,2 3, 1 4,4 5, 1 3,3 4, 1 6,3 5, 1 7,2 4,2 L 3,21 a d 4,2 15, 2 6,4 k 5,3 8,3 8,3 4,2 4. 1 5,1 W 7,2 6,3 5,5 6,2 h m (a) Use Kruskal's algorithm to find a minimum-cost set of freeways connecting all the vertices together. (b) Court action by conservationists rules out use of edges (c, e), (d. f), and (k, W). Now find the minimum-cost set of freeways. (c) Find two nonadjacent vertices such that the tree in part (a) does not contain the cheapest path between them. (d) Use Prim's algorithm to find a set of connecting freeways that minimizes the number of trees cut down.