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Notes for Chapter 23 641 23-4 Alternative minimum-spanning-tree algorithms In this problem, we give pseudocode for three different algorithms. Each one takes a connected graph and a weight function as input and returns a set of edges T. For each algorithm, either prove that T is a minimum spanning tree or prove that T is not necessarily a minimum spanning tree. Also describe the most efficient imple- mentation of each algorithm, whether or not it computes a minimum spanning tree. a. MAYBE-MST-A(G, w) 1 sort the edges into nonincreasing order of edge weights uw 3 for each edge e, taken in nonincreasing order by weight 4 if T -le is a connected graph T=T-{e} 6 return T b. MAYBE-MST-B (G, w) 2 for each edge e, taken in arbitrary order 3 if TU te) has no cycles 4 5 return T T=TU{e} c. MAYBE-MST-C(G, w) 2 for each edge e, taken in arbitrary order 4 if T has a cycle c let e' be a maximum-weight edge on c 6 7 return T