[Solved] Note Either Prove Algorithm Works Arguing T Produced Always Minimum Spanning Tree Prove Al Q37253711
Note: You either prove that the algorithm worksby arguing that the T produced is always a minimum spanning tree;or you prove that the algorithm does not work by providing acounterexample where the algorithm fails to produce an MST. In thecase of a counterexample, you should also explain why the Tproduced by the algorithm is not an MST.
Note: You do not have to come up with “the mostefficient implementation” of each algorithm since it is difficultto determine whether an implementation is indeed the mostefficient. Instead, describe a good implementation and provide itsrunning time.
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 Г 1s a minimum spanning tree or prove that not a minimum spanning tree. Also describe the most efficient implementation of each algorithm, whether or not it computes a minimum spanning tree. a. MAYBE-MST-A(G,לש 1 sort the edges into nonincreasing order of edge weights w 2 T-E 3 for each edge e, taken in nonincreasing order by weight 4if T -e is a connected graph 6 return T b. MAYBE-MST-B (G,לש 2 for each edge e, taken in arbitrary order 4 if T U sej has no cycles 5 return T MAY BE-MST-C(G, w) c. 2 for each edge e, taken in arbitrary order if T has a cycle c 4 let e’ be a maximum-weight edge on c 7 return T Show transcribed image text 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 Г 1s a minimum spanning tree or prove that not a minimum spanning tree. Also describe the most efficient implementation of each algorithm, whether or not it computes a minimum spanning tree. a. MAYBE-MST-A(G,לש 1 sort the edges into nonincreasing order of edge weights w 2 T-E 3 for each edge e, taken in nonincreasing order by weight 4if T -e is a connected graph 6 return T b. MAYBE-MST-B (G,לש 2 for each edge e, taken in arbitrary order 4 if T U sej has no cycles 5 return T MAY BE-MST-C(G, w) c. 2 for each edge e, taken in arbitrary order if T has a cycle c 4 let e’ be a maximum-weight edge on c 7 return T
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Answer to Note: You either prove that the algorithm works by arguing that the T produced is always a minimum spanning tree; or you… . . .
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