Question: Consider the following algorithm for finding the minimum spanning tree of a connected graph G=(V,E,w()) where w:ER+ is a weight function. (1) TE (2) while

Consider the following algorithm for finding the minimum spanning tree of

Consider the following algorithm for finding the minimum spanning tree of a connected graph G=(V,E,w()) where w:ER+ is a weight function. (1) TE (2) while T is not a tree (3) let C be an arbitrary cycle in T (4) let e be the heaviest edge in C (ties are broken arbitrarily) (5) TT\{e} (6) return T Does the algorithm always return a minimum spanning tree T of G ? If your answer is yes, prove it; if your answer is no, give an instance G for which the algorithm does not return a minimum spanning tree

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