Question: You are given a simple weighted graph G=(V,E) and its minimum spanning tree Tmst. Somebody added new edge e to the graph G. Let's call

You are given a simple weighted graph G=(V,E) and its minimum spanning tree Tmst. Somebody added new edge e to the graph G. Let's call new graph G=(V,Ee). Devise an algorithm which checks if Tmst is also a minimum spanning tree for the graph G or not. Prove correctness of your algorithm and provide running time analysis. You can assume that all edge weights in G are distinct. Tmst and G are given to you as adjacency lists. Your algorithm should work in O(V) time for a full score. For the algorithm working in O(V1+ ) time (for any positive ) you will get half points
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