3. (25 points) Given a weighted, undirected, and connected graph G -(V, E) with every edge weights is greater than 1. Answer each of the following questions. (a) The PWeight of a spanning tree is the product of all the edge weights ax spanning tree is a spanning tree of G with the maximum PWeight. Design a O(E log |V|) time algorithm of the spanning tree . A PM that computes a PMax spanning tree of b) Let P be the shortest path from vertex u to v in G. Let G' be a graph obtained from G by reducing every edge weight by 1, i.e. G and G' have the same set of vertices and edges. The only difference between G and G' is the edge weights. Is P still a shortest path from u tov in G'? If yes, prove it. If no, give a counter example. Recall that every edge weight in G is greater than 1, so every edge weight in G" is positive. You have to follow this assumption no matter you prove P is shortest path, or give a counter example