Consider a connected graph G-(V, E) where each edge has a non-zero positive weight Furthermore, assume that all edge weights are distinct. Using the cut property, first show that that for each vertex v V, the edge incident to v with minimum! weight belongs to a Minimum Spanning Tree (MST). Can you use this to devise an algorithm for MST - the above step identifies at least |V1/2 edges in MST - you can collapse these edges, by identifying the vertices and then recursively apply the same technique the graph in the next step has at most half of the vertices that you started with and so on. What is the running time of your algorithm:? Note that for an edge e = uv in the graph G (V,E), identifying vertex u with or collapsing e is the following operation: Replace the vertices u and v by a new vertex, say u'. Remove the edge between u and v. If there was an edge from u (respectively, v) to any vertex w (wu and wv), then we add an edge (with the same weight as of edge uw (respectively, vw)), between the vertices u' and w. This transforms graph G to a new graph G -(V', E), where |V'