initialize visitedvertices to {start if start=goalreturn path and exit otherwisecontinue find the edge (start,vof minimum weight such that is adjacent to start and is not in visitedvertices add to path add to visitedvertices set start equal to and go to step does this greedy strategy always find shortest path from start to goaleither explain intuitively why it worksor give counter example - show that if all the weights in connected weighted graph are distinctthen there is exactly one minimum spanning tree for - design an efficient algorithm for finding longest directed path from vertex to vertex of an acyclic weighted digraph specify the graph representation used and any auxiliary data structures used alsoanalyze the time complexity of your algorithm - consider diagram of telephone networkwhich is graph whose vertices represent switching centersand whose edges represent communication lines joining pairs of centers edges are marked by their bandwidthand the bandwidth of path is the bandwidth of its lowest bandwidth edge give an algorithm thatgiven diagram and two switching centers and boutputs the maximum bandwidth of path between and