graph algorithms figure graph used in exercise suppose all the edge weights in graph are integers between and |ehow fast can dijkstra' algorithm be implementedwrite program to solve the single-source shortest-path problem explain how to modify dijkstra' algorithm to produce count of the number of different minimum paths from to explain how to modify dijkstra' algorithm so that if there is more than one minimum path from to wa path with the fewest number of edges is chosen find the maximum flow in the network of figure suppose that (veis trees is the rootand we add vertex and edges of infinite capacity from all leaves in to give linear-time algorithm to find maximum flow from to bipartite graphg (ve)is graph such that can be partitioned into two subsetsv and and no edge has both its vertices in the same subset give linear algorithm to determine whether graph is bipartite the bipartite matching problem is to find the largest subset eof such that no vertex is included in more than one edge matching of four edges (indicated by dashed edgesis shown in figure there is matching of five edgeswhich is maximum show how the bipartite matching problem can be used to solve the following problemwe have set of instructorsa set of coursesand list of courses that each instructor is qualified to teach if no instructor is required to teach more than one courseand only one instructor may teach given coursewhat is the maximum number of courses that can be offeredc show that the network flow problem can be used to solve the bipartite matching problem what is the time complexity of your solution to part ( )