True or false. If true, give a brief explanation justifying the statement. If false, provide a counterexample. - If you are given a flow network (labeled F), let (L,R) be a minimum capacity cut in the flow graph. If the capacity of all of the graph edges is increased by 1, then (L,R) is still a minimum capacity cut in our new modified graph

4. (1) Draw a transition graph for the dfa M={Q,E,8,q,,F ), where Q={q,,91»92 }; E = {a,b},F = {qo,92} and ở is definded as S(90,a) = q,,8(q,b) =q,,5(q,,a)=q0,8(q,,b) =q2,8(q2,a) =q2,8(q2,b) =q2 (2) Give the language accepted by the above dfa.

We know that if the heuristic function in A* is good enough, then A* can always find a shortest weighted path between two vertices, and is generally much faster than Dijkstra. Assume we are using a graph where a good heuristic function is well defined for A*, such that A* can always find the same shortest paths as Dijkstra. Briefly explain when you should choose Dijkstra over A* in this case.

How do I find the minimum capacity of an s-t cut in this flow network?

How can we merge parallel edges that are in the same direction in a flow network G?

Could you also do question one please

Suppose that the road network is defined by the undirected graph, where the vertices represent cities and edges represent the road between two cities. The Department of Highways (DOH) decides to install the cameras to detect the bad driver. To reduce the cost, the cameras are strategically installed in the cities that a driver must pass through in order to go from one city to another city. For example, if there are two cities A and B such that the path that goes from A to B and the path that goes from B to A must pass the city C, then C must install the camera. Suppose that there are m cities and n roads. Write an O (m + n) to list all cities where cameras should be installed.