I. Let the states' space (v1, ..., V7) and the transition function illustrated in the following graph : an arc from the state vi to the state v; means that y; is one of the successor of vi; the label of each arc designates the transition's cost between two states. And h is the heuristic function. State 0+3,05 V7 | 2 Figure 1 For each of the following graph search strategies, work out the order in which states are expanded, as well as the path returned by graph search. In all cases, assume ties resolve in such a way that states with earlier alphabetical order are expanded first. The start and goal state are vo and V6, respectively. Remember that in graph search, a state is expanded only once. a) Depth-first search. b) Breadth-first search. c) Uniform cost search. d) Greedy search with the heuristic h shown on the graph. e) A* search with the same heuristic