I. Let the states' space (v1, ..., vy) and the transition function illustrated in the following graph : an arc from the state w to the state y means that y; is one of the successor of w; the label of each are designates the transition's cost between two states. And h is the heuristic function. 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 ve, 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. II. Suppose that we add a recursive transition at vg as shown in Figure 2. Repeat a), b), c), d), and e) using the same heuristic h with the graph of Figure 2