1. State Space Search (29 points total) In this graph, the initial state is S and the goal state is G. The heuristic estimate of the co from each node to the goal is provided by the function h. Assume that (1) we break ties picking the state that comes first alphabetically, and (2) we expand each state at most once (a) (4 pts) List the states in the order they would be expanded using Uniform-Cost Searc (b) (4 pts) List the states in the order they would be expanded using Greedy Search. (c) (4 pts) List the states in the order they would be expanded using A search. (d) (5 pts) Is h consistent? Briefly explain your answer. (e) (3 pts) Is h admissible? Briefly explain your answer. (f) (3 pts) Is h2( state )=min(2,h( state )) an admissible heuristic? Justify your answer. (g) (3 pts) Is h3( state )=max(2,h( state )) an admissible heuristic? Justify your answer. (h) (3 pts) Among h,h2, and h3, which is the best to use for this graph? Explain