Question Seven. In this problem the start state is $\backslash (\backslash$mathbf$\{$S$\}\backslash ),$ and the goal state is $\backslash (\backslash$mathbf$\{$G$\}\backslash ).$ The transition costs are next to the edges, and the heuristic estimate, $\backslash (\backslash$mathbf$\{$h$\}\backslash ),$ of the distance from the state to the goal is in the state's node. Assume ties are always broken by choosing the state which comes first alphabetically. $(4$ Points$)$

a$)$ What is the order of states expanded $($visited$)$ using Depth First Search? Assume DFS terminates as soon as it reaches the goal state.

b$)$ What is the order of states expanded $($visited$)$ using Breadth First Search?

c$)$ What is the order of states expanded $($visited$)$ using A$*$ search?

d$)$ What is a least cost path from $\backslash ($ S $\backslash )$ to $\backslash ($ G $\backslash )?$