$1.[15$ points$]$ Compute the order in which states of the above graph are expanded and the returned path for each of these graph search algorithms: i$)$ Depth$-$first search; ii$)$ Breadthfirst search; iii$)$ Uniform cost search; iv$)$ Greedy best first search using the heuristic $\backslash ($ h $\backslash )$ shown on the graph; and v$)$ A$*$ search using the same heuristic. Is the heuristic $\backslash ($ h$($n$)\backslash )$ admissible? Explain why or why not.