$26101$ B $32$ D E F $52$ G $10$ Figure $1$: State space graph Figure $2$ shows a state space graph, in which state A is the start state and state G is the goal state. Each edge is directed and associated with a cost. Please apply the five tree search $($not graph search$)$ algorithms $$ DFS$,$ BFS$,$ UCS, greedy, and A$*$ that you learned in the lectures to find the solution. Please read the hints at the end of this question before answering the question. $1.$ Please apply DFS to search the solution. Please consider that your fringe is implemented by stack and you always push the successor states following the alphabet order $($A$-$to$-$z$).$ For example, if you are expanding node A$,$ then you will push its three successor states in the order of B$,$ C$,$ F into the stack $($a$)$ How many nodes do you need to expand $($including expanding A and and the node containing G$)$ until you find the solution? $(1\mathrm{.}5$ points$)($b$)$ What is the solution $($i$.$e$.,$ state sequence$)$ outputted by DFS$?$ Your solution should contain both states A and G$.(1\mathrm{.}5$ points$]\backslash$