Question $5-\backslash (\backslash$mathbf$\{$A$\}^\{*\}\backslash )-$search. Given the search space on fig. $1,$ where $\backslash (\backslash$mathbf$\{$S$\}\backslash )$ is the initial state and $\backslash ($ G $1\backslash )$ and $\backslash ($ G $2\backslash )$ satisfy the goal test. Arcs are labeled with the cost of traversing them $($so lower is better$)$

Figure $1$: State space for search problems

and the estimated cost to a goal $($i$.$e$.$ value of heuristic function$)$ is reported inside nodes. For $\backslash (\backslash$mathrm$\{$A$\}^\{*\}\backslash )$ search of state space given on fig. $1$ answer the following questions

$1.(\backslash (25\backslash \%\backslash )$ of the credit$)$ Which goal will be reached?

$2.(\backslash (25\backslash \%\backslash )$ of the credit$)$ What is the state of the node that will be expanded $($popped off frontier$)\backslash (4^\{\backslash$text $\{$th $\}\}\backslash )?($note that every node popped off the frontier counts$)$

$3.(\backslash (50\backslash \%\backslash )$ of the credit$)$ Show what is the contents of the frontier $($i$.$e$.$ show in correct order all nodes$)$ after expansion of $\backslash (4^\{\backslash$text $\{$th $\}\}\backslash )$ node. Recall that a node in frontier is a $4-$tuple $($state$,$ parent$-$state, value of cost function $\backslash ($ g $\backslash ),$ value of evaluation function $\backslash ($ f $\backslash )).$ FOR EACH NODE IN FRONIER ALL COMPONENTS MUST BE SHOWN.