We define a state space as follows. The start state is $1.$ The successor function for state n returns two

states, which are numbered $3$n and $3$n $+2.$ The goal state is $35.$

$($a$)(4$ pts$)$ Draw the state space involving only states $1$ to $35.$

$($b$)(5$ pts$)$ List the order in which nodes will be visited for breadth first search.

$($c$)(5$ pts$)$ List the order in which the nodes will be visited for depth$-$limited search with limit $3.$

$($d$)(5$ pts$)$ List the order in which the nodes will be visited for iterative deepening search.

$($e$)(4$ pts$)$ Is bidirectional search appropriate for this problem? Explain your answer.