Q$3$: Consider a state space where the start state is number $1$ and the successor function for state $n$ returns three states, numbers $3n$ and $3n+1,3n+2.$

a$.$ Draw the state space for states $1$ to $32.$

b$.$ Suppose the goal state is $30,$ List the order in which nodes will be visited for i$.$ Breadth first search.

ii$.$ Depth$-$limited search with depth limit $2.$

iii. Iterative deepening search.