Uninformed Search

$(20$ points$)$

We define a state space as follows. The start state is $1.$ The successor function for state $n$ returns two states, which are numbered $2n$ and $2n+1.$ The goal state is $13.$ Answer the following questions:

$(4$ Points each$)$

a$)$ Draw the state space involving only states $1$ to $13.$

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

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

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

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