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.

$1$

Q$4$: Given the following tree representing a state space and assuming that I and $L$ are goal nodes, give the sequence in which nodes are visited using: BFS$,$ DFS$,$ DLS $($Depth Bound $-2),$ IDS.

BFS:

DFS:

DLS $($Depth Bound $-2)$:

IDS: