Consider the simplified road map of Romania found in Figure $3\mathrm{.}2.$ Substitute the first letter of the city name to represent each node $($e$.$g$.,$A$$ for $$Arad$).$

a$)$ Suppose you are at Sibiu. Draw the search tree, limited to depth $4,$ that would be generated using an explored set. Expand nodes counter$-$clockwise starting from the Western$-$most neighbor, placing the expanded nodes in the search tree from left to right. How many nodes are in the tree?

b$)$ Suppose you wish to find a path from Sibiu to Drobeta. List the order of the nodes that would be explored for depth$-$first and breadth$-$first search using the tree from part $($a$).$ Assume that, within a layer, nodes are explored left to right. How many nodes are explored for each? Which algorithm finds the goal faster?