Consider the diagram

Answer the following questions about the search problem shown above. Break any ties alphabetically.

For the

questions that ask for a path, please give your answers in the form $\text{'}S-A-D-G.\text{'}$

$($a$)$ What path would breadth$-$first graph search return for this search problem?

$($b$)$ What path would uniform cost graph search return for this search problem?

$($c$)$ What path would depth$-$first graph search return for this search problem?

$($d$)$ What path would $A**$ graph search, using a consistent heuristic, return for this search problem?