For each of the following search strategies, give $(1)$ the path that will be returned; $(2)$ the order that nodes are visited in the search. If there are ties, assume alphabetical tie$-$breaking $($i$.$e$.,$ nodes for states earlier in the alphabet are expanded first$).$

Depth$-$First search

Breadth$-$First search

A$*$ search using heuristic h$1$Question $41(15$ points$)$

Consider the search graph shown here. $S$ is the start state and $G$ is the goal state.