For the following graph, assume the heuristic shown in the table, and $A$ is

the start node, G is the goal node. Answer the following $($Note: You can

break ties randomly and many different solutions may be possible$)$

a$.$ What is the path that depth$-$first search will find and in which order will

nodes be expanded?

b$.$ What is the path that breadth$-$first search will find and in which order

will nodes be expanded?

c$.$ What is the path that best$-$first$-$search will find and in which order will

nodes be expanded?

d$.$ What is the path that A$*$ will find and in which order will nodes be

expanded?

e$.$ Is the heuristic admissible and consistent?