$1.$ Find a path from the start $($A$)$ to the goal $($F$)$ using the Depth First Search version of the Generic Search Algorithm discussed in class, making sure to

$($a$)$ Show the status of the open and closed data structures for each iteration.

$($b$)$ Show the final search tree after the goal state is reached.

$($c$)$ Show the final result $($path$).$

$2.$ Do $($a$),($b$),($c$)$ for a Uniform Cost Search version.

$3.$ Do $($a$),($b$),($c$)$ for A$*$ version using this heuristic:

State h$($State$)$

A $23$

B $3$

C $13$

D $7$

E $0$

F $0$

$4.$ Is this heuristic admissible? Explain why or why not?