Problem $1$: A$*$ Search

Consider the search space depicted above for a hypothetical search problem. $S$ is the initial state and $T$ is

the goal state. The cost of each edge has been labeled on the graph.

A $(4$ points$)$: Compute the shortest path and its cost using uniform cost search $($Djikstra$\text{'}$s algorithm$).$

B $(4$ points$)$: Consider the following table representing $h(s)$ for each state $s$ in the space. What path does $A^{**}$

search find using this $h(s),$ and what is its cost?

C $(4$ points$)$: Compare your results for $($a$)$ and $($b$).$ If they are the same, explain why. If they are different,

provide a specific reason.