Question $4[4$ pts$]$: Figure $4$ shows a state graph where A denotes the node corresponding to the

initial state, and $E$ is the goal node. In the figure, $h=x$ denotes the heuristic function value and

$c=x$ denotes the actual cost between nodes $($i$.$e$.,$ arch cost$).$

a$.$ Please explain why $($or why not$)$ the heuristic function in Figure $4$ is $($or is not$)$ an

admissible heuristic $(1pt).$

b$.$ Please explain why $($or why not$)$ the heuristic function in Figure $4$ is $($or is not$)$ a

consistent heuristic $(1pt).$

c$.$ Correct heuristic values in Figure $4,$ such that A$*$ search using corrected heuristics can find

optimal path from A to $E$ without revisiting nodes. Solutions must show corrected heuristic

values for all nodes $(1pt)$

d$.$ Create a search tree using corrected heuristic values to carry out A$*$ search from A to find

goal node $E($Node expanded$/$visited does not need to be revisited$).$ Show the search tree $($The

tree must show the complete search process with each node's $f(N),g(N),$ and $h(N)$ values$),$

and report the order of the nodes being expanded, and the final discovered path from $A$ to $E$

$(1$ pt$)$

Figure $4$