Task $3$: $(15$ points$)$

A search problem showing states and costs of moving from one state to another. Costs are undirected.

Consider the search space shown above. D is the only goal state. Costs are undirected. For each of

the following heuristics, determine if it is admissible or not. For non$-$admissible heuristics, modify

their values as needed to make them admissible.

Heuristic $1$:

$h(A)=5$

$h(B)=20$

$h(C)=15$

$h(D)=0$

$h(E)=10$

$h(F)=0$

Heuristic $2$:

$h(A)=40$

$h(B)=40$

$h(C)=40$

$h(D)=40$

$h(E)=40$

$h(F)=40$

Heuristic $3$:

$h(A)=10$

$h(B)=15$

$h(C)=0$

$h(D)=0$

$h(E)=25$

$h(F)=5$

Heuristic $4$:

$h(A)=0$

$h(B)=0$

$h(C)=0$

$h(D)=0$

$h(E)=0$

$h(F)=0$