Figure $3$: A search problem showing states and costs of moving from one state to another. Costs are undirected.

Consider the search space shown in Figure $3.$ D is the only goal state. Costs are undirected. For each of the follo 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 $2$:

$h(A)=45$

$h(B)=45$

$h(C)=45$

$h(D)=45$

$h(E)=45$

$h(F)=45$

Heuristic $3$:

$h(A)=10$

$h(B)=15$

$h(C)=0$