A$)$ Draw the search tree that is generated by a breadth$-$first search in an attempt to solve the eight$-$puzzle from the following start state without the assistance of any heuristic information. Continue the tree for $5$ levels or until a solution is obtained.

$13$

$425$

$786$

B$)$ Draw the search tree that is generated by the best$-$fit algorithm below in an attempt to solve the eight$-$puzzle from the state shown in the first problem if the number of tiles out of place is used as a heuristic. $[$the first heuristic$]$

C$)$ Draw the search tree that is generated by the best$-$fit algorithm as detailed in the previous question in an attempt to solve the eight$-$puzzle from the following start state, assuming the heuristic used is as follows:

Measure the distance each tile is from its destination and add these values to obtain a single quantity. $[$the second heuristic$]$

$123$

$576$

$48$

D$)$ When solving the eight$-$puzzle, why would the number of tiles out of place $[$the first heuristic$]$ not be as good a heuristic as the one described in the question above $[$the second heuristic$]?$