the search. The heuristic function h$($n$)$ used in the A$*$ search is a consistent heuristic function. The

goal is to find a solution path from root node $1$ to optimal goal node $1.$ In the following, f is the

evaluation function used in the A$*$ search, h is the heuristic function, g is the path cost of a node and

c is the step cost from a parent node to a child node. Nodes $2$ and $4$ are along the optimal path to

the optimal goal node $1.$ Leaf nodes $2$ and $3$ are suboptimal goal nodes.

$($a$)(2)(1)$

$($b$)(5)(7)$

$($c$)(6,3)(6)$

$($d$)(1)(4)$

$($e$)(3)(1)$