The heuristic path algorithm $($Pohl$,1977)$ is a best$-$first search in which the evaluation function is f$($n$)=(2-$ w$)$g$($n$)+$ wh$($n$).$ For what values of w is this complete? For what values is it optimal, assuming that h is admissible? What kind of search does this perform for w $=0,$ w $=1,$ and w $=2?$