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 $w=2$?
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