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The heuristic path algorithmPohl: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 $w=2$?