Problem 5 [15 points]. Consider an informed, best-first search algorithm in which the evaluation function is (n) (2-w)g(n)+wh(n), 0w2. For what values of w is this algorithm guaranteed to be optimal when h is admissible (consider the case of TREE-SEARCH)? What kind of search does this perform when w-07 when w = 1? When w 2? In your proof. you may assume that if the heuristic in a standard A" search is inadmissible, then optimality cannol be guaranteed. Note that f(n) here doos not always dircctly correspond to the evaluation function in a standard A scarch. en ui