Optimality of A* (proof)
n Suppose some suboptimal goal G2 has been generated and is in the
fringe. Let n be an unexpanded node in the fringe such that n is on a
shortest path to an optimal goal G.
n f(G2)  = g(G2)  since h(G2) = 0
n g(G2) > g(G)   since G2 is suboptimal
n f(G)   = g(G)   since h(G) = 0
n f(G2)  > f(G)   from above