$4.($a$)$ As presented in the text, best$-$first search uses the closed list to implement loop detection. What would be the effect of eliminating this test and relying on the depth test, g$($n$),$ to detect loops? Compare the efficiencies of the two approaches.

$($b$)$ best$-$first search does not test a state to see if it is a goal until it is removed from the open list. This test could be performed when new states are generated. What effect would doing so have on the efficiency of the algorithm? Admissibility?