def astar_search(problem, h, pdb):
    #F function: determines the next heuristic value based on the maximal 
    #admissiable heuristic from the depth, heuristic, and pdb
    def f(n):
	oneMax = max(n.path_cost + h(n) , pdb.find(n.state))
        return max(getattr(n, 'f', -infinity), oneMax)
    #f = memoize(f, 'f') THIS DOES NOT WORK
    fringe = PriorityQueue(min,f) #astar is Best-first w/ a priority ordering
    closed = {}
    fringe.append(Node(problem.initial)) #start off with the inital state
    
    #while there are nodes to be expanded, check them out.
    while fringe:
        node = fringe.pop()
	#if the present node contains a goal state, then return that node.
	if problem.goal_test(node.state): 
            return node
        if node.state not in closed: #this line prevents the repeated checking 
				     #of nodes, simplifing the runtime
            closed[node.state] = True
	    successor = node.expand(problem)
	    for i in successor:
		    i.f = f(i)
		    fringe.append(i)
    return None