def best_first_graph_search(problem, f):
"""
Search the nodes with the lowest f scores first.
You specify the function f(node) that you want to minimize; for example,
if f is a heuristic estimate to the goal, then we have greedy best
first search; if f is node.depth then we have breadth-first search.
There is a subtlety: the line "f = memoize(f, 'f')" means that the f
values will be cached on the nodes as they are computed. So after doing
a best first search you can examine the f values of the path returned.
"""
f = memoize(f, 'f')
node = Node(problem.getStartState())
if problem.isGoalState(node.state):
return node
frontier = PriorityQueue(min, f)
frontier.push(node)
explored = set()
while frontier:
node = frontier.pop()
if problem.isGoalState(node.state):
return node
explored.add(node.state)
for child in node.expand(problem):
if child.state not in explored and not frontier.contains(child):
frontier.push(child)
elif frontier.contains(child):
incumbent = frontier.__getitem__(child)
if f(child) < f(incumbent):
del frontier[incumbent]
frontier.push(child)
return None
