text: from aimacode.logic import PropKB
  from aimacode.planning import Action
  from aimacode.search import (
      Node, Problem,
  )
  from aimacode.utils import expr
  from lp_utils import (
      FluentState, encode_state, decode_state,
  )
  from my_planning_graph import PlanningGraph
  
  from functools import lru_cache
  
  
  class AirCargoProblem(Problem):
      def __init__(self, cargos, planes, airports, initial: FluentState, goal: list):
          """
  
          :param cargos: list of str
              cargos in the problem
          :param planes: list of str
              planes in the problem
          :param airports: list of str
              airports in the problem
          :param initial: FluentState object
              positive and negative literal fluents (as expr) describing initial state
          :param goal: list of expr
              literal fluents required for goal test
          """
          self.state_map = initial.pos + initial.neg
          self.initial_state_TF = encode_state(initial, self.state_map)
          Problem.__init__(self, self.initial_state_TF, goal=goal)
          self.cargos = cargos
          self.planes = planes
          self.airports = airports
          self.actions_list = self.get_actions()
  
      def get_actions(self):
          """
          This method creates concrete actions (no variables) for all actions in the problem
          domain action schema and turns them into complete Action objects as defined in the
          aimacode.planning module. It is computationally expensive to call this method directly;
          however, it is called in the constructor and the results cached in the `actions_list` property.
  
          Returns:
          ----------
          list<Action>
              list of Action objects
          """
  
          def load_actions():
              """Create all concrete Load actions and return a list
  
              :return: list of Action objects
              """
              loads = []
              for airport in self.airports:
                  for plane in self.planes:
                      for cargo in self.cargos:
                          precond_pos = [expr("At({}, {})".format(cargo, airport)),
                                         expr("At({}, {})".format(plane, airport)),
                                         ]
                          precond_neg = []
                          effect_add = [expr("In({}, {})".format(cargo, plane))]
                          effect_rem = [expr("At({}, {})".format(cargo, airport))]
                          load = Action(expr("Load({}, {}, {})".format(cargo, plane, airport)),
                                        [precond_pos, precond_neg],
                                        [effect_add, effect_rem])
                          loads.append(load)
              return loads
  
          def unload_actions():
              """Create all concrete Unload actions and return a list
  
              :return: list of Action objects
              """
              unloads = []
              for airport in self.airports:
                  for plane in self.planes:
                      for cargo in self.cargos:
                          precond_pos = [expr("In({}, {})".format(cargo, plane)),
                                         expr("At({}, {})".format(plane, airport)),
                                         ]
                          precond_neg = []
                          effect_add = [expr("At({}, {})".format(cargo, airport))]
                          effect_rem = [expr("In({}, {})".format(cargo, plane))]
                          unload = Action(expr("Unload({}, {}, {})".format(cargo, plane, airport)),
                                          [precond_pos, precond_neg],
                                          [effect_add, effect_rem])
                          unloads.append(unload)
              return unloads
  
          def fly_actions():
              """Create all concrete Fly actions and return a list
  
              :return: list of Action objects
              """
              flys = []
              for fr in self.airports:
                  for to in self.airports:
                      if fr != to:
                          for p in self.planes:
                              precond_pos = [expr("At({}, {})".format(p, fr)),
                                             ]
                              precond_neg = []
                              effect_add = [expr("At({}, {})".format(p, to))]
                              effect_rem = [expr("At({}, {})".format(p, fr))]
                              fly = Action(expr("Fly({}, {}, {})".format(p, fr, to)),
                                           [precond_pos, precond_neg],
                                           [effect_add, effect_rem])
                              flys.append(fly)
              return flys
  
          return load_actions() + unload_actions() + fly_actions()
  
      def actions(self, state: str) -> list:
          """ Return the actions that can be executed in the given state.
  
          :param state: str
              state represented as T/F string of mapped fluents (state variables)
              e.g. 'FTTTFF'
          :return: list of Action objects
          """
          possible_actions = []
          kb = PropKB()
          kb.tell(decode_state(state, self.state_map).pos_sentence())
          for action in self.actions_list:
              if action.check_precond(kb, action.args):
                  possible_actions.append(action)
          return possible_actions
  
      def result(self, state: str, action: Action):
          """ Return the state that results from executing the given
          action in the given state. The action must be one of
          self.actions(state).
  
          :param state: state entering node
          :param action: Action applied
          :return: resulting state after action
          """
          new_state = FluentState([], [])
          old_state = decode_state(state, self.state_map)
          for fluent in old_state.pos:
              if fluent not in action.effect_rem:
                  new_state.pos.append(fluent)
          for fluent in action.effect_add:
              if fluent not in new_state.pos:
                  new_state.pos.append(fluent)
          for fluent in old_state.neg:
              if fluent not in action.effect_add:
                  new_state.neg.append(fluent)
          for fluent in action.effect_rem:
              if fluent not in new_state.neg:
                  new_state.neg.append(fluent)
          return encode_state(new_state, self.state_map)
  
      def goal_test(self, state: str) -> bool:
          """ Test the state to see if goal is reached
  
          :param state: str representing state
          :return: bool
          """
          kb = PropKB()
          kb.tell(decode_state(state, self.state_map).pos_sentence())
          for clause in self.goal:
              if clause not in kb.clauses:
                  return False
          return True
  
      def h_1(self, node: Node):
          # note that this is not a true heuristic
          h_const = 1
          return h_const
  
      @lru_cache(maxsize=8192)
      def h_pg_levelsum(self, node: Node):
          """This heuristic uses a planning graph representation of the problem
          state space to estimate the sum of all actions that must be carried
          out from the current state in order to satisfy each individual goal
          condition.
          """
          # requires implemented PlanningGraph class
          pg = PlanningGraph(self, node.state)
          pg_levelsum = pg.h_levelsum()
          return pg_levelsum
  
      @lru_cache(maxsize=8192)
      def h_ignore_preconditions(self, node: Node):
          """This heuristic estimates the minimum number of actions that must be
          carried out from the current state in order to satisfy all of the goal
          conditions by ignoring the preconditions required for an action to be
          executed.
          """
          count = 0
          for clause in self.goal:
              states = list()
              states.append((node.state, 0))
              explored = set()
              while len(states) > 0:
                  state, level = states.pop()
  
                  kb = PropKB()
                  kb.tell(decode_state(state, self.state_map).pos_sentence())
                  if clause in kb.clauses:
                      if level > count:
                          count = level
                      break
                  explored.add(state)
  
                  possible_actions = self.actions(state)
                  for action in possible_actions:
                      state = self.result(state, action)
                      if state not in explored:
                          states.append((state, level + 1))
  
          return count
  
  
  def air_cargo_p1() -> AirCargoProblem:
      cargos = ['C1', 'C2']
      planes = ['P1', 'P2']
      airports = ['JFK', 'SFO']
      pos = [expr('At(C1, SFO)'),
             expr('At(C2, JFK)'),
             expr('At(P1, SFO)'),
             expr('At(P2, JFK)'),
             ]
      neg = [expr('At(C2, SFO)'),
             expr('In(C2, P1)'),
             expr('In(C2, P2)'),
             expr('At(C1, JFK)'),
             expr('In(C1, P1)'),
             expr('In(C1, P2)'),
             expr('At(P1, JFK)'),
             expr('At(P2, SFO)'),
             ]
      init = FluentState(pos, neg)
      goal = [expr('At(C1, JFK)'),
              expr('At(C2, SFO)'),
              ]
      return AirCargoProblem(cargos, planes, airports, init, goal)
  
  
  def air_cargo_p2() -> AirCargoProblem:
      cargos = ['C1', 'C2', 'C3']
      planes = ['P1', 'P2', 'P3']
      airports = ['JFK', 'SFO', 'ATL']
      pos = [expr('At(C1, SFO)'),
             expr('At(C2, JFK)'),
             expr('At(C3, ATL)'),
             expr('At(P1, SFO)'),
             expr('At(P2, JFK)'),
             expr('At(P3, ATL)'),
             ]
      neg = [expr('At(C2, SFO)'),
             expr('At(C2, ATL)'),
             expr('In(C2, P1)'),
             expr('In(C2, P2)'),
             expr('In(C2, P3)'),
             expr('At(C1, JFK)'),
             expr('At(C1, ATL)'),
             expr('In(C1, P1)'),
             expr('In(C1, P2)'),
             expr('In(C1, P3)'),
             expr('At(C3, JFK)'),
             expr('At(C3, SFO)'),
             expr('In(C3, P1)'),
             expr('In(C3, P2)'),
             expr('In(C3, P3)'),
             expr('At(P1, JFK)'),
             expr('At(P1, ATL)'),
             expr('At(P2, SFO)'),
             expr('At(P2, ATL)'),
             expr('At(P3, SFO)'),
             expr('At(P3, JFK)'),
             ]
      init = FluentState(pos, neg)
      goal = [expr('At(C1, JFK)'),
              expr('At(C2, SFO)'),
              expr('At(C3, SFO)'),
              ]
      return AirCargoProblem(cargos, planes, airports, init, goal)
  
  
  def air_cargo_p3() -> AirCargoProblem:
      cargos = ['C1', 'C2', 'C3', 'C4']
      planes = ['P1', 'P2']
      airports = ['JFK', 'SFO', 'ATL', 'ORD']
      pos = [expr('At(C1, SFO)'),
             expr('At(C2, JFK)'),
             expr('At(C3, ATL)'),
             expr('At(C4, ORD)'),
             expr('At(P1, SFO)'),
             expr('At(P2, JFK)'),
             ]
      neg = [expr('At(C2, SFO)'),
             expr('At(C2, ATL)'),
             expr('At(C2, ORD)'),
             expr('In(C2, P1)'),
             expr('In(C2, P2)'),
             expr('At(C1, JFK)'),
             expr('At(C1, ATL)'),
             expr('At(C1, ORD)'),
             expr('In(C1, P1)'),
             expr('In(C1, P2)'),
             expr('At(C3, SFO)'),
             expr('At(C3, JFK)'),
             expr('At(C3, ORD)'),
             expr('In(C3, P1)'),
             expr('In(C3, P2)'),
             expr('At(C4, SFO)'),
             expr('At(C4, ATL)'),
             expr('At(C4, JFK)'),
             expr('In(C4, P1)'),
             expr('In(C4, P2)'),
             expr('At(P1, JFK)'),
             expr('At(P1, ATL)'),
             expr('At(P1, ORD)'),
             expr('At(P2, SFO)'),
             expr('At(P2, ATL)'),
             expr('At(P2, ORD)'),
             ]
      init = FluentState(pos, neg)
      goal = [expr('At(C1, JFK)'),
              expr('At(C2, SFO)'),
              expr('At(C3, JFK)'),
              expr('At(C4, SFO)'),
              ]
      return AirCargoProblem(cargos, planes, airports, init, goal)
  