class PKERRTAgent:
    """
    Multi-goal Path Finding Agent using Probabilistic Kinematic Extend Rapidly 
    Exploring Random Tree (PKE-RRT) Algorithm to assess efficiency.
    """
    def __init__(self):
        self.tree = None  # RRT Tree

    def initialize_tree(self, start_point: tuple) -> None:
        """
        Initialize the RRT tree with the starting point.

        :param start_point: Start point coordinates in (x, y) format.
        """
        # Assuming we have a Tree class defined somewhere
        self.tree = Tree(start_point)

    def extend_tree(self, random_point: tuple) -> None:
        """
        Extend the RRT tree towards a randomly generated point.

        :param random_point: Random point coordinates in (x, y) format.
        """
        # This is a simplified representation of RRT extension process.
        # Real implementation would require handling complex factors
        # like obstacle avoidance, kinematic constraints, etc.
        nearest_node = self.tree.find_nearest_node(random_point)
        self.tree.add_node(random_point, parent=nearest_node)

    def find_multi_goal_path(self, goal_points: list) -> list:
        """
        Find a path in the tree that reaches all goal points.

        :param goal_points: List of goal points coordinates in (x, y) format.
        :return: List of points constituting the path.
        """
        # This is a simplified version for illustration.
        # Real implementation would require careful goal sequencing,
        # path optimality considerations, tree re-planning, etc.
        path = []
        for goal in goal_points:
            goal_path = self.tree.find_path_to_goal(goal)
            if goal_path:
                path.extend(goal_path)
        return path

    def assess_pkerrt_efficiency(self, start_point: tuple, goal_points: list) -> float:
        """
        Assess the efficiency of PKE-RRT algorithm by running it and measuring time taken.

        :param start_point: Start point coordinates in (x, y) format.
        :param goal_points: List of goal points coordinates in (x, y) format.
        :return: Simulation run time.
        """
        import time
        start_time = time.time()

        # Initialize the RRT tree with start point
        self.initialize_tree(start_point)

        # Extend the tree iteratively until all goals are reached or max iterations reached
        iteration = 0
        max_iterations = 10000  # Made up value, real value should be carefully chosen
        while goal_points and iteration < max_iterations:
            iteration += 1

            # Generate a random point
            # Here we just generate a uniform point in 2D space for simplicity,
            # real implementation would depend on environment representation.
            random_point = (random.uniform(-10, 10), random.uniform(-10, 10))

            # Extend the tree towards this random point
            self.extend_tree(random_point)

            # Check if any of the goal points can be reached now
            for goal in goal_points[:]:
                if self.tree.find_path_to_goal(goal):
                    goal_points.remove(goal)

        # Calculate and return the time taken for simulation
        end_time = time.time()
        duration = end_time - start_time
        return duration

# Create an instance of our PKE-RRT Agent
pkerrt_agent = PKERRTAgent()

# Simulate a multi-goal path finding problem
start_point = (0, 0)  
goal_points = [(5, 5), (10, 10), (-5, -5), (-10, -10)]

# assess pke-rrt efficiency
pkerrt_efficiency = pkerrt_agent.assess_pkerrt_efficiency(start_point, goal_points)

print("PKE-RRT Efficiency (in seconds): ", pkerrt_efficiency)
