





'''simple docstring'''




import numpy as np
import torch
import tqdm

from ...models.unet_ad import UNetaDModel
from ...pipelines import DiffusionPipeline
from ...utils import randn_tensor
from ...utils.dummy_pt_objects import DDPMScheduler


class 					SCREAMING_SNAKE_CASE       (a__				):


     def __init__(		self		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      ):

          '''simple docstring'''






          super().__init__()
          __A		:					List[Any]						=			value_function
          __A		:					str						=			unet
          __A		:					Tuple						=			scheduler
          __A		:					List[Any]						=			env
          __A		:					List[str]						=			env.get_dataset()
          __A		:					List[str]						=			{}
          for key in self.data.keys():
               try:
                    __A		:					Optional[int]						=			self.data[key].mean()
               except:  # noqa: E722
                    pass
          __A		:					str						=			{}
          for key in self.data.keys():
               try:
                    __A		:					Optional[int]						=			self.data[key].std()
               except:  # noqa: E722
                    pass
          __A		:					Optional[Any]						=			env.observation_space.shape[0]
          __A		:					List[Any]						=			env.action_space.shape[0]


     def 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase		,      _UpperCAmelCase):

          '''simple docstring'''






          return (x_in - self.means[key]) / self.stds[key]


     def 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase		,      _UpperCAmelCase):

          '''simple docstring'''






          return x_in * self.stds[key] + self.means[key]


     def 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase):

          '''simple docstring'''






          if type(_UpperCAmelCase) is dict:
               return {k: self.to_torch(_UpperCAmelCase) for k, v in x_in.items()}
          elif torch.is_tensor(_UpperCAmelCase):
               return x_in.to(self.unet.device)
          return torch.tensor(_UpperCAmelCase		,      device=self.unet.device)


     def 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase):

          '''simple docstring'''






          for key, val in cond.items():
               __A		:					List[Any]						=			val.clone()
          return x_in


     def 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase):

          '''simple docstring'''






          __A		:					List[str]						=			x.shape[0]
          __A		:					Union[str, Any]						=			None
          for i in tqdm.tqdm(self.scheduler.timesteps):
               # create batch of timesteps to pass into model
               __A		:					str						=			torch.full((batch_size,)		,      _UpperCAmelCase		,      device=self.unet.device		,      dtype=torch.long)
               for _ in range(_UpperCAmelCase):
                    with torch.enable_grad():
                         x.requires_grad_()

                         # permute to match dimension for pre-trained models
                         __A		:					Optional[int]						=			self.value_function(x.permute(0		,      2		,      1)		,      _UpperCAmelCase).sample
                         __A		:					int						=			torch.autograd.grad([y.sum()]		,      [x])[0]

                         __A		:					Optional[Any]						=			self.scheduler._get_variance(_UpperCAmelCase)
                         __A		:					int						=			torch.exp(0.5 * posterior_variance)
                         __A		:					int						=			model_std * grad

                    __A		:					Optional[Any]						=			0
                    __A		:					List[str]						=			x.detach()
                    __A		:					Tuple						=			x + scale * grad
                    __A		:					Optional[Any]						=			self.reset_xa(_UpperCAmelCase		,      _UpperCAmelCase		,      self.action_dim)

               __A		:					int						=			self.unet(x.permute(0		,      2		,      1)		,      _UpperCAmelCase).sample.permute(0		,      2		,      1)

               # TODO: verify deprecation of this kwarg
               __A		:					int						=			self.scheduler.step(_UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      predict_epsilon=_UpperCAmelCase)['prev_sample']

               # apply conditions to the trajectory (set the initial state)
               __A		:					Optional[int]						=			self.reset_xa(_UpperCAmelCase		,      _UpperCAmelCase		,      self.action_dim)
               __A		:					Dict						=			self.to_torch(_UpperCAmelCase)
          return x, y


     def __call__(		self		,      _UpperCAmelCase		,      _UpperCAmelCase=64		,      _UpperCAmelCase=32		,      _UpperCAmelCase=2		,      _UpperCAmelCase=0.1):

          '''simple docstring'''






          __A		:					str						=			self.normalize(_UpperCAmelCase		,      'observations')
          __A		:					str						=			obs[None].repeat(_UpperCAmelCase		,      axis=0)

          __A		:					Any						=			{0: self.to_torch(_UpperCAmelCase)}
          __A		:					Any						=			(batch_size, planning_horizon, self.state_dim + self.action_dim)

          # generate initial noise and apply our conditions (to make the trajectories start at current state)
          __A		:					Tuple						=			randn_tensor(_UpperCAmelCase		,      device=self.unet.device)
          __A		:					Tuple						=			self.reset_xa(_UpperCAmelCase		,      _UpperCAmelCase		,      self.action_dim)
          __A		:					Tuple						=			self.to_torch(_UpperCAmelCase)

          # run the diffusion process
          __A					,__A		:					Any						=			self.run_diffusion(_UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase)

          # sort output trajectories by value
          __A		:					Any						=			y.argsort(0		,      descending=_UpperCAmelCase).squeeze()
          __A		:					str						=			x[sorted_idx]
          __A		:					Dict						=			sorted_values[:, :, : self.action_dim]
          __A		:					Dict						=			actions.detach().cpu().numpy()
          __A		:					Dict						=			self.de_normalize(_UpperCAmelCase		,      key='actions')

          # select the action with the highest value
          if y is not None:
               __A		:					int						=			0
          else:
               # if we didn't run value guiding, select a random action
               __A		:					Any						=			np.random.randint(0		,      _UpperCAmelCase)

          __A		:					str						=			denorm_actions[selected_index, 0]
          return denorm_actions



'''simple docstring'''



import sys
from collections import defaultdict





class   UpperCAmelCase_    :





    """simple docstring"""






    def __init__(				self      )							->	int:
         __lowerCamelCase  :      Any														=						[]







    def  lowercase_							(				self     ,	SCREAMING_SNAKE_CASE_      )							->	Any:
         return self.node_position[vertex]







    def  lowercase_							(				self     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_      )							->	Tuple:
         __lowerCamelCase  :      Optional[int]														=						pos







    def  lowercase_							(				self     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_      )							->	int:
         if start > size // 2 - 1:
              return
         else:
              if 2 * start + 2 >= size:
                   __lowerCamelCase  :      str														=						2 * start + 1
              else:
                   if heap[2 * start + 1] < heap[2 * start + 2]:
                        __lowerCamelCase  :      Optional[Any]														=						2 * start + 1
                   else:
                        __lowerCamelCase  :      int														=						2 * start + 2
              if heap[smallest_child] < heap[start]:
                   __lowerCamelCase							,			__lowerCamelCase  :      Optional[Any]														=						heap[smallest_child], positions[smallest_child]
                   __lowerCamelCase							,			__lowerCamelCase  :      int														=						(
                       heap[start],
                       positions[start],
                   )
                   __lowerCamelCase							,			__lowerCamelCase  :      str														=						temp, tempa

                   __lowerCamelCase  :      Dict														=						self.get_position(positions[smallest_child]      )
                   self.set_position(
                       positions[smallest_child]     ,	self.get_position(positions[start]      )      )
                   self.set_position(positions[start]     ,	SCREAMING_SNAKE_CASE_      )

                   self.top_to_bottom(SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_      )







    def  lowercase_							(				self     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_      )							->	Any:
         __lowerCamelCase  :      Any														=						position[index]

         while index != 0:
              __lowerCamelCase  :      Union[str, Any]														=						int((index - 2) / 2      ) if index % 2 == 0 else int((index - 1) / 2      )

              if val < heap[parent]:
                   __lowerCamelCase  :      Union[str, Any]														=						heap[parent]
                   __lowerCamelCase  :      Any														=						position[parent]
                   self.set_position(position[parent]     ,	SCREAMING_SNAKE_CASE_      )
              else:
                   __lowerCamelCase  :      Tuple														=						val
                   __lowerCamelCase  :      List[str]														=						temp
                   self.set_position(SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_      )
                   break
              __lowerCamelCase  :      Tuple														=						parent
         else:
              __lowerCamelCase  :      Union[str, Any]														=						val
              __lowerCamelCase  :      Tuple														=						temp
              self.set_position(SCREAMING_SNAKE_CASE_     ,	0      )







    def  lowercase_							(				self     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_      )							->	Optional[int]:
         __lowerCamelCase  :      Optional[int]														=						len(SCREAMING_SNAKE_CASE_      ) // 2 - 1
         for i in range(SCREAMING_SNAKE_CASE_     ,	-1     ,	-1      ):
              self.top_to_bottom(SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_     ,	len(SCREAMING_SNAKE_CASE_      )     ,	SCREAMING_SNAKE_CASE_      )







    def  lowercase_							(				self     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_      )							->	List[Any]:
         __lowerCamelCase  :      Any														=						positions[0]
         __lowerCamelCase  :      Union[str, Any]														=						sys.maxsize
         self.top_to_bottom(SCREAMING_SNAKE_CASE_     ,	0     ,	len(SCREAMING_SNAKE_CASE_      )     ,	SCREAMING_SNAKE_CASE_      )
         return temp







def      UpperCAmelCase__   (      UpperCAmelCase_       :							Optional[int]				)	->						str:
     __lowerCamelCase  :      List[Any]														=						Heap()

     __lowerCamelCase  :      Optional[int]														=						[0] * len(UpperCAmelCase_				)
     __lowerCamelCase  :      str														=						[-1] * len(UpperCAmelCase_				)  # Neighboring Tree Vertex of selected vertex
     # Minimum Distance of explored vertex with neighboring vertex of partial tree
     # formed in graph
     __lowerCamelCase  :      List[str]														=						[]  # Heap of Distance of vertices from their neighboring vertex
     __lowerCamelCase  :      Tuple														=						[]

     for vertex in range(len(UpperCAmelCase_				)				):
          distance_tv.append(sys.maxsize				)
          positions.append(UpperCAmelCase_				)
          heap.node_position.append(UpperCAmelCase_				)

     __lowerCamelCase  :      Tuple														=						[]
     __lowerCamelCase  :      Dict														=						1
     __lowerCamelCase  :      str														=						sys.maxsize
     for neighbor, distance in adjacency_list[0]:
          __lowerCamelCase  :      Any														=						0
          __lowerCamelCase  :      Any														=						distance
     heap.heapify(UpperCAmelCase_ ,       UpperCAmelCase_				)

     for _ in range(1 ,       len(UpperCAmelCase_				)				):
          __lowerCamelCase  :      List[Any]														=						heap.delete_minimum(UpperCAmelCase_ ,       UpperCAmelCase_				)
          if visited[vertex] == 0:
               tree_edges.append((nbr_tv[vertex], vertex)				)
               __lowerCamelCase  :      Union[str, Any]														=						1
               for neighbor, distance in adjacency_list[vertex]:
                    if (
                        visited[neighbor] == 0
                        and distance < distance_tv[heap.get_position(UpperCAmelCase_				)]
                    ):
                         __lowerCamelCase  :      Dict														=						distance
                         heap.bottom_to_top(
                             UpperCAmelCase_ ,       heap.get_position(UpperCAmelCase_				) ,       UpperCAmelCase_ ,       UpperCAmelCase_				)
                         __lowerCamelCase  :      str														=						vertex
     return tree_edges


if __name__ == "__main__":  # pragma: no cover
      # < --------- Prims Algorithm --------- >
      A__						:   Tuple				=    int(input("""Enter number of edges: """).strip())
      A__						:   str				=    defaultdict(list)
      for _ in range(edges_number):
            A__						:   Optional[int]				=    [int(x) for x in input().strip().split()]
            adjacency_list[edge[0]].append([edge[1], edge[2]])
            adjacency_list[edge[1]].append([edge[0], edge[2]])
      print(prisms_algorithm(adjacency_list))






