




from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch





@dataclass
class 			lowerCamelCase_				:


 '''simple docstring'''







 lowercase_							       =       42  # [batch_size x 3]
 lowercase_							       =       42  # [batch_size x 3]
 lowercase_							       =       42  # [batch_size x 3]
 lowercase_							       =       42  # [batch_size x 3]
 lowercase_							       =       42
 lowercase_							       =       42
 lowercase_							       =       42
 lowercase_							       =       42
 lowercase_							       =       42



 def  lowerCAmelCase_    (				self    :						Dict		):
       assert self.x.shape[0] == self.y.shape[0] == self.z.shape[0] == self.origin.shape[0]
       assert self.x.shape[1] == self.y.shape[1] == self.z.shape[1] == self.origin.shape[1] == 3
       assert len(self.x.shape		) == len(self.y.shape		) == len(self.z.shape		) == len(self.origin.shape		) == 2



 def  lowerCAmelCase_    (				self    :						Optional[Any]		):
       return torch.from_numpy(np.array([self.width, self.height]							,							dtype=np.floataa		)		)



 def  lowerCAmelCase_    (				self    :						str		):
       return torch.from_numpy(np.array([self.x_fov, self.y_fov]							,							dtype=np.floataa		)		)



 def  lowerCAmelCase_    (				self    :						Any		):
       SCREAMING_SNAKE_CASE_      		=     torch.arange(self.height * self.width		)
       SCREAMING_SNAKE_CASE_      		=     torch.stack(
           [
               pixel_indices % self.width,
               torch.div(_lowerCAmelCase							,							self.width							,							rounding_mode='trunc'		),
           ]							,							axis=1							,							)
       return coords



 @property
 def  lowerCAmelCase_    (				self    :						str		):
       SCREAMING_SNAKE_CASE_		,					*SCREAMING_SNAKE_CASE_      		=     self.shape
       SCREAMING_SNAKE_CASE_      		=     int(np.prod(_lowerCAmelCase		)		)

       SCREAMING_SNAKE_CASE_      		=     self.get_image_coords()
       SCREAMING_SNAKE_CASE_      		=     torch.broadcast_to(coords.unsqueeze(0		)							,							[batch_size * inner_batch_size, *coords.shape]		)
       SCREAMING_SNAKE_CASE_      		=     self.get_camera_rays(_lowerCAmelCase		)

       SCREAMING_SNAKE_CASE_      		=     rays.view(_lowerCAmelCase							,							inner_batch_size * self.height * self.width							,							2							,							3		)

       return rays



 def  lowerCAmelCase_    (				self    :						str							,							_lowerCAmelCase    :						torch.Tensor		):
       SCREAMING_SNAKE_CASE_		,					*SCREAMING_SNAKE_CASE_		,					SCREAMING_SNAKE_CASE_      		=     coords.shape
       assert n_coords == 2
       assert batch_size == self.origin.shape[0]

       SCREAMING_SNAKE_CASE_      		=     coords.view(_lowerCAmelCase							,							-1							,							2		)

       SCREAMING_SNAKE_CASE_      		=     self.resolution()
       SCREAMING_SNAKE_CASE_      		=     self.fov()

       SCREAMING_SNAKE_CASE_      		=     (flat.float() / (res - 1)) * 2 - 1
       SCREAMING_SNAKE_CASE_      		=     fracs * torch.tan(fov / 2		)

       SCREAMING_SNAKE_CASE_      		=     fracs.view(_lowerCAmelCase							,							-1							,							2		)
       SCREAMING_SNAKE_CASE_      		=     (
           self.z.view(_lowerCAmelCase							,							1							,							3		)
           + self.x.view(_lowerCAmelCase							,							1							,							3		) * fracs[:, :, :1]
           + self.y.view(_lowerCAmelCase							,							1							,							3		) * fracs[:, :, 1:]
       )
       SCREAMING_SNAKE_CASE_      		=     directions / directions.norm(dim=-1							,							keepdim=_lowerCAmelCase		)
       SCREAMING_SNAKE_CASE_      		=     torch.stack(
           [
               torch.broadcast_to(self.origin.view(_lowerCAmelCase							,							1							,							3		)							,							[batch_size, directions.shape[1], 3]		),
               directions,
           ]							,							dim=2							,							)
       return rays.view(_lowerCAmelCase							,							*_lowerCAmelCase							,							2							,							3		)




 def  lowerCAmelCase_    (				self    :						Optional[Any]							,							_lowerCAmelCase    :						int							,							_lowerCAmelCase    :						int		):
       assert width * self.height == height * self.width, "The aspect ratio should not change."
       return DifferentiableProjectiveCamera(
           origin=self.origin							,							x=self.x							,							y=self.y							,							z=self.z							,							width=_lowerCAmelCase							,							height=_lowerCAmelCase							,							x_fov=self.x_fov							,							y_fov=self.y_fov							,							)


def    UpperCAmelCase_				( __UpperCAmelCase		:      int				)   ->					DifferentiableProjectiveCamera:
      SCREAMING_SNAKE_CASE_      		=     []
      SCREAMING_SNAKE_CASE_      		=     []
      SCREAMING_SNAKE_CASE_      		=     []
      SCREAMING_SNAKE_CASE_      		=     []
      for theta in np.linspace(0     ,     2 * np.pi     ,     num=20				):
            SCREAMING_SNAKE_CASE_      		=     np.array([np.sin(__UpperCAmelCase				), np.cos(__UpperCAmelCase				), -0.5]				)
            z /= np.sqrt(np.sum(z**2				)				)
            SCREAMING_SNAKE_CASE_      		=     -z * 4
            SCREAMING_SNAKE_CASE_      		=     np.array([np.cos(__UpperCAmelCase				), -np.sin(__UpperCAmelCase				), 0.0]				)
            SCREAMING_SNAKE_CASE_      		=     np.cross(__UpperCAmelCase     ,     __UpperCAmelCase				)
            origins.append(__UpperCAmelCase				)
            xs.append(__UpperCAmelCase				)
            ys.append(__UpperCAmelCase				)
            zs.append(__UpperCAmelCase				)
      return DifferentiableProjectiveCamera(
          origin=torch.from_numpy(np.stack(__UpperCAmelCase     ,     axis=0				)				).float()     ,     x=torch.from_numpy(np.stack(__UpperCAmelCase     ,     axis=0				)				).float()     ,     y=torch.from_numpy(np.stack(__UpperCAmelCase     ,     axis=0				)				).float()     ,     z=torch.from_numpy(np.stack(__UpperCAmelCase     ,     axis=0				)				).float()     ,     width=__UpperCAmelCase     ,     height=__UpperCAmelCase     ,     x_fov=0.7     ,     y_fov=0.7     ,     shape=(1, len(__UpperCAmelCase				))     ,     )





class 			lowerCamelCase_				:


 '''simple docstring'''







 def __init__(				self    :						str		):
       SCREAMING_SNAKE_CASE_      		=     {}



 def  lowerCAmelCase_    (				self    :						List[str]		):
       print(self.vertex		)
       for i in self.vertex:
             print(_lowerCAmelCase							,							' -> '							,							' -> '.join([str(_lowerCAmelCase		) for j in self.vertex[i]]		)		)



 def  lowerCAmelCase_    (				self    :						Union[str, Any]							,							_lowerCAmelCase    :						int							,							_lowerCAmelCase    :						int		):
       # check if vertex is already present,
       if from_vertex in self.vertex:
             self.vertex[from_vertex].append(_lowerCAmelCase		)
       else:
             # else make a new vertex
             SCREAMING_SNAKE_CASE_      		=     [to_vertex]



 def  lowerCAmelCase_    (				self    :						Optional[Any]		):
       # visited array for storing already visited nodes
       SCREAMING_SNAKE_CASE_      		=     [False] * len(self.vertex		)

       # call the recursive helper function
       for i in range(len(self.vertex		)		):
             if not visited[i]:
                   self.dfs_recursive(_lowerCAmelCase							,							_lowerCAmelCase		)




 def  lowerCAmelCase_    (				self    :						Tuple							,							_lowerCAmelCase    :						int							,							_lowerCAmelCase    :						list		):
       # mark start vertex as visited
       SCREAMING_SNAKE_CASE_      		=     True

       print(_lowerCAmelCase							,							end=' '		)

       # Recur for all the vertices that are adjacent to this node
       for i in self.vertex:
             if not visited[i]:
                   self.dfs_recursive(_lowerCAmelCase							,							_lowerCAmelCase		)


if __name__ == "__main__":
   lowerCamelCase__					:  List[Any]      							=				Graph()
   g.add_edge(0, 1)
   g.add_edge(0, 2)
   g.add_edge(1, 2)
   g.add_edge(2, 0)
   g.add_edge(2, 3)
   g.add_edge(3, 3)

   g.print_graph()
   print('DFS:')
   g.dfs()

   # OUTPUT:
   # 0  ->  1 -> 2
   # 1  ->  2
   # 2  ->  0 -> 3
   # 3  ->  3
   # DFS:
   #  0 1 2 3