"""simple docstring"""


from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch


@dataclass
class 				a :
    _snake_case   :     torch.Tensor  # [batch_size x 3]
    _snake_case   :     torch.Tensor  # [batch_size x 3]
    _snake_case   :     torch.Tensor  # [batch_size x 3]
    _snake_case   :     torch.Tensor  # [batch_size x 3]
    _snake_case   :     int
    _snake_case   :     int
    _snake_case   :     float
    _snake_case   :     float
    _snake_case   :     Tuple[int]


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


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


    def    lowerCAmelCase_     (    self		:     List[Any]    ):
      _UpperCAmelCase         =					torch.arange(self.height * self.width    )
      _UpperCAmelCase         =					torch.stack(
          [
              pixel_indices % self.width,
              torch.div(__lowerCAmelCase      , self.width      , rounding_mode="""trunc"""    ),
          ]      , axis=1      , )
      return coords


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

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

      _UpperCAmelCase         =					rays.view(__lowerCAmelCase      , inner_batch_size * self.height * self.width      , 2      , 3    )

      return rays


    def    lowerCAmelCase_     (    self		:     Union[str, Any]      , __lowerCAmelCase		:     torch.Tensor    ):
      _UpperCAmelCase       , *_UpperCAmelCase       , _UpperCAmelCase         =					coords.shape
      assert n_coords == 2
      assert batch_size == self.origin.shape[0]

      _UpperCAmelCase         =					coords.view(__lowerCAmelCase      , -1      , 2    )

      _UpperCAmelCase         =					self.resolution()
      _UpperCAmelCase         =					self.fov()

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

      _UpperCAmelCase         =					fracs.view(__lowerCAmelCase      , -1      , 2    )
      _UpperCAmelCase         =					(
          self.z.view(__lowerCAmelCase      , 1      , 3    )
          + self.x.view(__lowerCAmelCase      , 1      , 3    ) * fracs[:, :, :1]
          + self.y.view(__lowerCAmelCase      , 1      , 3    ) * fracs[:, :, 1:]
      )
      _UpperCAmelCase         =					directions / directions.norm(dim=-1      , keepdim=__lowerCAmelCase    )
      _UpperCAmelCase         =					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		:     List[str]      , __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    (	lowercase						):







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

"""simple docstring"""


UpperCAmelCase__     						=  [
    [0, 1_6, 1_3, 0, 0, 0],
    [0, 0, 1_0, 1_2, 0, 0],
    [0, 4, 0, 0, 1_4, 0],
    [0, 0, 9, 0, 0, 2_0],
    [0, 0, 0, 7, 0, 4],
    [0, 0, 0, 0, 0, 0],
]






def 			__UpperCAmelCase    (	lowercase      ,lowercase      ,lowercase      ,lowercase						):







  """simple docstring"""
  # Return True if there is node that has not iterated.
  _UpperCAmelCase         =					[False] * len(lowercase						)
  _UpperCAmelCase         =					[s]
  _UpperCAmelCase         =					True

  while queue:
    _UpperCAmelCase         =					queue.pop(0						)
    for ind in range(len(graph[u]						)						):
      if visited[ind] is False and graph[u][ind] > 0:
        queue.append(lowercase						)
        _UpperCAmelCase         =					True
        _UpperCAmelCase         =					u

  return visited[t]






def 			__UpperCAmelCase    (	lowercase      ,lowercase      ,lowercase						):







  """simple docstring"""
  _UpperCAmelCase         =					[-1] * (len(lowercase						))
  _UpperCAmelCase         =					0
  _UpperCAmelCase         =					[]
  _UpperCAmelCase         =					[i[:] for i in graph]  # Record original cut, copy.
  while bfs(lowercase      ,lowercase      ,lowercase      ,lowercase						):
    _UpperCAmelCase         =					float("""Inf"""						)
    _UpperCAmelCase         =					sink

    while s != source:
      # Find the minimum value in select path
      _UpperCAmelCase         =					min(lowercase      ,graph[parent[s]][s]						)
      _UpperCAmelCase         =					parent[s]

    max_flow += path_flow
    _UpperCAmelCase         =					sink

    while v != source:
      _UpperCAmelCase         =					parent[v]
      graph[u][v] -= path_flow
      graph[v][u] += path_flow
      _UpperCAmelCase         =					parent[v]

  for i in range(len(lowercase						)						):
    for j in range(len(graph[0]						)						):
      if graph[i][j] == 0 and temp[i][j] > 0:
        res.append((i, j)						)

  return res


if __name__ == "__main__":
    print(mincut(test_graph, source=0, sink=5))
