




'''simple docstring'''



from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch





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


       def    lowerCAmelCase   ( self	)   ->	Optional[Any]:



            '''simple docstring'''




            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[int]:



            '''simple docstring'''




            return torch.from_numpy(np.array([self.width, self.height]     ,	dtype=np.floataa	)	)


       def    lowerCAmelCase   ( self	)   ->	Union[str, Any]:



            '''simple docstring'''




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


       def    lowerCAmelCase   ( self	)   ->	int:



            '''simple docstring'''




            __snake_case            =	torch.arange(self.height * self.width	)
            __snake_case            =	torch.stack(
                [
                    pixel_indices % self.width,
                    torch.div(__a     ,	self.width     ,	rounding_mode='''trunc'''	),
                ]     ,	axis=1     ,	)
            return coords


       @property
       def    lowerCAmelCase   ( self	)   ->	str:



            '''simple docstring'''




            __snake_case       ,     *__snake_case            =	self.shape
            __snake_case            =	int(np.prod(__a	)	)

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

            __snake_case            =	rays.view(__a     ,	inner_batch_size * self.height * self.width     ,	2     ,	3	)

            return rays


       def    lowerCAmelCase   ( self     ,	__SCREAMING_SNAKE_CASE	)   ->	Union[str, Any]:



            '''simple docstring'''




            __snake_case       ,     *__snake_case       ,     __snake_case            =	coords.shape
            assert n_coords == 2
            assert batch_size == self.origin.shape[0]

            __snake_case            =	coords.view(__a     ,	-1     ,	2	)

            __snake_case            =	self.resolution()
            __snake_case            =	self.fov()

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

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




       def    lowerCAmelCase   ( self     ,	__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE	)   ->	Dict:



            '''simple docstring'''




            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=__a     ,	height=__a     ,	x_fov=self.x_fov     ,	y_fov=self.y_fov     ,	)







def       _UpperCamelCase			(_lowerCamelCase				:  Tuple						)-> Union[str, Any]:




     '''simple docstring'''





     __snake_case            =	[]
     __snake_case            =	[]
     __snake_case            =	[]
     __snake_case            =	[]
     for theta in np.linspace(0 ,						2 * np.pi ,						num=20						):
          __snake_case            =	np.array([np.sin(_UpperCamelCase						), np.cos(_UpperCamelCase						), -0.5]						)
          z /= np.sqrt(np.sum(z**2						)						)
          __snake_case            =	-z * 4
          __snake_case            =	np.array([np.cos(_UpperCamelCase						), -np.sin(_UpperCamelCase						), 0.0]						)
          __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						)) ,						)










"""simple docstring"""


def _lowerCamelCase      (						_UpperCamelCase       ,					_UpperCamelCase       ,					_UpperCamelCase       ,					_UpperCamelCase ):

			'''simple docstring'''




			__lowerCAmelCase							       =     [False] * len(_UpperCamelCase )
			__lowerCAmelCase							       =     []
			queue.append(_UpperCamelCase )
			__lowerCAmelCase							       =     True

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

			return visited[t]


def _lowerCamelCase      (						_UpperCamelCase       ,					_UpperCamelCase       ,					_UpperCamelCase ):

			'''simple docstring'''




			__lowerCAmelCase							       =     [-1] * (len(_UpperCamelCase ))
			__lowerCAmelCase							       =     0
			while bfs(_UpperCamelCase       ,					_UpperCamelCase       ,					_UpperCamelCase       ,					_UpperCamelCase ):
						__lowerCAmelCase							       =     float("Inf" )
						__lowerCAmelCase							       =     sink

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

						max_flow += path_flow
						__lowerCAmelCase							       =     sink

						while v != source:
									__lowerCAmelCase							       =     parent[v]
									graph[u][v] -= path_flow
									graph[v][u] += path_flow
									__lowerCAmelCase							       =     parent[v]
			return max_flow


A	:  Union[str, Any]            =     [
    [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],
]

A       ,       A	:  Any            =     0, 5


print(ford_fulkerson(graph, source, sink))




