

'''simple docstring'''


from typing import Callable, Dict, Optional, Tuple

import torch
from torch import nn
from torch.distributions import (
    AffineTransform,
    Distribution,
    Independent,
    NegativeBinomial,
    Normal,
    StudentT,
    TransformedDistribution,
)



class 					lowercase						(  a_ ):


							def __init__(			self    ,			_snake_case    ,			_snake_case=None    ,			_snake_case=None    ,			_snake_case=0)							->				Union[str, Any]:
								UpperCAmelCase_		:      List[str]       	=					1.0 if scale is None else scale
								UpperCAmelCase_		:      Optional[Any]       	=					0.0 if loc is None else loc

								super().__init__(_snake_case    ,			[AffineTransform(loc=self.loc    ,			scale=self.scale    ,			event_dim=_snake_case)])


							@property
							def 						_snake_case							(			self)							->				List[Any]:
								return self.base_dist.mean * self.scale + self.loc


							@property
							def 						_snake_case							(			self)							->				Optional[int]:
								return self.base_dist.variance * self.scale**2





							@property
							def 						_snake_case							(			self)							->				Tuple:
								return self.variance.sqrt()



class 					lowercase						(  nn.Module ):


							def __init__(			self    ,			_snake_case    ,			_snake_case    ,			_snake_case    ,			**_snake_case)							->				None:
								super().__init__(**_snake_case)
								UpperCAmelCase_		:      Tuple       	=					args_dim
								UpperCAmelCase_		:      int       	=					nn.ModuleList([nn.Linear(_snake_case    ,			_snake_case) for dim in args_dim.values()])
								UpperCAmelCase_		:      Any       	=					domain_map





							def 						_snake_case							(			self    ,			_snake_case)							->				Tuple[torch.Tensor]:
								UpperCAmelCase_		:      Optional[Any]       	=					[proj(_snake_case) for proj in self.proj]

								return self.domain_map(*_snake_case)



class 					lowercase						(  nn.Module ):


							def __init__(			self    ,			_snake_case)							->				List[str]:
								super().__init__()
								UpperCAmelCase_		:      Tuple       	=					function





							def 						_snake_case							(			self    ,			_snake_case    ,			*_snake_case)							->				Tuple:
								return self.function(_snake_case    ,			*_snake_case)



class 					lowercase						:
							_lowerCamelCase		:      type
							_lowerCamelCase		:      int
							_lowerCamelCase		:      Dict[str, int]


							def __init__(			self    ,			_snake_case = 1)							->				None:
								UpperCAmelCase_		:      List[str]       	=					dim
								UpperCAmelCase_		:      List[Any]       	=					{k: dim * self.args_dim[k] for k in self.args_dim}


							def 						_snake_case							(			self    ,			_snake_case)							->				Dict:
								if self.dim == 1:
									return self.distribution_class(*_snake_case)
								else:
									return Independent(self.distribution_class(*_snake_case)    ,			1)


							def 						_snake_case							(			self    ,			_snake_case    ,			_snake_case = None    ,			_snake_case = None    ,			)							->				Distribution:
								UpperCAmelCase_		:      List[Any]       	=					self._base_distribution(_snake_case)
								if loc is None and scale is None:
									return distr
								else:
									return AffineTransformed(_snake_case    ,			loc=_snake_case    ,			scale=_snake_case    ,			event_dim=self.event_dim)


							@property
							def 						_snake_case							(			self)							->				Tuple:
								return () if self.dim == 1 else (self.dim,)


							@property
							def 						_snake_case							(			self)							->				int:
								return len(self.event_shape)


							@property
							def 						_snake_case							(			self)							->				float:
								return 0.0


							def 						_snake_case							(			self    ,			_snake_case)							->				nn.Module:
								return ParameterProjection(
								    in_features=_snake_case    ,			args_dim=self.args_dim    ,			domain_map=LambdaLayer(self.domain_map)    ,			)


							def 						_snake_case							(			self    ,			*_snake_case)							->				Union[str, Any]:
								raise NotImplementedError()





							@staticmethod
							def 						_snake_case							(			_snake_case)							->				torch.Tensor:
								return (x + torch.sqrt(torch.square(_snake_case) + 4.0)) / 2.0



class 					lowercase						(  a_ ):
							_lowerCamelCase		:      Dict[str, int]=   {"df": 1, "loc": 1, "scale": 1}
							_lowerCamelCase		:      type=   StudentT


							@classmethod
							def 						_snake_case							(			cls    ,			_snake_case    ,			_snake_case    ,			_snake_case)							->				Dict:
								UpperCAmelCase_		:      Any       	=					cls.squareplus(_snake_case).clamp_min(torch.finfo(scale.dtype).eps)
								UpperCAmelCase_		:      Any       	=					2.0 + cls.squareplus(_snake_case)
								return df.squeeze(-1), loc.squeeze(-1), scale.squeeze(-1)



class 					lowercase						(  a_ ):
							_lowerCamelCase		:      Dict[str, int]=   {"loc": 1, "scale": 1}
							_lowerCamelCase		:      type=   Normal


							@classmethod
							def 						_snake_case							(			cls    ,			_snake_case    ,			_snake_case)							->				Dict:
								UpperCAmelCase_		:      Tuple       	=					cls.squareplus(_snake_case).clamp_min(torch.finfo(scale.dtype).eps)
								return loc.squeeze(-1), scale.squeeze(-1)



class 					lowercase						(  a_ ):
							_lowerCamelCase		:      Dict[str, int]=   {"total_count": 1, "logits": 1}
							_lowerCamelCase		:      type=   NegativeBinomial


							@classmethod
							def 						_snake_case							(			cls    ,			_snake_case    ,			_snake_case)							->				List[str]:
								UpperCAmelCase_		:      Optional[Any]       	=					cls.squareplus(_snake_case)
								return total_count.squeeze(-1), logits.squeeze(-1)


							def 						_snake_case							(			self    ,			_snake_case)							->				Distribution:
								UpperCAmelCase_	,    UpperCAmelCase_		:      Any       	=					distr_args
								if self.dim == 1:
									return self.distribution_class(total_count=_snake_case    ,			logits=_snake_case)
								else:
									return Independent(self.distribution_class(total_count=_snake_case    ,			logits=_snake_case)    ,			1)





							def 						_snake_case							(			self    ,			_snake_case    ,			_snake_case = None    ,			_snake_case = None)							->				Distribution:
								UpperCAmelCase_	,    UpperCAmelCase_		:      Union[str, Any]       	=					distr_args

								if scale is not None:
									# See scaling property of Gamma.
									logits += scale.log()

								return self._base_distribution((total_count, logits))









'''simple docstring'''


import math



class 					lowercase						:


							def __init__(			self    ,			_snake_case=0)							->				Union[str, Any]:  # a graph with Node 0,1,...,N-1
								UpperCAmelCase_		:      Tuple       	=					n
								UpperCAmelCase_		:      Optional[Any]       	=					[
								    [math.inf for j in range(0    ,			_snake_case)] for i in range(0    ,			_snake_case)
								]  # adjacency matrix for weight
								UpperCAmelCase_		:      Tuple       	=					[
								    [math.inf for j in range(0    ,			_snake_case)] for i in range(0    ,			_snake_case)
								]  # dp[i][j] stores minimum distance from i to j


							def 						_snake_case							(			self    ,			_snake_case    ,			_snake_case    ,			_snake_case)							->				List[Any]:
								UpperCAmelCase_		:      Union[str, Any]       	=					w


							def 						_snake_case							(			self)							->				str:
								for k in range(0    ,			self.n):
									for i in range(0    ,			self.n):
										for j in range(0    ,			self.n):
											UpperCAmelCase_		:      Optional[int]       	=					min(self.dp[i][j]    ,			self.dp[i][k] + self.dp[k][j])





							def 						_snake_case							(			self    ,			_snake_case    ,			_snake_case)							->				str:
								return self.dp[u][v]


if __name__ == "__main__":
						lowerCAmelCase__										= Graph(5)
						graph.add_edge(0, 2, 9)
						graph.add_edge(0, 4, 10)
						graph.add_edge(1, 3, 5)
						graph.add_edge(2, 3, 7)
						graph.add_edge(3, 0, 10)
						graph.add_edge(3, 1, 2)
						graph.add_edge(3, 2, 1)
						graph.add_edge(3, 4, 6)
						graph.add_edge(4, 1, 3)
						graph.add_edge(4, 2, 4)
						graph.add_edge(4, 3, 9)
						graph.floyd_warshall()
						graph.show_min(1, 4)
						graph.show_min(0, 3)






