




from __future__ import annotations




def 		lowerCAmelCase_ (						lowerCamelCase						,  lowerCamelCase ):
				print(F"Vertex\tShortest Distance from vertex {src}" )
				for i, d in enumerate(lowerCamelCase ):
								print(F"{i}\t\t{d}" )




def 		lowerCAmelCase_ (						lowerCamelCase						,  lowerCamelCase						,  lowerCamelCase ):
				for j in range(lowerCamelCase ):
								__magic_name__					,			__magic_name__					,			__magic_name__						:						Any										=(graph[j][k] for k in ["""src""", """dst""", """weight"""])
								if distance[u] != float("""inf""" ) and distance[u] + w < distance[v]:
												return True
				return False




def 		lowerCAmelCase_ (						lowerCamelCase						,  lowerCamelCase						,  lowerCamelCase						,  lowerCamelCase ):
				__magic_name__						:						Any										=[float("""inf""" )] * vertex_count
				__magic_name__						:						Optional[int]										=0.0

				for _ in range(vertex_count - 1 ):
								for j in range(lowerCamelCase ):
												__magic_name__					,			__magic_name__					,			__magic_name__						:						List[str]										=(graph[j][k] for k in ["""src""", """dst""", """weight"""])

												if distance[u] != float("""inf""" ) and distance[u] + w < distance[v]:
																__magic_name__						:						Optional[Any]										=distance[u] + w

				__magic_name__						:						Optional[Any]										=check_negative_cycle(lowerCamelCase						,  lowerCamelCase						,  lowerCamelCase )
				if negative_cycle_exists:
								raise Exception("""Negative cycle found""" )

				return distance


if __name__ == "__main__":
							import doctest

							doctest.testmod()

							UpperCAmelCase_		:					Dict          =  int(input("Enter number of vertices: ").strip())
							UpperCAmelCase_		:					Any          =  int(input("Enter number of edges: ").strip())

							UpperCAmelCase_		:					list[dict[str, int]]          =  [{} for _ in range(E)]

							for i in range(E):
														print("Edge ", i + 1)
														UpperCAmelCase_    ,  UpperCAmelCase_    ,  UpperCAmelCase_		:					List[str]          =  (
														    int(x)
														    for x in input("Enter source, destination, weight: ").strip().split(" ")
														)
														UpperCAmelCase_		:					str          =  {"src": src, "dst": dest, "weight": weight}

							UpperCAmelCase_		:					List[Any]          =  int(input("\nEnter shortest path source:").strip())
							UpperCAmelCase_		:					str          =  bellman_ford(graph, V, E, source)
							print_distance(shortest_distance, 0)










# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

import math
from typing import Union

import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import randn_tensor
from .scheduling_utils import SchedulerMixin




class 		__A   (      UpperCamelCase__       ,    UpperCamelCase__      ):
						UpperCamelCase      =       1

						@register_to_config
						def __init__(		self :Any     ,			__snake_case :Tuple=20_00     ,			__snake_case :Optional[Any]=0.1     ,			__snake_case :Any=20     ,			__snake_case :Optional[int]=1E-3			):
										'''simple docstring'''

										__magic_name__						:						Dict										=None
										__magic_name__						:						List[str]										=None
										__magic_name__						:						str										=None

						def      A__    (		self :Dict     ,			__snake_case :Optional[int]     ,			__snake_case :Union[str, torch.device] = None			):
										'''simple docstring'''

										__magic_name__						:						Union[str, Any]										=torch.linspace(1     ,			self.config.sampling_eps     ,			__snake_case     ,			device=__snake_case			)

						def      A__    (		self :List[str]     ,			__snake_case :List[str]     ,			__snake_case :int     ,			__snake_case :int     ,			__snake_case :List[str]=None			):
										'''simple docstring'''

										if self.timesteps is None:
														raise ValueError(
														    """`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""			)

										# TODO(Patrick) better comments + non-PyTorch
										# postprocess model score
										__magic_name__						:						int										=(
										    -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
										)
										__magic_name__						:						Optional[int]										=torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff			)			)
										__magic_name__						:						str										=std.flatten()
										while len(std.shape			) < len(score.shape			):
														__magic_name__						:						List[str]										=std.unsqueeze(-1			)
										__magic_name__						:						Union[str, Any]										=-score / std

										# compute
										__magic_name__						:						Tuple										=-1.0 / len(self.timesteps			)

										__magic_name__						:						int										=self.config.beta_min + t * (self.config.beta_max - self.config.beta_min)
										__magic_name__						:						Dict										=beta_t.flatten()
										while len(beta_t.shape			) < len(x.shape			):
														__magic_name__						:						Any										=beta_t.unsqueeze(-1			)
										__magic_name__						:						Dict										=-0.5 * beta_t * x

										__magic_name__						:						Optional[int]										=torch.sqrt(__snake_case			)
										__magic_name__						:						int										=drift - diffusion**2 * score
										__magic_name__						:						List[str]										=x + drift * dt

										# add noise
										__magic_name__						:						Optional[int]										=randn_tensor(x.shape     ,			layout=x.layout     ,			generator=__snake_case     ,			device=x.device     ,			dtype=x.dtype			)
										__magic_name__						:						Optional[Any]										=x_mean + diffusion * math.sqrt(-dt			) * noise

										return x, x_mean


						def __len__(		self :List[Any]			):
										'''simple docstring'''

										return self.config.num_train_timesteps




