

'''simple docstring'''

from __future__ import annotations

from typing import Any






class    snake_case     :






				"""simple docstring"""



				def __init__(    self,     _lowercase       )     ->							None:
											SCREAMING_SNAKE_CASE_				=				num_of_nodes
											SCREAMING_SNAKE_CASE_				=				[]
											SCREAMING_SNAKE_CASE_				=				{}



				def   a__					(    self,     _lowercase,     _lowercase,     _lowercase       )     ->							None:
											self.m_edges.append([u_node, v_node, weight]       )



				def   a__					(    self,     _lowercase       )     ->							int:

											if self.m_component[u_node] == u_node:
																		return u_node
											return self.find_component(self.m_component[u_node]       )



				def   a__					(    self,     _lowercase       )     ->							None:

											if self.m_component[u_node] != u_node:
																		for k in self.m_component:
																									SCREAMING_SNAKE_CASE_				=				self.find_component(_lowercase       )



				def   a__					(    self,     _lowercase,     _lowercase,     _lowercase       )     ->							None:

											if component_size[u_node] <= component_size[v_node]:
																		SCREAMING_SNAKE_CASE_				=				v_node
																		component_size[v_node] += component_size[u_node]
																		self.set_component(_lowercase       )

											elif component_size[u_node] >= component_size[v_node]:
																		SCREAMING_SNAKE_CASE_				=				self.find_component(_lowercase       )
																		component_size[u_node] += component_size[v_node]
																		self.set_component(_lowercase       )





				def   a__					(    self       )     ->							None:
											SCREAMING_SNAKE_CASE_				=				[]
											SCREAMING_SNAKE_CASE_				=				0

											SCREAMING_SNAKE_CASE_				=				[-1] * self.m_num_of_nodes

											# A list of components (initialized to all of the nodes)
											for node in range(self.m_num_of_nodes       ):
																		self.m_component.update({node: node}       )
																		component_size.append(1       )

											SCREAMING_SNAKE_CASE_				=				self.m_num_of_nodes

											while num_of_components > 1:
																		for edge in self.m_edges:
																									SCREAMING_SNAKE_CASE_				,    SCREAMING_SNAKE_CASE_				,    SCREAMING_SNAKE_CASE_				=				edge

																									SCREAMING_SNAKE_CASE_				=				self.m_component[u]
																									SCREAMING_SNAKE_CASE_				=				self.m_component[v]

																									if u_component != v_component:

																																for component in (u_component, v_component):
																																							if (
																																							    minimum_weight_edge[component] == -1
																																							    or minimum_weight_edge[component][2] > w
																																							):
																																														SCREAMING_SNAKE_CASE_				=				[u, v, w]

																		for edge in minimum_weight_edge:
																									if isinstance(_lowercase,     _lowercase       ):
																																SCREAMING_SNAKE_CASE_				,    SCREAMING_SNAKE_CASE_				,    SCREAMING_SNAKE_CASE_				=				edge

																																SCREAMING_SNAKE_CASE_				=				self.m_component[u]
																																SCREAMING_SNAKE_CASE_				=				self.m_component[v]

																																if u_component != v_component:
																																							mst_weight += w
																																							self.union(_lowercase,     _lowercase,     _lowercase       )
																																							print(f"""Added edge [{u} - {v}]\nAdded weight: {w}\n"""       )
																																							num_of_components -= 1

																		SCREAMING_SNAKE_CASE_				=				[-1] * self.m_num_of_nodes
											print(f"""The total weight of the minimal spanning tree is: {mst_weight}"""       )




def 							_UpperCamelCase				(   )      -> None:
							pass


if __name__ == "__main__":
							import doctest

							doctest.testmod()








'''simple docstring'''

from dataclasses import dataclass
from typing import Optional, Tuple, Union

import flax
import jax.numpy as jnp
from jax import random

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils_flax import FlaxSchedulerMixin






@flax.struct.dataclass
class    snake_case     :






				"""simple docstring"""
				# setable values
				_a    	=     None
				_a    	=     None
				_a    	=     None  # sigma(t_i)



				@classmethod
				def   a__					(    cls       )     ->							Dict:
											return cls()






@dataclass
class    snake_case     (      lowercase_		):






				"""simple docstring"""
				_a    	=     42
				_a    	=     42
				_a    	=     42






class    snake_case     (      lowercase_,						lowercase_		):






				"""simple docstring"""



				@property
				def   a__					(    self       )     ->							int:
											return True



				@register_to_config
				def __init__(    self,     _lowercase = 0.02,     _lowercase = 100,     _lowercase = 1.007,     _lowercase = 80,     _lowercase = 0.05,     _lowercase = 50,     )     ->							List[Any]:
											pass



				def   a__					(    self       )     ->							List[Any]:
											return KarrasVeSchedulerState.create()



				def   a__					(    self,     _lowercase,     _lowercase,     _lowercase = ()       )     ->							KarrasVeSchedulerState:
											SCREAMING_SNAKE_CASE_				=				jnp.arange(0,     _lowercase       )[::-1].copy()
											SCREAMING_SNAKE_CASE_				=				[
											    (
											        self.config.sigma_max**2
											        * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
											    )
											    for i in timesteps
											]

											return state.replace(
											    num_inference_steps=_lowercase,     schedule=jnp.array(_lowercase,     dtype=jnp.floataa       ),     timesteps=_lowercase,     )



				def   a__					(    self,     _lowercase,     _lowercase,     _lowercase,     _lowercase,     )     ->							Tuple[jnp.ndarray, float]:
											if self.config.s_min <= sigma <= self.config.s_max:
																		SCREAMING_SNAKE_CASE_				=				min(self.config.s_churn / state.num_inference_steps,     2**0.5 - 1       )
											else:
																		SCREAMING_SNAKE_CASE_				=				0

											# sample eps ~ N(0, S_noise^2 * I)
											SCREAMING_SNAKE_CASE_				=				random.split(_lowercase,     num=1       )
											SCREAMING_SNAKE_CASE_				=				self.config.s_noise * random.normal(key=_lowercase,     shape=sample.shape       )
											SCREAMING_SNAKE_CASE_				=				sigma + gamma * sigma
											SCREAMING_SNAKE_CASE_				=				sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

											return sample_hat, sigma_hat



				def   a__					(    self,     _lowercase,     _lowercase,     _lowercase,     _lowercase,     _lowercase,     _lowercase = True,     )     ->							Union[FlaxKarrasVeOutput, Tuple]:
											SCREAMING_SNAKE_CASE_				=				sample_hat + sigma_hat * model_output
											SCREAMING_SNAKE_CASE_				=				(sample_hat - pred_original_sample) / sigma_hat
											SCREAMING_SNAKE_CASE_				=				sample_hat + (sigma_prev - sigma_hat) * derivative

											if not return_dict:
																		return (sample_prev, derivative, state)

											return FlaxKarrasVeOutput(prev_sample=_lowercase,     derivative=_lowercase,     state=_lowercase       )



				def   a__					(    self,     _lowercase,     _lowercase,     _lowercase,     _lowercase,     _lowercase,     _lowercase,     _lowercase,     _lowercase = True,     )     ->							Union[FlaxKarrasVeOutput, Tuple]:
											SCREAMING_SNAKE_CASE_				=				sample_prev + sigma_prev * model_output
											SCREAMING_SNAKE_CASE_				=				(sample_prev - pred_original_sample) / sigma_prev
											SCREAMING_SNAKE_CASE_				=				sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

											if not return_dict:
																		return (sample_prev, derivative, state)

											return FlaxKarrasVeOutput(prev_sample=_lowercase,     derivative=_lowercase,     state=_lowercase       )





				def   a__					(    self,     _lowercase,     _lowercase,     _lowercase,     _lowercase       )     ->							List[Any]:
											raise NotImplementedError()





