



'''simple docstring'''
from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

snake_case_					:      Any    			=    TypeVar('T')






def A__       (	UpperCAmelCase_				):
						return (position - 1) // 2






def A__       (	UpperCAmelCase_				):
						return (2 * position) + 1






def A__       (	UpperCAmelCase_				):
						return (2 * position) + 2






class 				lowercase__      (				Generic[T]  ):





	def __init__(					self   :							List[Any]					):







							'''simple docstring'''
							_UpperCamelCase   :						list[tuple[T, int]]												=  []
							_UpperCamelCase   :						dict[T, int]												=  {}
							_UpperCamelCase   :						int												=  0





	def __len__(					self   :							Union[str, Any]					):







							'''simple docstring'''
							return self.elements





	def __repr__(					self   :							List[str]					):







							'''simple docstring'''
							return str(self.heap					)





	def       UpperCamelCase_    (					self   :							Dict					):







							'''simple docstring'''
							# Check if the priority queue is empty
							return self.elements == 0





	def       UpperCamelCase_    (					self   :							Any					,lowerCamelCase__   :							T					,lowerCamelCase__   :							int					):







							'''simple docstring'''
							# Add an element with given priority to the queue
							self.heap.append((elem, weight)					)
							_UpperCamelCase   :						List[str]												=  self.elements
							self.elements += 1
							self._bubble_up(lowerCamelCase__					)





	def       UpperCamelCase_    (					self   :							List[str]					):







							'''simple docstring'''
							# Remove and return the element with lowest weight (highest priority)
							if self.elements > 1:
													self._swap_nodes(0					,self.elements - 1					)
							_UpperCamelCase							,     _UpperCamelCase   :						List[Any]												=  self.heap.pop()
							del self.position_map[elem]
							self.elements -= 1
							if self.elements > 0:
													_UpperCamelCase							,     _UpperCamelCase   :						Any												=  self.heap[0]
													self._bubble_down(lowerCamelCase__					)
							return elem





	def       UpperCamelCase_    (					self   :							Dict					,lowerCamelCase__   :							T					,lowerCamelCase__   :							int					):







							'''simple docstring'''
							# Update the weight of the given key
							_UpperCamelCase   :						Any												=  self.position_map[elem]
							_UpperCamelCase   :						List[str]												=  (elem, weight)
							if position > 0:
													_UpperCamelCase   :						Optional[int]												=  get_parent_position(lowerCamelCase__					)
													_UpperCamelCase							,     _UpperCamelCase   :						Tuple												=  self.heap[parent_position]
													if parent_weight > weight:
																			self._bubble_up(lowerCamelCase__					)
													else:
																			self._bubble_down(lowerCamelCase__					)
							else:
													self._bubble_down(lowerCamelCase__					)





	def       UpperCamelCase_    (					self   :							str					,lowerCamelCase__   :							T					):







							'''simple docstring'''
							# Place a node at the proper position (upward movement) [to be used internally
							# only]
							_UpperCamelCase   :						List[Any]												=  self.position_map[elem]
							if curr_pos == 0:
													return None
							_UpperCamelCase   :						List[str]												=  get_parent_position(lowerCamelCase__					)
							_UpperCamelCase							,     _UpperCamelCase   :						List[Any]												=  self.heap[curr_pos]
							_UpperCamelCase							,     _UpperCamelCase   :						Union[str, Any]												=  self.heap[parent_position]
							if parent_weight > weight:
													self._swap_nodes(lowerCamelCase__					,lowerCamelCase__					)
													return self._bubble_up(lowerCamelCase__					)
							return None





	def       UpperCamelCase_    (					self   :							str					,lowerCamelCase__   :							T					):







							'''simple docstring'''
							# Place a node at the proper position (downward movement) [to be used
							# internally only]
							_UpperCamelCase   :						int												=  self.position_map[elem]
							_UpperCamelCase							,     _UpperCamelCase   :						Optional[int]												=  self.heap[curr_pos]
							_UpperCamelCase   :						int												=  get_child_left_position(lowerCamelCase__					)
							_UpperCamelCase   :						Union[str, Any]												=  get_child_right_position(lowerCamelCase__					)
							if child_left_position < self.elements and child_right_position < self.elements:
													_UpperCamelCase							,     _UpperCamelCase   :						List[Any]												=  self.heap[child_left_position]
													_UpperCamelCase							,     _UpperCamelCase   :						str												=  self.heap[child_right_position]
													if child_right_weight < child_left_weight and child_right_weight < weight:
																			self._swap_nodes(lowerCamelCase__					,lowerCamelCase__					)
																			return self._bubble_down(lowerCamelCase__					)
							if child_left_position < self.elements:
													_UpperCamelCase							,     _UpperCamelCase   :						Optional[int]												=  self.heap[child_left_position]
													if child_left_weight < weight:
																			self._swap_nodes(lowerCamelCase__					,lowerCamelCase__					)
																			return self._bubble_down(lowerCamelCase__					)
							else:
													return None
							if child_right_position < self.elements:
													_UpperCamelCase							,     _UpperCamelCase   :						Dict												=  self.heap[child_right_position]
													if child_right_weight < weight:
																			self._swap_nodes(lowerCamelCase__					,lowerCamelCase__					)
																			return self._bubble_down(lowerCamelCase__					)
							return None





	def       UpperCamelCase_    (					self   :							List[Any]					,lowerCamelCase__   :							int					,lowerCamelCase__   :							int					):







							'''simple docstring'''
							# Swap the nodes at the given positions
							_UpperCamelCase   :						Dict												=  self.heap[nodea_pos][0]
							_UpperCamelCase   :						List[Any]												=  self.heap[nodea_pos][0]
							_UpperCamelCase							,     _UpperCamelCase   :						Dict												=  (
							    self.heap[nodea_pos],
							    self.heap[nodea_pos],
							)
							_UpperCamelCase   :						Union[str, Any]												=  nodea_pos
							_UpperCamelCase   :						str												=  nodea_pos






class 				lowercase__      (				Generic[T]  ):





	def __init__(					self   :							int					):







							'''simple docstring'''
							_UpperCamelCase   :						dict[T, dict[T, int]]												=  {}
							_UpperCamelCase   :						int												=  0





	def __repr__(					self   :							int					):







							'''simple docstring'''
							return str(self.connections					)





	def __len__(					self   :							str					):







							'''simple docstring'''
							return self.nodes





	def       UpperCamelCase_    (					self   :							Union[str, Any]					,lowerCamelCase__   :							T					):







							'''simple docstring'''
							# Add a node in the graph if it is not in the graph
							if node not in self.connections:
													_UpperCamelCase   :						Optional[Any]												=  {}
													self.nodes += 1





	def       UpperCamelCase_    (					self   :							List[str]					,lowerCamelCase__   :							T					,lowerCamelCase__   :							T					,lowerCamelCase__   :							int					):







							'''simple docstring'''
							# Add an edge between 2 nodes in the graph
							self.add_node(lowerCamelCase__					)
							self.add_node(lowerCamelCase__					)
							_UpperCamelCase   :						List[str]												=  weight
							_UpperCamelCase   :						Optional[int]												=  weight






def A__       (	UpperCAmelCase_    ,    ):
						_UpperCamelCase   :						dict[T, int]												=  {node: maxsize for node in graph.connections}
						_UpperCamelCase   :						dict[T, T | None]												=  {node: None for node in graph.connections}

						_UpperCamelCase   :						MinPriorityQueue[T]												=  MinPriorityQueue()
						for node, weight in dist.items():
												priority_queue.push(UpperCAmelCase_    ,    UpperCAmelCase_				)

						if priority_queue.is_empty():
												return dist, parent

						# initialization
						_UpperCamelCase   :						Optional[Any]												=  priority_queue.extract_min()
						_UpperCamelCase   :						List[Any]												=  0
						for neighbour in graph.connections[node]:
												if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
																		_UpperCamelCase   :						str												=  dist[node] + graph.connections[node][neighbour]
																		priority_queue.update_key(UpperCAmelCase_    ,    dist[neighbour]				)
																		_UpperCamelCase   :						Optional[int]												=  node

    # running prim's algorithm
						while not priority_queue.is_empty():
												_UpperCamelCase   :						str												=  priority_queue.extract_min()
												for neighbour in graph.connections[node]:
																		if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
																								_UpperCamelCase   :						Optional[Any]												=  dist[node] + graph.connections[node][neighbour]
																								priority_queue.update_key(UpperCAmelCase_    ,    dist[neighbour]				)
																								_UpperCamelCase   :						Dict												=  node
						return dist, parent







'''simple docstring'''
from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tf_available, is_torch_available


snake_case_					:      Union[str, Any]    			=    {
    'configuration_transfo_xl': ['TRANSFO_XL_PRETRAINED_CONFIG_ARCHIVE_MAP', 'TransfoXLConfig'],
    'tokenization_transfo_xl': ['TransfoXLCorpus', 'TransfoXLTokenizer'],
}

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					snake_case_					:      str    			=    [
					    'TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST',
					    'AdaptiveEmbedding',
					    'TransfoXLForSequenceClassification',
					    'TransfoXLLMHeadModel',
					    'TransfoXLModel',
					    'TransfoXLPreTrainedModel',
					    'load_tf_weights_in_transfo_xl',
					]

try:
					if not is_tf_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					snake_case_					:      Any    			=    [
					    'TF_TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST',
					    'TFAdaptiveEmbedding',
					    'TFTransfoXLForSequenceClassification',
					    'TFTransfoXLLMHeadModel',
					    'TFTransfoXLMainLayer',
					    'TFTransfoXLModel',
					    'TFTransfoXLPreTrainedModel',
					]


if TYPE_CHECKING:
					from .configuration_transfo_xl import TRANSFO_XL_PRETRAINED_CONFIG_ARCHIVE_MAP, TransfoXLConfig
					from .tokenization_transfo_xl import TransfoXLCorpus, TransfoXLTokenizer

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_transfo_xl import (
										    TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST,
										    AdaptiveEmbedding,
										    TransfoXLForSequenceClassification,
										    TransfoXLLMHeadModel,
										    TransfoXLModel,
										    TransfoXLPreTrainedModel,
										    load_tf_weights_in_transfo_xl,
										)

					try:
										if not is_tf_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_tf_transfo_xl import (
										    TF_TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST,
										    TFAdaptiveEmbedding,
										    TFTransfoXLForSequenceClassification,
										    TFTransfoXLLMHeadModel,
										    TFTransfoXLMainLayer,
										    TFTransfoXLModel,
										    TFTransfoXLPreTrainedModel,
										)

else:
					import sys

					snake_case_					:      Dict    			=    _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)


