


from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

UpperCAmelCase      =   TypeVar("""T""")






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE )->  int:




      """simple docstring"""

      return (position - 1) // 2






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE )->  int:




      """simple docstring"""

      return (2 * position) + 1






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE )->  int:




      """simple docstring"""

      return (2 * position) + 2







class lowerCAmelCase_						(			Generic[T]	):

 '''simple docstring'''

 def __init__(     self ):
       snake_case_	=				[]
       snake_case_	=				{}
       snake_case_	=				0



 def __len__(     self ):
       return self.elements



 def __repr__(     self ):
       return str(self.heap )



 def 						UpperCamelCase__					(     self ):
       # Check if the priority queue is empty
       return self.elements == 0



 def 						UpperCamelCase__					(     self		,				_UpperCAmelCase		,				_UpperCAmelCase ):
       # Add an element with given priority to the queue
       self.heap.append((elem, weight) )
       snake_case_	=				self.elements
       self.elements += 1
       self._bubble_up(_UpperCAmelCase )



 def 						UpperCamelCase__					(     self ):
       # Remove and return the element with lowest weight (highest priority)
       if self.elements > 1:
             self._swap_nodes(0		,				self.elements - 1 )
       snake_case_	,   snake_case_	=				self.heap.pop()
       del self.position_map[elem]
       self.elements -= 1
       if self.elements > 0:
             snake_case_	,   snake_case_	=				self.heap[0]
             self._bubble_down(_UpperCAmelCase )
       return elem



 def 						UpperCamelCase__					(     self		,				_UpperCAmelCase		,				_UpperCAmelCase ):
       # Update the weight of the given key
       snake_case_	=				self.position_map[elem]
       snake_case_	=				(elem, weight)
       if position > 0:
             snake_case_	=				get_parent_position(_UpperCAmelCase )
             snake_case_	,   snake_case_	=				self.heap[parent_position]
             if parent_weight > weight:
                   self._bubble_up(_UpperCAmelCase )
             else:
                   self._bubble_down(_UpperCAmelCase )
       else:
             self._bubble_down(_UpperCAmelCase )



 def 						UpperCamelCase__					(     self		,				_UpperCAmelCase ):
       # Place a node at the proper position (upward movement) [to be used internally
       # only]
       snake_case_	=				self.position_map[elem]
       if curr_pos == 0:
             return None
       snake_case_	=				get_parent_position(_UpperCAmelCase )
       snake_case_	,   snake_case_	=				self.heap[curr_pos]
       snake_case_	,   snake_case_	=				self.heap[parent_position]
       if parent_weight > weight:
             self._swap_nodes(_UpperCAmelCase		,				_UpperCAmelCase )
             return self._bubble_up(_UpperCAmelCase )
       return None



 def 						UpperCamelCase__					(     self		,				_UpperCAmelCase ):
       # Place a node at the proper position (downward movement) [to be used
       # internally only]
       snake_case_	=				self.position_map[elem]
       snake_case_	,   snake_case_	=				self.heap[curr_pos]
       snake_case_	=				get_child_left_position(_UpperCAmelCase )
       snake_case_	=				get_child_right_position(_UpperCAmelCase )
       if child_left_position < self.elements and child_right_position < self.elements:
             snake_case_	,   snake_case_	=				self.heap[child_left_position]
             snake_case_	,   snake_case_	=				self.heap[child_right_position]
             if child_right_weight < child_left_weight and child_right_weight < weight:
                   self._swap_nodes(_UpperCAmelCase		,				_UpperCAmelCase )
                   return self._bubble_down(_UpperCAmelCase )
       if child_left_position < self.elements:
             snake_case_	,   snake_case_	=				self.heap[child_left_position]
             if child_left_weight < weight:
                   self._swap_nodes(_UpperCAmelCase		,				_UpperCAmelCase )
                   return self._bubble_down(_UpperCAmelCase )
       else:
             return None
       if child_right_position < self.elements:
             snake_case_	,   snake_case_	=				self.heap[child_right_position]
             if child_right_weight < weight:
                   self._swap_nodes(_UpperCAmelCase		,				_UpperCAmelCase )
                   return self._bubble_down(_UpperCAmelCase )
       return None





 def 						UpperCamelCase__					(     self		,				_UpperCAmelCase		,				_UpperCAmelCase ):
       # Swap the nodes at the given positions
       snake_case_	=				self.heap[nodea_pos][0]
       snake_case_	=				self.heap[nodea_pos][0]
       snake_case_	,   snake_case_	=				(
           self.heap[nodea_pos],
           self.heap[nodea_pos],
       )
       snake_case_	=				nodea_pos
       snake_case_	=				nodea_pos







class lowerCAmelCase_						(			Generic[T]	):

 '''simple docstring'''

 def __init__(     self ):
       snake_case_	=				{}
       snake_case_	=				0



 def __repr__(     self ):
       return str(self.connections )



 def __len__(     self ):
       return self.nodes



 def 						UpperCamelCase__					(     self		,				_UpperCAmelCase ):
       # Add a node in the graph if it is not in the graph
       if node not in self.connections:
             snake_case_	=				{}
             self.nodes += 1





 def 						UpperCamelCase__					(     self		,				_UpperCAmelCase		,				_UpperCAmelCase		,				_UpperCAmelCase ):
       # Add an edge between 2 nodes in the graph
       self.add_node(_UpperCAmelCase )
       self.add_node(_UpperCAmelCase )
       snake_case_	=				weight
       snake_case_	=				weight






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , )->  tuple[dict[T, int], dict[T, T | None]]:




      """simple docstring"""

      snake_case_	=				{node: maxsize for node in graph.connections}
      snake_case_	=				{node: None for node in graph.connections}

      snake_case_	=				MinPriorityQueue()
      for node, weight in dist.items():
            priority_queue.push(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )

      if priority_queue.is_empty():
            return dist, parent

      # initialization
      snake_case_	=				priority_queue.extract_min()
      snake_case_	=				0
      for neighbour in graph.connections[node]:
            if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
                  snake_case_	=				dist[node] + graph.connections[node][neighbour]
                  priority_queue.update_key(SCREAMING_SNAKE_CASE , dist[neighbour] )
                  snake_case_	=				node

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



from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


UpperCAmelCase      =   {"""configuration_xglm""": ["""XGLM_PRETRAINED_CONFIG_ARCHIVE_MAP""", """XGLMConfig"""]}

try:
   if not is_sentencepiece_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase      =   ["""XGLMTokenizer"""]

try:
   if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase      =   ["""XGLMTokenizerFast"""]

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase      =   [
       """XGLM_PRETRAINED_MODEL_ARCHIVE_LIST""",
       """XGLMForCausalLM""",
       """XGLMModel""",
       """XGLMPreTrainedModel""",
   ]


try:
   if not is_flax_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase      =   [
       """FlaxXGLMForCausalLM""",
       """FlaxXGLMModel""",
       """FlaxXGLMPreTrainedModel""",
   ]


try:
   if not is_tf_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase      =   [
       """TF_XGLM_PRETRAINED_MODEL_ARCHIVE_LIST""",
       """TFXGLMForCausalLM""",
       """TFXGLMModel""",
       """TFXGLMPreTrainedModel""",
   ]


if TYPE_CHECKING:
   from .configuration_xglm import XGLM_PRETRAINED_CONFIG_ARCHIVE_MAP, XGLMConfig

   try:
      if not is_sentencepiece_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .tokenization_xglm import XGLMTokenizer

   try:
      if not is_tokenizers_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .tokenization_xglm_fast import XGLMTokenizerFast

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_xglm import XGLM_PRETRAINED_MODEL_ARCHIVE_LIST, XGLMForCausalLM, XGLMModel, XGLMPreTrainedModel

   try:
      if not is_flax_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_flax_xglm import FlaxXGLMForCausalLM, FlaxXGLMModel, FlaxXGLMPreTrainedModel

   try:
      if not is_tf_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_tf_xglm import (
          TF_XGLM_PRETRAINED_MODEL_ARCHIVE_LIST,
          TFXGLMForCausalLM,
          TFXGLMModel,
          TFXGLMPreTrainedModel,
      )


else:
   import sys

   UpperCAmelCase      =   _LazyModule(__name__, globals()["""__file__"""], _import_structure)