





"""simple docstring"""


from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

lowerCamelCase__				  =   TypeVar("T")




def 					lowercase__    (					lowercase_			)					->		Dict:




      """simple docstring"""

      return (position - 1) // 2




def 					lowercase__    (					lowercase_			)					->		Tuple:




      """simple docstring"""

      return (2 * position) + 1




def 					lowercase__    (					lowercase_			)					->		Dict:




      """simple docstring"""

      return (2 * position) + 2



class      __SCREAMING_SNAKE_CASE    (						Generic[T]   ):

  def __init__(		self   :       str	)		->				None:
        _UpperCamelCase      :	list[tuple[T, int]]						=       []
        _UpperCamelCase      :	dict[T, int]						=       {}
        _UpperCamelCase      :	int						=       0

  def __len__(		self   :       Any	)		->				int:
        return self.elements

  def __repr__(		self   :       Union[str, Any]	)		->				str:
        return str(self.heap	)

  def    __SCREAMING_SNAKE_CASE				(		self   :       Any	)		->				bool:
        return self.elements == 0

  def    __SCREAMING_SNAKE_CASE				(		self   :       List[Any]					,   __a   :       Union[str, Any]					,   __a   :       str	)		->				None:
        self.heap.append((elem, weight)	)
        _UpperCamelCase      :	Optional[Any]						=       self.elements
        self.elements += 1
        self._bubble_up(lowercase__	)

  def    __SCREAMING_SNAKE_CASE				(		self   :       Tuple	)		->				T:





        if self.elements > 1:
              self._swap_nodes(0					,   self.elements - 1	)
        _UpperCamelCase      :	List[str]						=       self.heap.pop()
        del self.position_map[elem]
        self.elements -= 1
        if self.elements > 0:
              _UpperCamelCase      :	Tuple						=       self.heap[0]
              self._bubble_down(lowercase__	)
        return elem

  def    __SCREAMING_SNAKE_CASE				(		self   :       Optional[Any]					,   __a   :       List[str]					,   __a   :       int	)		->				None:
        _UpperCamelCase      :	List[str]						=       self.position_map[elem]
        _UpperCamelCase      :	Any						=       (elem, weight)
        if position > 0:
              _UpperCamelCase      :	Optional[int]						=       get_parent_position(lowercase__	)
              _UpperCamelCase      :	Tuple						=       self.heap[parent_position]
              if parent_weight > weight:
                    self._bubble_up(lowercase__	)
              else:
                    self._bubble_down(lowercase__	)
        else:
              self._bubble_down(lowercase__	)

  def    __SCREAMING_SNAKE_CASE				(		self   :       Union[str, Any]					,   __a   :       str	)		->				None:
        _UpperCamelCase      :	Tuple						=       self.position_map[elem]
        if curr_pos == 0:
              return None
        _UpperCamelCase      :	Optional[int]						=       get_parent_position(lowercase__	)
        _UpperCamelCase      :	Optional[Any]						=       self.heap[curr_pos]
        _UpperCamelCase      :	int						=       self.heap[parent_position]
        if parent_weight > weight:
              self._swap_nodes(lowercase__					,   lowercase__	)
              return self._bubble_up(lowercase__	)
        return None

  def    __SCREAMING_SNAKE_CASE				(		self   :       List[Any]					,   __a   :       List[Any]	)		->				None:
        _UpperCamelCase      :	Any						=       self.position_map[elem]
        _UpperCamelCase      :	List[Any]						=       self.heap[curr_pos]
        _UpperCamelCase      :	Dict						=       get_child_left_position(lowercase__	)
        _UpperCamelCase      :	Optional[int]						=       get_child_right_position(lowercase__	)
        if child_left_position < self.elements and child_right_position < self.elements:
              _UpperCamelCase      :	Any						=       self.heap[child_left_position]
              _UpperCamelCase      :	str						=       self.heap[child_right_position]
              if child_right_weight < child_left_weight and child_right_weight < weight:
                    self._swap_nodes(lowercase__					,   lowercase__	)
                    return self._bubble_down(lowercase__	)
        if child_left_position < self.elements:
              _UpperCamelCase      :	List[str]						=       self.heap[child_left_position]
              if child_left_weight < weight:
                    self._swap_nodes(lowercase__					,   lowercase__	)
                    return self._bubble_down(lowercase__	)
        else:
              return None
        if child_right_position < self.elements:
              _UpperCamelCase      :	Optional[int]						=       self.heap[child_right_position]
              if child_right_weight < weight:
                    self._swap_nodes(lowercase__					,   lowercase__	)
                    return self._bubble_down(lowercase__	)
        return None


  def    __SCREAMING_SNAKE_CASE				(		self   :       Optional[int]					,   __a   :       List[str]					,   __a   :       Dict	)		->				None:
        _UpperCamelCase      :	List[Any]						=       self.heap[nodea_pos][0]
        _UpperCamelCase      :	str						=       self.heap[nodea_pos][0]
        _UpperCamelCase      :	Union[str, Any]						=       (
            self.heap[nodea_pos],
            self.heap[nodea_pos],
        )
        _UpperCamelCase      :	Dict						=       nodea_pos
        _UpperCamelCase      :	Any						=       nodea_pos





class      __SCREAMING_SNAKE_CASE    (						Generic[T]   ):

  def __init__(		self   :       Dict	)		->				None:
        _UpperCamelCase      :	dict[T, dict[T, int]]						=       {}
        _UpperCamelCase      :	int						=       0

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

  def __len__(		self   :       Tuple	)		->				int:
        return self.nodes

  def    __SCREAMING_SNAKE_CASE				(		self   :       Optional[Any]					,   __a   :       Any	)		->				None:





        if node not in self.connections:
              _UpperCamelCase      :	Optional[int]						=       {}
              self.nodes += 1


  def    __SCREAMING_SNAKE_CASE				(		self   :       List[Any]					,   __a   :       str					,   __a   :       Tuple					,   __a   :       Tuple	)		->				None:
        self.add_node(lowercase__	)
        self.add_node(lowercase__	)
        _UpperCamelCase      :	Union[str, Any]						=       weight
        _UpperCamelCase      :	Any						=       weight





def 					lowercase__    (					lowercase_		,)					->		Tuple:




      """simple docstring"""

      _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(lowerCAmelCase_		,lowerCAmelCase_			)

      if priority_queue.is_empty():
            return dist, parent

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

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







"""simple docstring"""


lowerCamelCase__				  =   "\n# Installazione di Transformers\n! pip install transformers datasets\n# Per installare dalla fonte invece dell'ultima versione rilasciata, commenta il comando sopra e\n# rimuovi la modalità commento al comando seguente.\n# ! pip install git+https://github.com/huggingface/transformers.git\n"

lowerCamelCase__				  =   [{"type": "code", "content": INSTALL_CONTENT}]
lowerCamelCase__				  =   {
    "{processor_class}": "FakeProcessorClass",
    "{model_class}": "FakeModelClass",
    "{object_class}": "FakeObjectClass",
}
