





from ...utils import is_torch_available, is_transformers_available


if is_transformers_available() and is_torch_available():
     from .pipeline_vq_diffusion import LearnedClassifierFreeSamplingEmbeddings, VQDiffusionPipeline











from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

__lowercase  :   Optional[int]						      =TypeVar("""T""")




def     a__ (					lowercase__  ):






   '''simple docstring'''






   return (position - 1) // 2




def     a__ (					lowercase__  ):






   '''simple docstring'''






   return (2 * position) + 1




def     a__ (					lowercase__  ):






   '''simple docstring'''






   return (2 * position) + 2

class      A       (	Generic[T]						):



      def __init__(	self:						List[str]       )						->    None:
         '''simple docstring'''

         UpperCAmelCase_											=[]
         UpperCAmelCase_											={}
         UpperCAmelCase_											=0



      def __len__(	self:						Union[str, Any]       )						->    int:
         '''simple docstring'''

         return self.elements



      def __repr__(	self:						Dict       )						->    str:
         '''simple docstring'''

         return str(self.heap       )



      def 	lowerCAmelCase__    (	self:						Any       )						->    bool:
         '''simple docstring'''

         return self.elements == 0



      def 	lowerCAmelCase__    (	self:						Optional[int]		,  _lowerCAmelCase:						T		,  _lowerCAmelCase:						int       )						->    None:
         '''simple docstring'''

         self.heap.append((elem, weight)       )
         UpperCAmelCase_											=self.elements
         self.elements += 1
         self._bubble_up(_lowerCAmelCase       )



      def 	lowerCAmelCase__    (	self:						Tuple       )						->    T:
         '''simple docstring'''

         if self.elements > 1:
            self._swap_nodes(0		,  self.elements - 1       )
         UpperCAmelCase_						,       UpperCAmelCase_											=self.heap.pop()
         del self.position_map[elem]
         self.elements -= 1
         if self.elements > 0:
            UpperCAmelCase_						,       UpperCAmelCase_											=self.heap[0]
            self._bubble_down(_lowerCAmelCase       )
         return elem



      def 	lowerCAmelCase__    (	self:						Optional[Any]		,  _lowerCAmelCase:						T		,  _lowerCAmelCase:						int       )						->    None:
         '''simple docstring'''

         UpperCAmelCase_											=self.position_map[elem]
         UpperCAmelCase_											=(elem, weight)
         if position > 0:
            UpperCAmelCase_											=get_parent_position(_lowerCAmelCase       )
            UpperCAmelCase_						,       UpperCAmelCase_											=self.heap[parent_position]
            if parent_weight > weight:
               self._bubble_up(_lowerCAmelCase       )
            else:
               self._bubble_down(_lowerCAmelCase       )
         else:
            self._bubble_down(_lowerCAmelCase       )



      def 	lowerCAmelCase__    (	self:						Any		,  _lowerCAmelCase:						T       )						->    None:
         '''simple docstring'''

         UpperCAmelCase_											=self.position_map[elem]
         if curr_pos == 0:
            return None
         UpperCAmelCase_											=get_parent_position(_lowerCAmelCase       )
         UpperCAmelCase_						,       UpperCAmelCase_											=self.heap[curr_pos]
         UpperCAmelCase_						,       UpperCAmelCase_											=self.heap[parent_position]
         if parent_weight > weight:
            self._swap_nodes(_lowerCAmelCase		,  _lowerCAmelCase       )
            return self._bubble_up(_lowerCAmelCase       )
         return None



      def 	lowerCAmelCase__    (	self:						Optional[Any]		,  _lowerCAmelCase:						T       )						->    None:
         '''simple docstring'''

         UpperCAmelCase_											=self.position_map[elem]
         UpperCAmelCase_						,       UpperCAmelCase_											=self.heap[curr_pos]
         UpperCAmelCase_											=get_child_left_position(_lowerCAmelCase       )
         UpperCAmelCase_											=get_child_right_position(_lowerCAmelCase       )
         if child_left_position < self.elements and child_right_position < self.elements:
            UpperCAmelCase_						,       UpperCAmelCase_											=self.heap[child_left_position]
            UpperCAmelCase_						,       UpperCAmelCase_											=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_											=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_											=self.heap[child_right_position]
            if child_right_weight < weight:
               self._swap_nodes(_lowerCAmelCase		,  _lowerCAmelCase       )
               return self._bubble_down(_lowerCAmelCase       )
         return None






      def 	lowerCAmelCase__    (	self:						Optional[Any]		,  _lowerCAmelCase:						int		,  _lowerCAmelCase:						int       )						->    None:
         '''simple docstring'''

         UpperCAmelCase_											=self.heap[nodea_pos][0]
         UpperCAmelCase_											=self.heap[nodea_pos][0]
         UpperCAmelCase_						,       UpperCAmelCase_											=(
             self.heap[nodea_pos],
             self.heap[nodea_pos],
         )
         UpperCAmelCase_											=nodea_pos
         UpperCAmelCase_											=nodea_pos

class      A       (	Generic[T]						):



      def __init__(	self:						Tuple       )						->    None:
         '''simple docstring'''

         UpperCAmelCase_											={}
         UpperCAmelCase_											=0



      def __repr__(	self:						List[str]       )						->    str:
         '''simple docstring'''

         return str(self.connections       )



      def __len__(	self:						Optional[Any]       )						->    int:
         '''simple docstring'''

         return self.nodes



      def 	lowerCAmelCase__    (	self:						Union[str, Any]		,  _lowerCAmelCase:						T       )						->    None:
         '''simple docstring'''

         if node not in self.connections:
            UpperCAmelCase_											={}
            self.nodes += 1






      def 	lowerCAmelCase__    (	self:						Optional[Any]		,  _lowerCAmelCase:						T		,  _lowerCAmelCase:						T		,  _lowerCAmelCase:						int       )						->    None:
         '''simple docstring'''

         self.add_node(_lowerCAmelCase       )
         self.add_node(_lowerCAmelCase       )
         UpperCAmelCase_											=weight
         UpperCAmelCase_											=weight




def     a__ (					lowercase__  ,    ):






   '''simple docstring'''






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

   UpperCAmelCase_											=MinPriorityQueue()
   for node, weight in dist.items():
      priority_queue.push(lowercase__  ,    lowercase__  )

   if priority_queue.is_empty():
      return dist, parent

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

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




