


'''simple docstring'''



from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

A__		:					int												=  TypeVar("""T""")



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				int							)     ->		int:
     return (position - 1) // 2



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				int							)     ->		int:
     return (2 * position) + 1



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				int							)     ->		int:
     return (2 * position) + 2





class    UpperCAmelCase_  (Generic[T]  ):





    """simple docstring"""






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







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







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







    def       lowercase_				(							self	)				->     bool:
         # Check if the priority queue is empty
         return self.elements == 0







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)				->     None:
         # Add an element with given priority to the queue
         self.heap.append((elem, weight)	)
         __lowerCamelCase   :	Tuple								=		self.elements
         self.elements += 1
         self._bubble_up(SCREAMING_SNAKE_CASE_	)







    def       lowercase_				(							self	)				->     T:
         # Remove and return the element with lowest weight (highest priority)
         if self.elements > 1:
              self._swap_nodes(0			,     self.elements - 1	)
         __lowerCamelCase				,       __lowerCamelCase   :	Any								=		self.heap.pop()
         del self.position_map[elem]
         self.elements -= 1
         if self.elements > 0:
              __lowerCamelCase				,       __lowerCamelCase   :	Tuple								=		self.heap[0]
              self._bubble_down(SCREAMING_SNAKE_CASE_	)
         return elem







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)				->     None:
         # Update the weight of the given key
         __lowerCamelCase   :	Optional[int]								=		self.position_map[elem]
         __lowerCamelCase   :	Dict								=		(elem, weight)
         if position > 0:
              __lowerCamelCase   :	str								=		get_parent_position(SCREAMING_SNAKE_CASE_	)
              __lowerCamelCase				,       __lowerCamelCase   :	Any								=		self.heap[parent_position]
              if parent_weight > weight:
                   self._bubble_up(SCREAMING_SNAKE_CASE_	)
              else:
                   self._bubble_down(SCREAMING_SNAKE_CASE_	)
         else:
              self._bubble_down(SCREAMING_SNAKE_CASE_	)







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_	)				->     None:
         # Place a node at the proper position (upward movement) [to be used internally
         # only]
         __lowerCamelCase   :	Union[str, Any]								=		self.position_map[elem]
         if curr_pos == 0:
              return None
         __lowerCamelCase   :	Tuple								=		get_parent_position(SCREAMING_SNAKE_CASE_	)
         __lowerCamelCase				,       __lowerCamelCase   :	Optional[Any]								=		self.heap[curr_pos]
         __lowerCamelCase				,       __lowerCamelCase   :	int								=		self.heap[parent_position]
         if parent_weight > weight:
              self._swap_nodes(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)
              return self._bubble_up(SCREAMING_SNAKE_CASE_	)
         return None







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_	)				->     None:
         # Place a node at the proper position (downward movement) [to be used
         # internally only]
         __lowerCamelCase   :	List[Any]								=		self.position_map[elem]
         __lowerCamelCase				,       __lowerCamelCase   :	Optional[int]								=		self.heap[curr_pos]
         __lowerCamelCase   :	Optional[Any]								=		get_child_left_position(SCREAMING_SNAKE_CASE_	)
         __lowerCamelCase   :	Any								=		get_child_right_position(SCREAMING_SNAKE_CASE_	)
         if child_left_position < self.elements and child_right_position < self.elements:
              __lowerCamelCase				,       __lowerCamelCase   :	Optional[int]								=		self.heap[child_left_position]
              __lowerCamelCase				,       __lowerCamelCase   :	Optional[Any]								=		self.heap[child_right_position]
              if child_right_weight < child_left_weight and child_right_weight < weight:
                   self._swap_nodes(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)
                   return self._bubble_down(SCREAMING_SNAKE_CASE_	)
         if child_left_position < self.elements:
              __lowerCamelCase				,       __lowerCamelCase   :	List[Any]								=		self.heap[child_left_position]
              if child_left_weight < weight:
                   self._swap_nodes(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)
                   return self._bubble_down(SCREAMING_SNAKE_CASE_	)
         else:
              return None
         if child_right_position < self.elements:
              __lowerCamelCase				,       __lowerCamelCase   :	int								=		self.heap[child_right_position]
              if child_right_weight < weight:
                   self._swap_nodes(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)
                   return self._bubble_down(SCREAMING_SNAKE_CASE_	)
         return None







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)				->     None:
         # Swap the nodes at the given positions
         __lowerCamelCase   :	Tuple								=		self.heap[nodea_pos][0]
         __lowerCamelCase   :	Optional[Any]								=		self.heap[nodea_pos][0]
         __lowerCamelCase				,       __lowerCamelCase   :	Optional[int]								=		(
             self.heap[nodea_pos],
             self.heap[nodea_pos],
         )
         __lowerCamelCase   :	List[Any]								=		nodea_pos
         __lowerCamelCase   :	List[str]								=		nodea_pos







class    UpperCAmelCase_  (Generic[T]  ):





    """simple docstring"""






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







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







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







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_	)				->     None:
         # Add a node in the graph if it is not in the graph
         if node not in self.connections:
              __lowerCamelCase   :	Tuple								=		{}
              self.nodes += 1







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)				->     None:
         # Add an edge between 2 nodes in the graph
         self.add_node(SCREAMING_SNAKE_CASE_	)
         self.add_node(SCREAMING_SNAKE_CASE_	)
         __lowerCamelCase   :	List[Any]								=		weight
         __lowerCamelCase   :	Optional[int]								=		weight







def 			UpperCAmelCase__					(	UpperCAmelCase_    :				GraphUndirectedWeighted[T]      ,    )     ->		tuple[dict[T, int], dict[T, T | None]]:
     __lowerCamelCase   :	dict[T, int]								=		{node: maxsize for node in graph.connections}
     __lowerCamelCase   :	dict[T, T | None]								=		{node: None for node in graph.connections}

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

     if priority_queue.is_empty():
          return dist, parent

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

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










'''simple docstring'''



from . import (
    albert,
    align,
    altclip,
    audio_spectrogram_transformer,
    auto,
    autoformer,
    bark,
    bart,
    barthez,
    bartpho,
    beit,
    bert,
    bert_generation,
    bert_japanese,
    bertweet,
    big_bird,
    bigbird_pegasus,
    biogpt,
    bit,
    blenderbot,
    blenderbot_small,
    blip,
    blip_a,
    bloom,
    bridgetower,
    byta,
    camembert,
    canine,
    chinese_clip,
    clap,
    clip,
    clipseg,
    codegen,
    conditional_detr,
    convbert,
    convnext,
    convnextva,
    cpm,
    cpmant,
    ctrl,
    cvt,
    dataavec,
    deberta,
    deberta_va,
    decision_transformer,
    deformable_detr,
    deit,
    deprecated,
    deta,
    detr,
    dialogpt,
    dinat,
    distilbert,
    dit,
    donut,
    dpr,
    dpt,
    efficientformer,
    efficientnet,
    electra,
    encodec,
    encoder_decoder,
    ernie,
    ernie_m,
    esm,
    falcon,
    flaubert,
    flava,
    fnet,
    focalnet,
    fsmt,
    funnel,
    git,
    glpn,
    gpta,
    gpt_bigcode,
    gpt_neo,
    gpt_neox,
    gpt_neox_japanese,
    gpt_swa,
    gptj,
    gptsan_japanese,
    graphormer,
    groupvit,
    herbert,
    hubert,
    ibert,
    imagegpt,
    informer,
    instructblip,
    jukebox,
    layoutlm,
    layoutlmva,
    layoutlmva,
    layoutxlm,
    led,
    levit,
    lilt,
    llama,
    longformer,
    longta,
    luke,
    lxmert,
    mam_aaa,
    marian,
    markuplm,
    maskaformer,
    maskformer,
    mbart,
    mbartaa,
    mega,
    megatron_bert,
    megatron_gpta,
    mgp_str,
    mluke,
    mobilebert,
    mobilenet_va,
    mobilenet_va,
    mobilevit,
    mobilevitva,
    mpnet,
    mra,
    mta,
    musicgen,
    mvp,
    nat,
    nezha,
    nllb,
    nllb_moe,
    nystromformer,
    oneformer,
    open_llama,
    openai,
    opt,
    owlvit,
    pegasus,
    pegasus_x,
    perceiver,
    phobert,
    pixastruct,
    plbart,
    poolformer,
    prophetnet,
    qdqbert,
    rag,
    realm,
    reformer,
    regnet,
    rembert,
    resnet,
    roberta,
    roberta_prelayernorm,
    roc_bert,
    roformer,
    rwkv,
    sam,
    segformer,
    sew,
    sew_d,
    speech_encoder_decoder,
    speech_to_text,
    speech_to_text_a,
    speechta,
    splinter,
    squeezebert,
    swiftformer,
    swin,
    swinasr,
    swinva,
    switch_transformers,
    ta,
    table_transformer,
    tapas,
    time_series_transformer,
    timesformer,
    timm_backbone,
    transfo_xl,
    trocr,
    tvlt,
    umta,
    unispeech,
    unispeech_sat,
    upernet,
    videomae,
    vilt,
    vision_encoder_decoder,
    vision_text_dual_encoder,
    visual_bert,
    vit,
    vit_hybrid,
    vit_mae,
    vit_msn,
    vivit,
    wavaveca,
    wavaveca_conformer,
    wavaveca_phoneme,
    wavaveca_with_lm,
    wavlm,
    whisper,
    x_clip,
    xglm,
    xlm,
    xlm_prophetnet,
    xlm_roberta,
    xlm_roberta_xl,
    xlnet,
    xmod,
    yolos,
    yoso,
)






