



import heapq as hq
import math
from collections.abc import Iterator






class    SCREAMING_SNAKE_CASE			:





       def __init__(   self		:		Any      ,				__lowercase		:		Optional[int]	):

           '''simple docstring'''
           __a       =		str(id_	)
           __a       =		None
           __a       =		None
           __a       =		[]
           __a       =		{}  # {vertex:distance}





       def __lt__(   self		:		Optional[Any]      ,				__lowercase		:		int	):

           '''simple docstring'''
           return self.key < other.key





       def __repr__(   self		:		List[Any]	):

           '''simple docstring'''
           return self.id





       def 						UpperCamelCase_					(   self		:		Tuple      ,				__lowercase		:		List[Any]	):

           '''simple docstring'''
           self.neighbors.append(__lowercase	)







       def 						UpperCamelCase_					(   self		:		Any      ,				__lowercase		:		Any      ,				__lowercase		:		str	):

           '''simple docstring'''
           __a       =		weight



def   lowerCAmelCase__						(							_SCREAMING_SNAKE_CASE       :			Any				,     _SCREAMING_SNAKE_CASE       :			Union[str, Any]				,     _SCREAMING_SNAKE_CASE       :			List[str]				,     _SCREAMING_SNAKE_CASE       :			Optional[Any]    ):
    """simple docstring"""







    graph[a - 1].add_neighbor(graph[b - 1]    )
    graph[b - 1].add_neighbor(graph[a - 1]    )
    # add the edges:
    graph[a - 1].add_edge(graph[b - 1]				,     _SCREAMING_SNAKE_CASE    )
    graph[b - 1].add_edge(graph[a - 1]				,     _SCREAMING_SNAKE_CASE    )

def   lowerCAmelCase__						(							_SCREAMING_SNAKE_CASE       :			list				,     _SCREAMING_SNAKE_CASE       :			Vertex    ):
    """simple docstring"""







    __a       =		[]
    for u in graph:
        __a       =		math.inf
        __a       =		None
    __a       =		0
    __a       =		graph[:]
    while q:
        __a       =		min(_SCREAMING_SNAKE_CASE    )
        q.remove(_SCREAMING_SNAKE_CASE    )
        for v in u.neighbors:
            if (v in q) and (u.edges[v.id] < v.key):
                __a       =		u
                __a       =		u.edges[v.id]
    for i in range(1				,     len(_SCREAMING_SNAKE_CASE    )    ):
        a.append((int(graph[i].id    ) + 1, int(graph[i].pi.id    ) + 1)    )
    return a

def   lowerCAmelCase__						(							_SCREAMING_SNAKE_CASE       :			list				,     _SCREAMING_SNAKE_CASE       :			Vertex    ):
    """simple docstring"""







    for u in graph:
        __a       =		math.inf
        __a       =		None
    __a       =		0

    __a       =		list(_SCREAMING_SNAKE_CASE    )
    hq.heapify(_SCREAMING_SNAKE_CASE    )

    while h:
        __a       =		hq.heappop(_SCREAMING_SNAKE_CASE    )
        for v in u.neighbors:
            if (v in h) and (u.edges[v.id] < v.key):
                __a       =		u
                __a       =		u.edges[v.id]
                hq.heapify(_SCREAMING_SNAKE_CASE    )

    for i in range(1				,     len(_SCREAMING_SNAKE_CASE    )    ):
        yield (int(graph[i].id    ) + 1, int(graph[i].pi.id    ) + 1)

def   lowerCAmelCase__						(							):
    """simple docstring"""
















if __name__ == "__main__":
      import doctest

      doctest.testmod()





from typing import TYPE_CHECKING

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


lowerCamelCase__			= {"""configuration_speech_encoder_decoder""": ["""SpeechEncoderDecoderConfig"""]}

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCamelCase__			= ["""SpeechEncoderDecoderModel"""]

try:
						if not is_flax_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCamelCase__			= ["""FlaxSpeechEncoderDecoderModel"""]

if TYPE_CHECKING:
						from .configuration_speech_encoder_decoder import SpeechEncoderDecoderConfig

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_speech_encoder_decoder import SpeechEncoderDecoderModel

						try:
												if not is_flax_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_flax_speech_encoder_decoder import FlaxSpeechEncoderDecoderModel

else:
						import sys

						lowerCamelCase__			= _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)
