






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


class    _lowerCAmelCase			:



				"""simple docstring"""



				def __init__(      self    :    Union[str, Any]			,		UpperCamelCase__    :    Dict):






											'''simple docstring'''







											snake_case__	  =       str(id_)
											snake_case__	  =       None
											snake_case__	  =       None
											snake_case__	  =       []
											snake_case__	  =       {}  # {vertex:distance}



				def __lt__(      self    :    List[str]			,		UpperCamelCase__    :    Tuple):






											'''simple docstring'''







											return self.key < other.key



				def __repr__(      self    :    List[Any]):






											'''simple docstring'''







											return self.id



				def 					__magic_name__							(      self    :    str			,		UpperCamelCase__    :    Any):






											'''simple docstring'''







											self.neighbors.append(UpperCamelCase__)



				def 					__magic_name__							(      self    :    Union[str, Any]			,		UpperCamelCase__    :    Optional[Any]			,		UpperCamelCase__    :    List[Any]):






											'''simple docstring'''







											snake_case__	  =       weight


def _UpperCAmelCase   (	a						:	Optional[int]  ,					a						:	Any  ,					a						:	Any  ,					a						:	Tuple		):
							# add the neighbors:
							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]  ,					a		)
							graph[b - 1].add_edge(graph[a - 1]  ,					a		)

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

def _UpperCAmelCase   (	a						:	list  ,					a						:	Vertex		):
							for u in graph:
														snake_case__	  =       math.inf
														snake_case__	  =       None
							snake_case__	  =       0

							snake_case__	  =       list(a		)
							hq.heapify(a		)

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

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

def _UpperCAmelCase   (	):
							pass


if __name__ == "__main__":
	import doctest

	doctest.testmod()








from typing import TYPE_CHECKING

# rely on isort to merge the imports
from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


a__       =     {
    """configuration_autoformer""": [
        """AUTOFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP""",
        """AutoformerConfig""",
    ],
}

try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	a__       =     [
	    """AUTOFORMER_PRETRAINED_MODEL_ARCHIVE_LIST""",
	    """AutoformerForPrediction""",
	    """AutoformerModel""",
	    """AutoformerPreTrainedModel""",
	]


if TYPE_CHECKING:
	from .configuration_autoformer import (
	    AUTOFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
	    AutoformerConfig,
	)

	try:
		if not is_torch_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_autoformer import (
		    AUTOFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
		    AutoformerForPrediction,
		    AutoformerModel,
		    AutoformerPreTrainedModel,
		)

else:
	import sys

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