import copy
import os
import tempfile
from unittest import TestCase
from unittest.mock import patch

import numpy as np
import pyarrow as pa
import pyarrow.parquet as pq
import pytest

from datasets.arrow_writer import ArrowWriter, OptimizedTypedSequence, ParquetWriter, TypedSequence
from datasets.features import ArrayaD, ClassLabel, Features, Image, Value
from datasets.features.features import ArrayaDExtensionType, cast_to_python_objects
from datasets.keyhash import DuplicatedKeysError, InvalidKeyError

from .utils import require_pil

class       snake_case					(      lowerCamelCase__						):




		def 	__lowercase(      self     :	Optional[int]				)->       Union[str, Any]:




							"""simple docstring"""
							SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		pa.array(TypedSequence([1, 2, 3]				)				)
							self.assertEqual(arr.type     , pa.intaa()				)




		def 	__lowercase(      self     :	Union[str, Any]				)->       str:




							"""simple docstring"""






							with self.assertRaises(__lowerCamelCase				):
												SCREAMING_SNAKE_CASE__				:				Tuple			=		pa.array(TypedSequence([1, 2, 3]				)     , type=pa.intaa()				)




		def 	__lowercase(      self     :	Optional[Any]				)->       List[Any]:




							"""simple docstring"""






							with self.assertRaises(__lowerCamelCase				):
												SCREAMING_SNAKE_CASE__				:				Dict			=		pa.array(TypedSequence([1, 2, 3]     , try_type=Value('bool'				)     , type=Value('int64'				)				)				)




		def 	__lowercase(      self     :	Dict				)->       Optional[int]:




							"""simple docstring"""
							SCREAMING_SNAKE_CASE__				:				Dict			=		pa.array(TypedSequence([1, 2, 3]     , type=Value('int32'				)				)				)
							self.assertEqual(arr.type     , pa.intaa()				)




		def 	__lowercase(      self     :	Optional[int]				)->       int:




							"""simple docstring"""






							with self.assertRaises((TypeError, pa.lib.ArrowInvalid)				):
												SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		pa.array(TypedSequence(['foo', 'bar']     , type=Value('int64'				)				)				)




		def 	__lowercase(      self     :	str				)->       Optional[Any]:




							"""simple docstring"""
							SCREAMING_SNAKE_CASE__				:				Tuple			=		pa.array(TypedSequence([1, 2, 3]     , try_type=Value('int32'				)				)				)
							self.assertEqual(arr.type     , pa.intaa()				)




		def 	__lowercase(      self     :	int				)->       str:




							"""simple docstring"""
							SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		pa.array(TypedSequence(['foo', 'bar']     , try_type=Value('int64'				)				)				)
							self.assertEqual(arr.type     , pa.string()				)




		def 	__lowercase(      self     :	str				)->       Optional[Any]:




							"""simple docstring"""
							SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		pa.array(TypedSequence([[[1, 2, 3]]]     , type=ArrayaD((1, 3)     , 'int64'				)				)				)
							self.assertEqual(arr.type     , ArrayaDExtensionType((1, 3)     , 'int64'				)				)




		def 	__lowercase(      self     :	Optional[Any]				)->       Optional[int]:




							"""simple docstring"""






							with self.assertRaises((TypeError, pa.lib.ArrowInvalid)				):
												SCREAMING_SNAKE_CASE__				:				List[str]			=		pa.array(TypedSequence(['foo', 'bar']     , type=ArrayaD((1, 3)     , 'int64'				)				)				)




		def 	__lowercase(      self     :	int				)->       Dict:




							"""simple docstring"""
							SCREAMING_SNAKE_CASE__				:				Optional[int]			=		pa.array(TypedSequence([[[1, 2, 3]]]     , try_type=ArrayaD((1, 3)     , 'int64'				)				)				)
							self.assertEqual(arr.type     , ArrayaDExtensionType((1, 3)     , 'int64'				)				)




		def 	__lowercase(      self     :	Optional[int]				)->       str:




							"""simple docstring"""
							SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		pa.array(TypedSequence(['foo', 'bar']     , try_type=ArrayaD((1, 3)     , 'int64'				)				)				)
							self.assertEqual(arr.type     , pa.string()				)




		@require_pil
		def 	__lowercase(      self     :	Dict				)->       List[Any]:




							"""simple docstring"""
							import PIL.Image

							SCREAMING_SNAKE_CASE__				:				List[Any]			=		PIL.Image.fromarray(np.arange(10     , dtype=np.uinta				).reshape(2     , 5				)				)
							with patch(
							    'datasets.arrow_writer.cast_to_python_objects'     , side_effect=__lowerCamelCase				) as mock_cast_to_python_objects:
												SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		pa.array(TypedSequence([{'path': None, 'bytes': B'image_bytes'}, pil_image]     , type=Image()				)				)
												SCREAMING_SNAKE_CASE__				:				Optional[int]			=		mock_cast_to_python_objects.call_args_list[-1]
												self.assertIn('optimize_list_casting'     , __lowerCamelCase				)
												self.assertFalse(kwargs['optimize_list_casting']				)







def     _a				(      lowercase__  :			Union[str, Any]     ,  lowercase__  :			int ):







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				Dict			=		pa.BufferReader(lowerCamelCase_ ) if isinstance(lowerCamelCase_     ,  pa.Buffer ) else pa.memory_map(lowerCamelCase_ )
					SCREAMING_SNAKE_CASE__				:				List[Any]			=		pa.ipc.open_stream(lowerCamelCase_ )
					SCREAMING_SNAKE_CASE__				:				pa.Table			=		f.read_all()
					assert len(pa_table.to_batches() ) == expected_num_chunks
					assert pa_table.to_pydict() == {"col_1": ["foo", "bar"], "col_2": [1, 2]}
					del pa_table







@pytest.mark.parametrize('writer_batch_size'     ,  [None, 1, 10] )
@pytest.mark.parametrize(
    'fields'     ,  [None, {'col_1': pa.string(), 'col_2': pa.intaa()}, {'col_1': pa.string(), 'col_2': pa.intaa()}] )
def     _a				(      lowercase__  :			int     ,  lowercase__  :			Tuple ):







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				Tuple			=		pa.BufferOutputStream()
					SCREAMING_SNAKE_CASE__				:				Any			=		pa.schema(lowerCamelCase_ ) if fields else None
					with ArrowWriter(stream=lowerCamelCase_     ,  schema=lowerCamelCase_     ,  writer_batch_size=lowerCamelCase_ ) as writer:
										writer.write({'col_1': 'foo', 'col_2': 1} )
										writer.write({'col_1': 'bar', 'col_2': 2} )
										SCREAMING_SNAKE_CASE__				:				Any			=		writer.finalize()
					assert num_examples == 2
					assert num_bytes > 0
					if not fields:
										SCREAMING_SNAKE_CASE__				:				int			=		{'''col_1''': pa.string(), '''col_2''': pa.intaa()}
					assert writer._schema == pa.schema(lowerCamelCase_     ,  metadata=writer._schema.metadata )
					_check_output(output.getvalue()     ,  expected_num_chunks=num_examples if writer_batch_size == 1 else 1 )







def     _a				(      ):







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				Tuple			=		pa.BufferOutputStream()
					SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		Features({'labels': ClassLabel(names=['neg', 'pos'] )} )
					with ArrowWriter(stream=lowerCamelCase_     ,  features=lowerCamelCase_ ) as writer:
										writer.write({'labels': 0} )
										writer.write({'labels': 1} )
										SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		writer.finalize()
					assert num_examples == 2
					assert num_bytes > 0
					assert writer._schema == features.arrow_schema
					assert writer._schema.metadata == features.arrow_schema.metadata
					SCREAMING_SNAKE_CASE__				:				Tuple			=		pa.BufferReader(output.getvalue() )
					SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		pa.ipc.open_stream(lowerCamelCase_ )
					SCREAMING_SNAKE_CASE__				:				pa.Table			=		f.read_all()
					SCREAMING_SNAKE_CASE__				:				Any			=		pa_table.schema
					assert pa_table.num_rows == 2
					assert schema == features.arrow_schema
					assert schema.metadata == features.arrow_schema.metadata
					assert features == Features.from_arrow_schema(lowerCamelCase_ )







@pytest.mark.parametrize('writer_batch_size'     ,  [None, 1, 10] )
def     _a				(      lowercase__  :			Union[str, Any] ):







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				List[Any]			=		pa.BufferOutputStream()
					with ArrowWriter(
					    stream=lowerCamelCase_     ,  writer_batch_size=lowerCamelCase_     ,  hash_salt='split_name'     ,  check_duplicates=lowerCamelCase_     ,  ) as writer:
										with pytest.raises(lowerCamelCase_ ):
															writer.write({'col_1': 'foo', 'col_2': 1}     ,  key=[1, 2] )
															SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		writer.finalize()







@pytest.mark.parametrize('writer_batch_size'     ,  [None, 2, 10] )
def     _a				(      lowercase__  :			List[Any] ):







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				Tuple			=		pa.BufferOutputStream()
					with ArrowWriter(
					    stream=lowerCamelCase_     ,  writer_batch_size=lowerCamelCase_     ,  hash_salt='split_name'     ,  check_duplicates=lowerCamelCase_     ,  ) as writer:
										with pytest.raises(lowerCamelCase_ ):
															writer.write({'col_1': 'foo', 'col_2': 1}     ,  key=10 )
															writer.write({'col_1': 'bar', 'col_2': 2}     ,  key=10 )
															SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		writer.finalize()







@pytest.mark.parametrize('writer_batch_size'     ,  [None, 2, 10] )
def     _a				(      lowercase__  :			Union[str, Any] ):







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				Tuple			=		pa.BufferOutputStream()
					with ArrowWriter(
					    stream=lowerCamelCase_     ,  writer_batch_size=lowerCamelCase_     ,  hash_salt='split_name'     ,  check_duplicates=lowerCamelCase_     ,  ) as writer:
										writer.write({'col_1': 'foo', 'col_2': 1}     ,  key=1 )
										writer.write({'col_1': 'bar', 'col_2': 2}     ,  key=2 )
										SCREAMING_SNAKE_CASE__				:				int			=		writer.finalize()
					assert num_examples == 2
					assert num_bytes > 0
					_check_output(output.getvalue()     ,  expected_num_chunks=num_examples if writer_batch_size == 1 else 1 )







@pytest.mark.parametrize('writer_batch_size'     ,  [None, 1, 10] )
@pytest.mark.parametrize(
    'fields'     ,  [None, {'col_1': pa.string(), 'col_2': pa.intaa()}, {'col_1': pa.string(), 'col_2': pa.intaa()}] )
def     _a				(      lowercase__  :			str     ,  lowercase__  :			Any ):







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				int			=		pa.BufferOutputStream()
					SCREAMING_SNAKE_CASE__				:				int			=		pa.schema(lowerCamelCase_ ) if fields else None
					with ArrowWriter(stream=lowerCamelCase_     ,  schema=lowerCamelCase_     ,  writer_batch_size=lowerCamelCase_ ) as writer:
										writer.write_batch({'col_1': ['foo', 'bar'], 'col_2': [1, 2]} )
										writer.write_batch({'col_1': [], 'col_2': []} )
										SCREAMING_SNAKE_CASE__				:				int			=		writer.finalize()
					assert num_examples == 2
					assert num_bytes > 0
					if not fields:
										SCREAMING_SNAKE_CASE__				:				List[Any]			=		{'''col_1''': pa.string(), '''col_2''': pa.intaa()}
					assert writer._schema == pa.schema(lowerCamelCase_     ,  metadata=writer._schema.metadata )
					_check_output(output.getvalue()     ,  expected_num_chunks=num_examples if writer_batch_size == 1 else 1 )







@pytest.mark.parametrize('writer_batch_size'     ,  [None, 1, 10] )
@pytest.mark.parametrize(
    'fields'     ,  [None, {'col_1': pa.string(), 'col_2': pa.intaa()}, {'col_1': pa.string(), 'col_2': pa.intaa()}] )
def     _a				(      lowercase__  :			Optional[Any]     ,  lowercase__  :			Optional[Any] ):







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		pa.BufferOutputStream()
					SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		pa.schema(lowerCamelCase_ ) if fields else None
					with ArrowWriter(stream=lowerCamelCase_     ,  schema=lowerCamelCase_     ,  writer_batch_size=lowerCamelCase_ ) as writer:
										writer.write_table(pa.Table.from_pydict({'col_1': ['foo', 'bar'], 'col_2': [1, 2]} ) )
										SCREAMING_SNAKE_CASE__				:				int			=		writer.finalize()
					assert num_examples == 2
					assert num_bytes > 0
					if not fields:
										SCREAMING_SNAKE_CASE__				:				Dict			=		{'''col_1''': pa.string(), '''col_2''': pa.intaa()}
					assert writer._schema == pa.schema(lowerCamelCase_     ,  metadata=writer._schema.metadata )
					_check_output(output.getvalue()     ,  expected_num_chunks=num_examples if writer_batch_size == 1 else 1 )







@pytest.mark.parametrize('writer_batch_size'     ,  [None, 1, 10] )
@pytest.mark.parametrize(
    'fields'     ,  [None, {'col_1': pa.string(), 'col_2': pa.intaa()}, {'col_1': pa.string(), 'col_2': pa.intaa()}] )
def     _a				(      lowercase__  :			List[Any]     ,  lowercase__  :			Tuple ):







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				int			=		pa.BufferOutputStream()
					SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		pa.schema(lowerCamelCase_ ) if fields else None
					with ArrowWriter(stream=lowerCamelCase_     ,  schema=lowerCamelCase_     ,  writer_batch_size=lowerCamelCase_ ) as writer:
										writer.write_row(pa.Table.from_pydict({'col_1': ['foo'], 'col_2': [1]} ) )
										writer.write_row(pa.Table.from_pydict({'col_1': ['bar'], 'col_2': [2]} ) )
										SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		writer.finalize()
					assert num_examples == 2
					assert num_bytes > 0
					if not fields:
										SCREAMING_SNAKE_CASE__				:				Tuple			=		{'''col_1''': pa.string(), '''col_2''': pa.intaa()}
					assert writer._schema == pa.schema(lowerCamelCase_     ,  metadata=writer._schema.metadata )
					_check_output(output.getvalue()     ,  expected_num_chunks=num_examples if writer_batch_size == 1 else 1 )







def     _a				(      ):







					'''simple docstring'''


					with tempfile.TemporaryDirectory() as tmp_dir:
										SCREAMING_SNAKE_CASE__				:				Optional[int]			=		{'''col_1''': pa.string(), '''col_2''': pa.intaa()}
										SCREAMING_SNAKE_CASE__				:				Tuple			=		os.path.join(lowerCamelCase_     ,  'test.arrow' )
										with ArrowWriter(path=lowerCamelCase_     ,  schema=pa.schema(lowerCamelCase_ ) ) as writer:
															writer.write_batch({'col_1': ['foo', 'bar'], 'col_2': [1, 2]} )
															SCREAMING_SNAKE_CASE__				:				List[Any]			=		writer.finalize()
										assert num_examples == 2
										assert num_bytes > 0
										assert writer._schema == pa.schema(lowerCamelCase_     ,  metadata=writer._schema.metadata )
										_check_output(lowerCamelCase_     ,  1 )







def     _a				(      lowercase__  :			int ):







					'''simple docstring'''


					if pa.types.is_list(lowerCamelCase_ ):
										return get_base_dtype(arr_type.value_type )
					else:
										return arr_type







def     _a				(      lowercase__  :			Dict     ,  lowercase__  :			List[str] ):







					'''simple docstring'''


					if isinstance(lst[0]     ,  lowerCamelCase_ ):
										change_first_primitive_element_in_list(lst[0]     ,  lowerCamelCase_ )
					else:
										SCREAMING_SNAKE_CASE__				:				List[str]			=		value







@pytest.mark.parametrize('optimized_int_type, expected_dtype'     ,  [(None, pa.intaa()), (Value('int32' ), pa.intaa())] )
@pytest.mark.parametrize('sequence'     ,  [[1, 2, 3], [[1, 2, 3]], [[[1, 2, 3]]]] )
def     _a				(      lowercase__  :			List[str]     ,  lowercase__  :			int     ,  lowercase__  :			Union[str, Any] ):







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				Dict			=		pa.array(TypedSequence(lowerCamelCase_     ,  optimized_int_type=lowerCamelCase_ ) )
					assert get_base_dtype(arr.type ) == expected_dtype







@pytest.mark.parametrize(
    'col, expected_dtype'     ,  [
        ('attention_mask', pa.inta()),
        ('special_tokens_mask', pa.inta()),
        ('token_type_ids', pa.inta()),
        ('input_ids', pa.intaa()),
        ('other', pa.intaa()),
    ]     ,  )
@pytest.mark.parametrize('sequence'     ,  [[1, 2, 3], [[1, 2, 3]], [[[1, 2, 3]]]] )
def     _a				(      lowercase__  :			List[Any]     ,  lowercase__  :			Optional[Any]     ,  lowercase__  :			Optional[Any] ):







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		pa.array(OptimizedTypedSequence(lowerCamelCase_     ,  col=lowerCamelCase_ ) )
					assert get_base_dtype(arr.type ) == expected_dtype

					# not in range
					if col != "other":
										# avoids errors due to in-place modifications
										SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		copy.deepcopy(lowerCamelCase_ )
										SCREAMING_SNAKE_CASE__				:				Any			=		np.iinfo(expected_dtype.to_pandas_dtype() ).max + 1
										change_first_primitive_element_in_list(lowerCamelCase_     ,  lowerCamelCase_ )
										SCREAMING_SNAKE_CASE__				:				Tuple			=		pa.array(OptimizedTypedSequence(lowerCamelCase_     ,  col=lowerCamelCase_ ) )
										assert get_base_dtype(arr.type ) == pa.intaa()







@pytest.mark.parametrize('raise_exception'     ,  [False, True] )
def     _a				(      lowercase__  :			List[str]     ,  lowercase__  :			Dict ):







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				str			=		str(tmp_path / 'dataset-train.arrow' )
					try:
										with ArrowWriter(path=lowerCamelCase_ ) as writer:
															if raise_exception:
																				raise pa.lib.ArrowInvalid()
															else:
																				writer.stream.close()
					except pa.lib.ArrowInvalid:
										pass
					finally:
										assert writer.stream.closed







def     _a				(      lowercase__  :			Any ):







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		'''mock://dataset-train.arrow'''
					with ArrowWriter(path=lowerCamelCase_     ,  storage_options=mockfs.storage_options ) as writer:
										assert isinstance(writer._fs     ,  type(lowerCamelCase_ ) )
										assert writer._fs.storage_options == mockfs.storage_options
										writer.write({'col_1': 'foo', 'col_2': 1} )
										writer.write({'col_1': 'bar', 'col_2': 2} )
										SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		writer.finalize()
					assert num_examples == 2
					assert num_bytes > 0
					assert mockfs.exists(lowerCamelCase_ )







def     _a				(      ):







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		pa.BufferOutputStream()
					with ParquetWriter(stream=lowerCamelCase_ ) as writer:
										writer.write({'col_1': 'foo', 'col_2': 1} )
										writer.write({'col_1': 'bar', 'col_2': 2} )
										SCREAMING_SNAKE_CASE__				:				List[Any]			=		writer.finalize()
					assert num_examples == 2
					assert num_bytes > 0
					SCREAMING_SNAKE_CASE__				:				List[Any]			=		pa.BufferReader(output.getvalue() )
					SCREAMING_SNAKE_CASE__				:				pa.Table			=		pq.read_table(lowerCamelCase_ )
					assert pa_table.to_pydict() == {"col_1": ["foo", "bar"], "col_2": [1, 2]}







@require_pil
@pytest.mark.parametrize('embed_local_files'     ,  [False, True] )
def     _a				(      lowercase__  :			int     ,  lowercase__  :			List[str] ):







					'''simple docstring'''


					import PIL.Image

					SCREAMING_SNAKE_CASE__				:				Optional[int]			=		str(tmp_path / 'test_image_rgb.jpg' )
					PIL.Image.fromarray(np.zeros((5, 5)     ,  dtype=np.uinta ) ).save(lowerCamelCase_     ,  format='png' )
					SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		pa.BufferOutputStream()
					with ParquetWriter(
					    stream=lowerCamelCase_     ,  features=Features({'image': Image()} )     ,  embed_local_files=lowerCamelCase_ ) as writer:
										writer.write({'image': image_path} )
										writer.finalize()
					SCREAMING_SNAKE_CASE__				:				Dict			=		pa.BufferReader(output.getvalue() )
					SCREAMING_SNAKE_CASE__				:				pa.Table			=		pq.read_table(lowerCamelCase_ )
					SCREAMING_SNAKE_CASE__				:				List[Any]			=		pa_table.to_pydict()
					if embed_local_files:
										assert isinstance(out['image'][0]['path']     ,  lowerCamelCase_ )
										with open(lowerCamelCase_     ,  'rb' ) as f:
															assert out["image"][0]["bytes"] == f.read()
					else:
										assert out["image"][0]["path"] == image_path
										assert out["image"][0]["bytes"] is None







def     _a				(      ):







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				Dict			=		pa.schema([pa.field('col_1'     ,  pa.string()     ,  nullable=lowerCamelCase_ )] )
					SCREAMING_SNAKE_CASE__				:				List[str]			=		pa.BufferOutputStream()
					with ArrowWriter(stream=lowerCamelCase_ ) as writer:
										writer._build_writer(inferred_schema=lowerCamelCase_ )
										assert writer._schema == pa.schema([pa.field('col_1'     ,  pa.string() )] )




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

class       snake_case					:




  def __init__(      self     :	str     , a_     :	str				)->       Any:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				List[str]			=		str(id_				)
       SCREAMING_SNAKE_CASE__				:				Any			=		None
       SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		None
       SCREAMING_SNAKE_CASE__				:				Any			=		[]
       SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		{}  # {vertex:distance}




  def __lt__(      self     :	int     , a_     :	Tuple				)->       Union[str, Any]:




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




  def __repr__(      self     :	Any				)->       Dict:




       """simple docstring"""
       return self.id




  def 	__lowercase(      self     :	Optional[Any]     , a_     :	int				)->       List[str]:




       """simple docstring"""
       self.neighbors.append(a_				)




  def 	__lowercase(      self     :	int     , a_     :	int     , a_     :	Optional[Any]				)->       Any:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Tuple			=		weight







def     _a				(      lowercase__  :			Optional[Any]     ,  lowercase__  :			Union[str, Any]     ,  lowercase__  :			Tuple     ,  lowercase__  :			Dict ):







     '''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]     ,  lowercase__ )
     graph[b - 1].add_edge(graph[a - 1]     ,  lowercase__ )







def     _a				(      lowercase__  :			list     ,  lowercase__  :			Vertex ):







     '''simple docstring'''


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







def     _a				(      lowercase__  :			list     ,  lowercase__  :			Vertex ):







     '''simple docstring'''


     for u in graph:
          SCREAMING_SNAKE_CASE__				:				List[str]			=		math.inf
          SCREAMING_SNAKE_CASE__				:				int			=		None
     SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		0

     SCREAMING_SNAKE_CASE__				:				Tuple			=		list(lowercase__ )
     hq.heapify(lowercase__ )

     while h:
          SCREAMING_SNAKE_CASE__				:				Optional[int]			=		hq.heappop(lowercase__ )
          for v in u.neighbors:
               if (v in h) and (u.edges[v.id] < v.key):
                    SCREAMING_SNAKE_CASE__				:				List[str]			=		u
                    SCREAMING_SNAKE_CASE__				:				Dict			=		u.edges[v.id]
                    hq.heapify(lowercase__ )

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







def     _a				(      ):







     '''simple docstring'''




if __name__ == "__main__":
      import doctest

      doctest.testmod()



