

"""simple docstring"""


from __future__ import annotations

import random

# Adjacency list representation of this graph:
# https://en.wikipedia.org/wiki/File:Single_run_of_Karger%E2%80%99s_Mincut_algorithm.svg
__A		     =    {
    '''1''': ['''2''', '''3''', '''4''', '''5'''],
    '''2''': ['''1''', '''3''', '''4''', '''5'''],
    '''3''': ['''1''', '''2''', '''4''', '''5''', '''10'''],
    '''4''': ['''1''', '''2''', '''3''', '''5''', '''6'''],
    '''5''': ['''1''', '''2''', '''3''', '''4''', '''7'''],
    '''6''': ['''7''', '''8''', '''9''', '''10''', '''4'''],
    '''7''': ['''6''', '''8''', '''9''', '''10''', '''5'''],
    '''8''': ['''6''', '''7''', '''9''', '''10'''],
    '''9''': ['''6''', '''7''', '''8''', '''10'''],
    '''10''': ['''6''', '''7''', '''8''', '''9''', '''3'''],
}






def 					a__					(					__SCREAMING_SNAKE_CASE				):
		__lowerCAmelCase: List[Any]					   =    {node: {node} for node in graph}

		__lowerCAmelCase: List[str]					   =    {node: graph[node][:] for node in graph}

		while len(_UpperCAmelCase				) > 2:
				# Choose a random edge.
				__lowerCAmelCase: List[Any]					   =    random.choice(list(graph_copy.keys()				)				)
				__lowerCAmelCase: Any					   =    random.choice(graph_copy[u]				)

				# Contract edge (u, v) to new node uv
				__lowerCAmelCase: str					   =    u + v
				__lowerCAmelCase: Optional[Any]					   =    list(set(graph_copy[u] + graph_copy[v]				)				)
				uv_neighbors.remove(_UpperCAmelCase				)
				uv_neighbors.remove(_UpperCAmelCase				)
				__lowerCAmelCase: Dict					   =    uv_neighbors
				for neighbor in uv_neighbors:
						graph_copy[neighbor].append(_UpperCAmelCase				)

				__lowerCAmelCase: int					   =    set(contracted_nodes[u].union(contracted_nodes[v]				)				)

				# Remove nodes u and v.
				del graph_copy[u]
				del graph_copy[v]
				for neighbor in uv_neighbors:
						if u in graph_copy[neighbor]:
								graph_copy[neighbor].remove(_UpperCAmelCase				)
						if v in graph_copy[neighbor]:
								graph_copy[neighbor].remove(_UpperCAmelCase				)

    # Find cutset.
		__lowerCAmelCase: str					   =    [contracted_nodes[node] for node in graph_copy]
		return {
		    (node, neighbor)
		    for node in groups[0]
		    for neighbor in graph[node]
		    if neighbor in groups[1]
		}


if __name__ == "__main__":
			print(partition_graph(TEST_GRAPH))





"""simple docstring"""


from __future__ import annotations

import unittest

from transformers import OpenAIGPTConfig, is_tf_available
from transformers.testing_utils import require_tf, slow

from ...test_configuration_common import ConfigTester
from ...test_modeling_tf_common import TFModelTesterMixin, ids_tensor, random_attention_mask
from ...test_pipeline_mixin import PipelineTesterMixin


if is_tf_available():
			import tensorflow as tf

			from transformers.models.openai.modeling_tf_openai import (
			    TF_OPENAI_GPT_PRETRAINED_MODEL_ARCHIVE_LIST,
			    TFOpenAIGPTDoubleHeadsModel,
			    TFOpenAIGPTForSequenceClassification,
			    TFOpenAIGPTLMHeadModel,
			    TFOpenAIGPTModel,
			)





class 					snake_case			:

				def __init__(			self							:       str  ,						UpperCamelCase__							:       Optional[int]  ,						)->     Optional[Any]:



						'''simple docstring'''


						__lowerCAmelCase: str					   =    parent
						__lowerCAmelCase: Union[str, Any]					   =    1_3
						__lowerCAmelCase: Union[str, Any]					   =    7
						__lowerCAmelCase: List[Any]					   =    True
						__lowerCAmelCase: Any					   =    True
						__lowerCAmelCase: List[Any]					   =    True
						__lowerCAmelCase: str					   =    True
						__lowerCAmelCase: List[Any]					   =    True
						__lowerCAmelCase: Tuple					   =    9_9
						__lowerCAmelCase: Dict					   =    3_2
						__lowerCAmelCase: Optional[Any]					   =    2
						__lowerCAmelCase: Union[str, Any]					   =    4
						__lowerCAmelCase: Union[str, Any]					   =    3_7
						__lowerCAmelCase: List[str]					   =    "gelu"
						__lowerCAmelCase: List[str]					   =    0.1
						__lowerCAmelCase: List[str]					   =    0.1
						__lowerCAmelCase: Union[str, Any]					   =    5_1_2
						__lowerCAmelCase: int					   =    1_6
						__lowerCAmelCase: int					   =    2
						__lowerCAmelCase: str					   =    0.02
						__lowerCAmelCase: Union[str, Any]					   =    3
						__lowerCAmelCase: str					   =    4
						__lowerCAmelCase: List[Any]					   =    None
						__lowerCAmelCase: int					   =    self.vocab_size - 1

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



						'''simple docstring'''


						__lowerCAmelCase: Any					   =    ids_tensor([self.batch_size, self.seq_length]  ,						self.vocab_size)

						__lowerCAmelCase: str					   =    None
						if self.use_input_mask:
								__lowerCAmelCase: List[Any]					   =    random_attention_mask([self.batch_size, self.seq_length])

						__lowerCAmelCase: int					   =    None
						if self.use_token_type_ids:
								__lowerCAmelCase: Any					   =    ids_tensor([self.batch_size, self.seq_length]  ,						self.type_vocab_size)

						__lowerCAmelCase: Dict					   =    None
						if self.use_mc_token_ids:
								__lowerCAmelCase: Union[str, Any]					   =    ids_tensor([self.batch_size, self.num_choices]  ,						self.seq_length)

						__lowerCAmelCase: int					   =    None
						__lowerCAmelCase: Optional[Any]					   =    None
						__lowerCAmelCase: int					   =    None
						if self.use_labels:
								__lowerCAmelCase: Tuple					   =    ids_tensor([self.batch_size]  ,						self.type_sequence_label_size)
								__lowerCAmelCase: str					   =    ids_tensor([self.batch_size, self.seq_length]  ,						self.num_labels)
								__lowerCAmelCase: int					   =    ids_tensor([self.batch_size]  ,						self.num_choices)

						__lowerCAmelCase: int					   =    OpenAIGPTConfig(
						    vocab_size=self.vocab_size  ,						n_embd=self.hidden_size  ,						n_layer=self.num_hidden_layers  ,						n_head=self.num_attention_heads  ,						n_positions=self.max_position_embeddings  ,						pad_token_id=self.pad_token_id  ,						)

						__lowerCAmelCase: Union[str, Any]					   =    ids_tensor([self.num_hidden_layers, self.num_attention_heads]  ,						2)

						return (
						    config,
						    input_ids,
						    input_mask,
						    head_mask,
						    token_type_ids,
						    mc_token_ids,
						    sequence_labels,
						    token_labels,
						    choice_labels,
						)

				def 							lowercase_  (			self							:       Optional[int]  ,						UpperCamelCase__							:       int  ,						UpperCamelCase__							:       Any  ,						UpperCamelCase__							:       List[Any]  ,						UpperCamelCase__							:       int  ,						UpperCamelCase__							:       Dict  ,						*UpperCamelCase__							:       Dict)->     Union[str, Any]:



						'''simple docstring'''


						__lowerCAmelCase: List[str]					   =    TFOpenAIGPTModel(config=UpperCamelCase__)
						__lowerCAmelCase: Tuple					   =    {"input_ids": input_ids, "attention_mask": input_mask, "token_type_ids": token_type_ids}
						__lowerCAmelCase: List[Any]					   =    model(UpperCamelCase__)

						__lowerCAmelCase: List[Any]					   =    [input_ids, input_mask]
						__lowerCAmelCase: Tuple					   =    model(UpperCamelCase__)

						__lowerCAmelCase: List[Any]					   =    model(UpperCamelCase__)

						self.parent.assertEqual(result.last_hidden_state.shape  ,						(self.batch_size, self.seq_length, self.hidden_size))

				def 							lowercase_  (			self							:       Dict  ,						UpperCamelCase__							:       List[str]  ,						UpperCamelCase__							:       Union[str, Any]  ,						UpperCamelCase__							:       List[Any]  ,						UpperCamelCase__							:       Optional[int]  ,						UpperCamelCase__							:       int  ,						*UpperCamelCase__							:       Optional[Any])->     Union[str, Any]:



						'''simple docstring'''


						__lowerCAmelCase: Any					   =    TFOpenAIGPTLMHeadModel(config=UpperCamelCase__)
						__lowerCAmelCase: int					   =    {"input_ids": input_ids, "attention_mask": input_mask, "token_type_ids": token_type_ids}
						__lowerCAmelCase: Any					   =    model(UpperCamelCase__)
						self.parent.assertEqual(result.logits.shape  ,						(self.batch_size, self.seq_length, self.vocab_size))

				def 							lowercase_  (			self							:       Tuple  ,						UpperCamelCase__							:       str  ,						UpperCamelCase__							:       Union[str, Any]  ,						UpperCamelCase__							:       Tuple  ,						UpperCamelCase__							:       Optional[int]  ,						UpperCamelCase__							:       List[str]  ,						UpperCamelCase__							:       Optional[Any]  ,						*UpperCamelCase__							:       Optional[Any])->     Optional[int]:



						'''simple docstring'''


						__lowerCAmelCase: Union[str, Any]					   =    TFOpenAIGPTDoubleHeadsModel(config=UpperCamelCase__)

						__lowerCAmelCase: List[str]					   =    tf.tile(tf.expand_dims(UpperCamelCase__  ,						1)  ,						(1, self.num_choices, 1))
						__lowerCAmelCase: Union[str, Any]					   =    tf.tile(tf.expand_dims(UpperCamelCase__  ,						1)  ,						(1, self.num_choices, 1))
						__lowerCAmelCase: Optional[Any]					   =    tf.tile(tf.expand_dims(UpperCamelCase__  ,						1)  ,						(1, self.num_choices, 1))

						__lowerCAmelCase: str					   =    {
						    "input_ids": multiple_choice_inputs_ids,
						    "mc_token_ids": mc_token_ids,
						    "attention_mask": multiple_choice_input_mask,
						    "token_type_ids": multiple_choice_token_type_ids,
						}
						__lowerCAmelCase: Optional[int]					   =    model(UpperCamelCase__)
						self.parent.assertEqual(
						    result.logits.shape  ,						(self.batch_size, self.num_choices, self.seq_length, self.vocab_size))
						self.parent.assertEqual(result.mc_logits.shape  ,						(self.batch_size, self.num_choices))

				def 							lowercase_  (			self							:       List[str]  ,						UpperCamelCase__							:       List[Any]  ,						UpperCamelCase__							:       Optional[Any]  ,						UpperCamelCase__							:       Any  ,						UpperCamelCase__							:       str  ,						UpperCamelCase__							:       Optional[Any]  ,						*UpperCamelCase__							:       List[str])->     Any:



						'''simple docstring'''


						__lowerCAmelCase: str					   =    self.num_labels
						__lowerCAmelCase: Dict					   =    ids_tensor([self.batch_size]  ,						self.type_sequence_label_size)
						__lowerCAmelCase: List[str]					   =    {
						    "input_ids": input_ids,
						    "attention_mask": input_mask,
						    "token_type_ids": token_type_ids,
						    "labels": sequence_labels,
						}
						__lowerCAmelCase: str					   =    TFOpenAIGPTForSequenceClassification(UpperCamelCase__)
						__lowerCAmelCase: Optional[int]					   =    model(UpperCamelCase__)
						self.parent.assertEqual(result.logits.shape  ,						(self.batch_size, self.num_labels))




				def 							lowercase_  (			self							:       Any)->     List[str]:



						'''simple docstring'''


						__lowerCAmelCase: List[str]					   =    self.prepare_config_and_inputs()

						(
						    (
						    __lowerCAmelCase
						)   ,				(
						    __lowerCAmelCase
						)   ,				(
						    __lowerCAmelCase
						)   ,				(
						    __lowerCAmelCase
						)   ,				(
						    __lowerCAmelCase
						)   ,				(
						    __lowerCAmelCase
						)   ,				(
						    __lowerCAmelCase
						)   ,				(
						    __lowerCAmelCase
						)   ,				(
						    __lowerCAmelCase
						)   ,				
						): List[Any]					   =    config_and_inputs

						__lowerCAmelCase: List[Any]					   =    {"input_ids": input_ids, "token_type_ids": token_type_ids, "attention_mask": input_mask}
						return config, inputs_dict





@require_tf
class 					snake_case			(       __snake_case,							__snake_case,							unittest.TestCase						):
				SCREAMING_SNAKE_CASE_     :   Dict        =						(
				    (TFOpenAIGPTModel, TFOpenAIGPTLMHeadModel, TFOpenAIGPTDoubleHeadsModel, TFOpenAIGPTForSequenceClassification)
				    if is_tf_available()
				    else ()
				)
				SCREAMING_SNAKE_CASE_     :   List[str]        =						(
				    (TFOpenAIGPTLMHeadModel,) if is_tf_available() else ()
				)  # TODO (PVP): Add Double HeadsModel when generate() function is changed accordingly
				SCREAMING_SNAKE_CASE_     :   int        =						(
				    {
				        """feature-extraction""": TFOpenAIGPTModel,
				        """text-classification""": TFOpenAIGPTForSequenceClassification,
				        """text-generation""": TFOpenAIGPTLMHeadModel,
				        """zero-shot""": TFOpenAIGPTForSequenceClassification,
				    }
				    if is_tf_available()
				    else {}
				)
				SCREAMING_SNAKE_CASE_     :   List[Any]        =						False
				SCREAMING_SNAKE_CASE_     :   Tuple        =						False

				def 							lowercase_  (			self							:       List[str]  ,						UpperCamelCase__							:       int  ,						UpperCamelCase__							:       Union[str, Any]  ,						UpperCamelCase__							:       Optional[int]  ,						UpperCamelCase__							:       Union[str, Any]  ,						UpperCamelCase__							:       Optional[Any])->     Union[str, Any]:



						'''simple docstring'''


						if pipeline_test_casse_name == "ZeroShotClassificationPipelineTests":
								# Get `tokenizer does not have a padding token` error for both fast/slow tokenizers.
								# `OpenAIGPTConfig` was never used in pipeline tests, either because of a missing checkpoint or because a
								# tiny config could not be created.
								return True

						return False

				def 							lowercase_  (			self							:       str)->     Tuple:



						'''simple docstring'''


						__lowerCAmelCase: Optional[int]					   =    TFOpenAIGPTModelTester(self)
						__lowerCAmelCase: List[Any]					   =    ConfigTester(self  ,						config_class=UpperCamelCase__  ,						n_embd=3_7)

				def 							lowercase_  (			self							:       List[Any])->     List[Any]:



						'''simple docstring'''


						self.config_tester.run_common_tests()

				def 							lowercase_  (			self							:       Tuple)->     Optional[int]:



						'''simple docstring'''


						__lowerCAmelCase: Optional[Any]					   =    self.model_tester.prepare_config_and_inputs()
						self.model_tester.create_and_check_openai_gpt_model(*UpperCamelCase__)

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



						'''simple docstring'''


						__lowerCAmelCase: Optional[Any]					   =    self.model_tester.prepare_config_and_inputs()
						self.model_tester.create_and_check_openai_gpt_lm_head(*UpperCamelCase__)

				def 							lowercase_  (			self							:       Optional[Any])->     Dict:



						'''simple docstring'''


						__lowerCAmelCase: List[Any]					   =    self.model_tester.prepare_config_and_inputs()
						self.model_tester.create_and_check_openai_gpt_double_head(*UpperCamelCase__)

				def 							lowercase_  (			self							:       List[str])->     Tuple:



						'''simple docstring'''


						__lowerCAmelCase: Optional[int]					   =    self.model_tester.prepare_config_and_inputs()
						self.model_tester.create_and_check_openai_gpt_for_sequence_classification(*UpperCamelCase__)




				@slow
				def 							lowercase_  (			self							:       str)->     Dict:



						'''simple docstring'''


						for model_name in TF_OPENAI_GPT_PRETRAINED_MODEL_ARCHIVE_LIST[:1]:
								__lowerCAmelCase: str					   =    TFOpenAIGPTModel.from_pretrained(UpperCamelCase__)
								self.assertIsNotNone(UpperCamelCase__)





@require_tf
class 					snake_case			(       unittest.TestCase						):

				@slow
				def 							lowercase_  (			self							:       Union[str, Any])->     List[str]:



						'''simple docstring'''


						__lowerCAmelCase: Optional[Any]					   =    TFOpenAIGPTLMHeadModel.from_pretrained("openai-gpt")
						__lowerCAmelCase: List[str]					   =    tf.convert_to_tensor([[4_8_1, 4_7_3_5, 5_4_4]]  ,						dtype=tf.intaa)  # the president is
						__lowerCAmelCase: Union[str, Any]					   =    [
						    4_8_1,
						    4_7_3_5,
						    5_4_4,
						    2_4_6,
						    9_6_3,
						    8_7_0,
						    7_6_2,
						    2_3_9,
						    2_4_4,
						    4_0_4_7_7,
						    2_4_4,
						    2_4_9,
						    7_1_9,
						    8_8_1,
						    4_8_7,
						    5_4_4,
						    2_4_0,
						    2_4_4,
						    6_0_3,
						    4_8_1,
						]  # the president is a very good man. " \n " i\'m sure he is, " said the

						__lowerCAmelCase: str					   =    model.generate(UpperCamelCase__  ,						do_sample=UpperCamelCase__)
						self.assertListEqual(output_ids[0].numpy().tolist()  ,						UpperCamelCase__)


