






'''simple docstring'''


from __future__ import annotations

import random
from collections.abc import Iterable
class  _SCREAMING_SNAKE_CASE				:


			'''simple docstring'''





			def __init__( self				:    Union[str, Any]			,   lowercase				:    list[str]      )				->     None:

									'''simple docstring'''







									UpperCamelCase__       =			{literal: None for literal in literals}






			def __str__( self				:    Dict      )				->     str:

									'''simple docstring'''







									return "{" + " , ".join(self.literals      ) + "}"






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

									'''simple docstring'''







									return len(self.literals      )






			def 					A   ( self				:    Any			,   lowercase				:    dict[str, bool | None]      )				->     None:

									'''simple docstring'''







									for literal in self.literals:
															UpperCamelCase__       =			literal[:2]
															if symbol in model:
																					UpperCamelCase__       =			model[symbol]
															else:
																					continue
															if value is not None:
																					# Complement assignment if literal is in complemented form
																					if literal.endswith("""'"""      ):
																											UpperCamelCase__       =			not value
															UpperCamelCase__       =			value







			def 					A   ( self				:    List[Any]			,   lowercase				:    dict[str, bool | None]      )				->     bool | None:

									'''simple docstring'''







									for literal in self.literals:
															UpperCamelCase__       =			literal.rstrip("""'"""      ) if literal.endswith("""'"""      ) else literal + """'"""
															if symbol in self.literals:
																					return True

									self.assign(lowercase      )
									for value in self.literals.values():
															if value in (True, None):
																					return value
									return any(self.literals.values()      )
class  _SCREAMING_SNAKE_CASE				:


			'''simple docstring'''





			def __init__( self				:    Optional[Any]			,   lowercase				:    Iterable[Clause]      )				->     None:

									'''simple docstring'''







									UpperCamelCase__       =			list(lowercase      )







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

									'''simple docstring'''







									return "{" + " , ".join(str(lowercase      ) for clause in self.clauses      ) + "}"







def 						__magic_name__(			):
						'''simple docstring'''





						UpperCamelCase__       =			[]
						UpperCamelCase__       =			random.randint(1    ,   5       )
						UpperCamelCase__       =			"""A"""
						UpperCamelCase__       =			0
						while i < no_of_literals:
												UpperCamelCase__       =			random.randint(1    ,   5       )
												UpperCamelCase__       =			base_var + str(_A       )
												UpperCamelCase__       =			random.randint(0    ,   1       )
												if var_complement == 1:
																		var_name += "'"
												if var_name in literals:
																		i -= 1
												else:
																		literals.append(_A       )
												i += 1
						return Clause(_A       )







def 						__magic_name__(			):
						'''simple docstring'''





						UpperCamelCase__       =			set()
						UpperCamelCase__       =			random.randint(1    ,   10       )
						while len(_A       ) < no_of_clauses:
												clauses.add(generate_clause()       )
						return Formula(_A       )







def 						__magic_name__(			_A       ):
						'''simple docstring'''





						UpperCamelCase__       =			formula.clauses
						UpperCamelCase__       =			[]
						for clause in formula.clauses:
												for literal in clause.literals:
																		UpperCamelCase__       =			literal[:2]
																		if symbol not in symbols_set:
																								symbols_set.append(_A       )
						return clauses, symbols_set







def 						__magic_name__(			_A    ,   _A    ,   _A       ):
						'''simple docstring'''





						UpperCamelCase__       =			[]
						UpperCamelCase__       =			{}
						UpperCamelCase__       =			[]

						for clause in clauses:
												if clause.evaluate(_A       ):
																		continue
												for literal in clause.literals:
																		literals.append(_A       )

						for s in symbols:
												UpperCamelCase__       =			s + """'"""
												if (s in literals and sym not in literals) or (
												    s not in literals and sym in literals
												):
																		pure_symbols.append(_A       )
						for p in pure_symbols:
												UpperCamelCase__       =			None
						for s in pure_symbols:
												UpperCamelCase__       =			s + """'"""
												if s in literals:
																		UpperCamelCase__       =			True
												elif sym in literals:
																		UpperCamelCase__       =			False
						return pure_symbols, assignment







def 						__magic_name__(			_A    ,   _A       ):
						'''simple docstring'''





						UpperCamelCase__       =			[]
						for clause in clauses:
												if len(_A       ) == 1:
																		unit_symbols.append(list(clause.literals.keys()       )[0]       )
												else:
																		UpperCamelCase__     , UpperCamelCase__       =			0, 0
																		for literal, value in clause.literals.items():
																								if value is False:
																														f_count += 1
																								elif value is None:
																														UpperCamelCase__       =			literal
																														n_count += 1
																		if f_count == len(_A       ) - 1 and n_count == 1:
																								unit_symbols.append(_A       )
						UpperCamelCase__       =			{}
						for i in unit_symbols:
												UpperCamelCase__       =			i[:2]
												UpperCamelCase__       =			len(_A       ) == 2
						UpperCamelCase__       =			[i[:2] for i in unit_symbols]

						return unit_symbols, assignment







def 						__magic_name__(			_A    ,   _A    ,   _A       ):
						'''simple docstring'''





						UpperCamelCase__       =			True
						for clause in clauses:
												UpperCamelCase__       =			clause.evaluate(_A       )
												if clause_check is False:
																		return False, None
												elif clause_check is None:
																		UpperCamelCase__       =			False
																		continue

						if check_clause_all_true:
												return True, model

						try:
												UpperCamelCase__     , UpperCamelCase__       =			find_pure_symbols(_A    ,   _A    ,   _A       )
						except RecursionError:
												print("""raises a RecursionError and is"""       )
												return None, {}
						UpperCamelCase__       =			None
						if len(_A       ) > 0:
												UpperCamelCase__     , UpperCamelCase__       =			pure_symbols[0], assignment[pure_symbols[0]]

						if p:
												UpperCamelCase__       =			model
												UpperCamelCase__       =			value
												UpperCamelCase__       =			list(_A       )
												if p in tmp_symbols:
																		tmp_symbols.remove(_A       )
												return dpll_algorithm(_A    ,   _A    ,   _A       )

						UpperCamelCase__     , UpperCamelCase__       =			find_unit_clauses(_A    ,   _A       )
						UpperCamelCase__       =			None
						if len(_A       ) > 0:
												UpperCamelCase__     , UpperCamelCase__       =			unit_symbols[0], assignment[unit_symbols[0]]
						if p:
												UpperCamelCase__       =			model
												UpperCamelCase__       =			value
												UpperCamelCase__       =			list(_A       )
												if p in tmp_symbols:
																		tmp_symbols.remove(_A       )
												return dpll_algorithm(_A    ,   _A    ,   _A       )
						UpperCamelCase__       =			symbols[0]
						UpperCamelCase__       =			symbols[1:]
						UpperCamelCase__     , UpperCamelCase__       =			model, model
						UpperCamelCase__     , UpperCamelCase__       =			True, False

						return dpll_algorithm(_A    ,   _A    ,   _A       ) or dpll_algorithm(_A    ,   _A    ,   _A       )


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					lowerCamelCase_					:			Any     						=				generate_formula()
					print(f"""The formula {formula} is""", end=''' ''')

					lowerCamelCase_						,  lowerCamelCase_					:			List[Any]     						=				generate_parameters(formula)
					lowerCamelCase_						,  lowerCamelCase_					:			List[Any]     						=				dpll_algorithm(clauses, symbols, {})

					if solution:
										print(f"""satisfiable with the assignment {model}.""")
					else:
										print('''not satisfiable.''')








'''simple docstring'''


import unittest

import numpy as np

from transformers.testing_utils import require_torch, require_vision
from transformers.utils import is_torch_available, is_vision_available

from ...test_image_processing_common import ImageProcessingSavingTestMixin, prepare_image_inputs


if is_torch_available():
					import torch

if is_vision_available():
					from PIL import Image

					from transformers import EfficientNetImageProcessor
class  _SCREAMING_SNAKE_CASE				(		unittest.TestCase						):


			'''simple docstring'''





			def __init__( self				:    List[str]			,   lowercase				:    Optional[Any]			,   lowercase				:    int=1_3			,   lowercase				:    List[Any]=3			,   lowercase				:    int=1_8			,   lowercase				:    List[Any]=3_0			,   lowercase				:    Optional[int]=4_0_0			,   lowercase				:    Any=True			,   lowercase				:    int=None			,   lowercase				:    Any=True			,   lowercase				:    Optional[int]=[0.5, 0.5, 0.5]			,   lowercase				:    List[Any]=[0.5, 0.5, 0.5]			,   )				->     List[Any]:

									'''simple docstring'''







									UpperCamelCase__       =			size if size is not None else {"""height""": 1_8, """width""": 1_8}
									UpperCamelCase__       =			parent
									UpperCamelCase__       =			batch_size
									UpperCamelCase__       =			num_channels
									UpperCamelCase__       =			image_size
									UpperCamelCase__       =			min_resolution
									UpperCamelCase__       =			max_resolution
									UpperCamelCase__       =			do_resize
									UpperCamelCase__       =			size
									UpperCamelCase__       =			do_normalize
									UpperCamelCase__       =			image_mean
									UpperCamelCase__       =			image_std







			def 					A   ( self				:    Optional[Any]      )				->     Any:

									'''simple docstring'''







									return {
									    "image_mean": self.image_mean,
									    "image_std": self.image_std,
									    "do_normalize": self.do_normalize,
									    "do_resize": self.do_resize,
									    "size": self.size,
									}
@require_torch
@require_vision
class  _SCREAMING_SNAKE_CASE				(		SCREAMING_SNAKE_CASE							,unittest.TestCase						):


			'''simple docstring'''





			__a				:				List[Any]         =       EfficientNetImageProcessor if is_vision_available() else None






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

									'''simple docstring'''







									UpperCamelCase__       =			EfficientNetImageProcessorTester(self      )






			@property
			def 					A   ( self				:    Optional[int]      )				->     Optional[Any]:

									'''simple docstring'''







									return self.image_processor_tester.prepare_image_processor_dict()






			def 					A   ( self				:    Dict      )				->     str:

									'''simple docstring'''







									UpperCamelCase__       =			self.image_processing_class(**self.image_processor_dict      )
									self.assertTrue(hasattr(lowercase			,   """image_mean"""      )      )
									self.assertTrue(hasattr(lowercase			,   """image_std"""      )      )
									self.assertTrue(hasattr(lowercase			,   """do_normalize"""      )      )
									self.assertTrue(hasattr(lowercase			,   """do_resize"""      )      )
									self.assertTrue(hasattr(lowercase			,   """size"""      )      )






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

									'''simple docstring'''







									UpperCamelCase__       =			self.image_processing_class.from_dict(self.image_processor_dict      )
									self.assertEqual(image_processor.size			,   {"""height""": 1_8, """width""": 1_8}      )

									UpperCamelCase__       =			self.image_processing_class.from_dict(self.image_processor_dict			,   size=4_2      )
									self.assertEqual(image_processor.size			,   {"""height""": 4_2, """width""": 4_2}      )






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

									'''simple docstring'''







									UpperCamelCase__       =			self.image_processing_class(**self.image_processor_dict      )
									# create random PIL images
									UpperCamelCase__       =			prepare_image_inputs(self.image_processor_tester			,   equal_resolution=lowercase      )
									for image in image_inputs:
															self.assertIsInstance(lowercase			,   Image.Image      )

									# Test not batched input
									UpperCamelCase__       =			image_processing(image_inputs[0]			,   return_tensors="""pt"""      ).pixel_values
									self.assertEqual(
									    encoded_images.shape			,   (
									        1,
									        self.image_processor_tester.num_channels,
									        self.image_processor_tester.size["""height"""],
									        self.image_processor_tester.size["""width"""],
									    )			,   )

									# Test batched
									UpperCamelCase__       =			image_processing(lowercase			,   return_tensors="""pt"""      ).pixel_values
									self.assertEqual(
									    encoded_images.shape			,   (
									        self.image_processor_tester.batch_size,
									        self.image_processor_tester.num_channels,
									        self.image_processor_tester.size["""height"""],
									        self.image_processor_tester.size["""width"""],
									    )			,   )






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

									'''simple docstring'''







									UpperCamelCase__       =			self.image_processing_class(**self.image_processor_dict      )
									# create random numpy tensors
									UpperCamelCase__       =			prepare_image_inputs(self.image_processor_tester			,   equal_resolution=lowercase			,   numpify=lowercase      )
									for image in image_inputs:
															self.assertIsInstance(lowercase			,   np.ndarray      )

									# Test not batched input
									UpperCamelCase__       =			image_processing(image_inputs[0]			,   return_tensors="""pt"""      ).pixel_values
									self.assertEqual(
									    encoded_images.shape			,   (
									        1,
									        self.image_processor_tester.num_channels,
									        self.image_processor_tester.size["""height"""],
									        self.image_processor_tester.size["""width"""],
									    )			,   )

									# Test batched
									UpperCamelCase__       =			image_processing(lowercase			,   return_tensors="""pt"""      ).pixel_values
									self.assertEqual(
									    encoded_images.shape			,   (
									        self.image_processor_tester.batch_size,
									        self.image_processor_tester.num_channels,
									        self.image_processor_tester.size["""height"""],
									        self.image_processor_tester.size["""width"""],
									    )			,   )







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

									'''simple docstring'''







									UpperCamelCase__       =			self.image_processing_class(**self.image_processor_dict      )
									# create random PyTorch tensors
									UpperCamelCase__       =			prepare_image_inputs(self.image_processor_tester			,   equal_resolution=lowercase			,   torchify=lowercase      )
									for image in image_inputs:
															self.assertIsInstance(lowercase			,   torch.Tensor      )

									# Test not batched input
									UpperCamelCase__       =			image_processing(image_inputs[0]			,   return_tensors="""pt"""      ).pixel_values
									self.assertEqual(
									    encoded_images.shape			,   (
									        1,
									        self.image_processor_tester.num_channels,
									        self.image_processor_tester.size["""height"""],
									        self.image_processor_tester.size["""width"""],
									    )			,   )

									# Test batched
									UpperCamelCase__       =			image_processing(lowercase			,   return_tensors="""pt"""      ).pixel_values
									self.assertEqual(
									    encoded_images.shape			,   (
									        self.image_processor_tester.batch_size,
									        self.image_processor_tester.num_channels,
									        self.image_processor_tester.size["""height"""],
									        self.image_processor_tester.size["""width"""],
									    )			,   )
