





"""simple docstring"""






from __future__ import annotations

import random
from collections.abc import Iterable



class 						lowerCAmelCase       :






       def __init__( self     ,	a__  ):
              _UpperCAmelCase			     =  {literal: None for literal in literals}






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






       def __len__( self  ):
              return len(self.literals  )






       def 				__A			( self     ,	a__  ):
              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     ,	a__  ):
              for literal in self.literals:
                     _UpperCAmelCase			     =  literal.rstrip('\''  ) if literal.endswith('\''  ) else literal + '\''
                     if symbol in self.literals:
                            return True

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



class 						lowerCAmelCase       :






       def __init__( self     ,	a__  ):
              _UpperCAmelCase			     =  list(a__  )






       def __str__( self  ):
              return "{" + " , ".join(str(a__  ) for clause in self.clauses  ) + "}"


def    __lowerCamelCase     (							)		->							Clause:






       """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(SCREAMING_SNAKE_CASE				)
              _UpperCAmelCase			     =  random.randint(0,1				)
              if var_complement == 1:
                     var_name += "'"
              if var_name in literals:
                     i -= 1
              else:
                     literals.append(SCREAMING_SNAKE_CASE				)
              i += 1
       return Clause(SCREAMING_SNAKE_CASE				)

def    __lowerCamelCase     (							)		->							Formula:






       """simple docstring"""




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

def    __lowerCamelCase     (							SCREAMING_SNAKE_CASE				)		->							tuple[list[Clause], list[str]]:






       """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(SCREAMING_SNAKE_CASE				)
       return clauses, symbols_set

def    __lowerCamelCase     (							SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE				)		->							tuple[list[str], dict[str, bool | None]]:






       """simple docstring"""




       _UpperCAmelCase			     =  []
       _UpperCAmelCase			     =  {}
       _UpperCAmelCase			     =  []

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

       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(SCREAMING_SNAKE_CASE				)
       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    __lowerCamelCase     (							SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE				)		->							tuple[list[str], dict[str, bool | None]]:






       """simple docstring"""




       _UpperCAmelCase			     =  []
       for clause in clauses:
              if len(SCREAMING_SNAKE_CASE				) == 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(SCREAMING_SNAKE_CASE				) - 1 and n_count == 1:
                            unit_symbols.append(SCREAMING_SNAKE_CASE				)
       _UpperCAmelCase			     =  {}
       for i in unit_symbols:
              _UpperCAmelCase			     =  i[:2]
              _UpperCAmelCase			     =  len(SCREAMING_SNAKE_CASE				) == 2
       _UpperCAmelCase			     =  [i[:2] for i in unit_symbols]

       return unit_symbols, assignment

def    __lowerCamelCase     (							SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE				)		->							tuple[bool | None, dict[str, bool | None] | None]:






       """simple docstring"""




       _UpperCAmelCase			     =  True
       for clause in clauses:
              _UpperCAmelCase			     =  clause.evaluate(SCREAMING_SNAKE_CASE				)
              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(SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE				)
       except RecursionError:
              print('raises a RecursionError and is'				)
              return None, {}
       _UpperCAmelCase			     =  None
       if len(SCREAMING_SNAKE_CASE				) > 0:
              _UpperCAmelCase     ,				_UpperCAmelCase			     =  pure_symbols[0], assignment[pure_symbols[0]]

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

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

       return dpll_algorithm(SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE				) or dpll_algorithm(SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE				)


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    lowerCAmelCase_      =				generate_formula()
    print(F'''The formula {formula} is''', end=''' ''')

    lowerCAmelCase_      ,					lowerCAmelCase_      =				generate_parameters(formula)
    lowerCAmelCase_      ,					lowerCAmelCase_      =				dpll_algorithm(clauses, symbols, {})

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













"""simple docstring"""






import copy
import inspect

from transformers.testing_utils import require_torch, torch_device
from transformers.utils.backbone_utils import BackboneType



@require_torch
class 						lowerCAmelCase       :
       lowerCAmelCase__    			=	()
       lowerCAmelCase__    			=	True






       def 				__A			( self  ):
              _UpperCAmelCase			     =  self.config_class

              # test default config
              _UpperCAmelCase			     =  config_class()
              self.assertIsNotNone(a__  )
              _UpperCAmelCase			     =  ['stem'] + [f"""stage{idx}""" for idx in range(1     ,	len(config.depths  ) + 1  )]
              self.assertEqual(config.stage_names     ,	a__  )
              self.assertTrue(set(config.out_features  ).issubset(set(config.stage_names  )  )  )

              # Test out_features and out_indices are correctly set
              # out_features and out_indices both None
              _UpperCAmelCase			     =  config_class(out_features=a__     ,	out_indices=a__  )
              self.assertEqual(config.out_features     ,	[config.stage_names[-1]]  )
              self.assertEqual(config.out_indices     ,	[len(config.stage_names  ) - 1]  )

              # out_features and out_indices both set
              _UpperCAmelCase			     =  config_class(out_features=['stem', 'stage1']     ,	out_indices=[0, 1]  )
              self.assertEqual(config.out_features     ,	['stem', 'stage1']  )
              self.assertEqual(config.out_indices     ,	[0, 1]  )

              # Only out_features set
              _UpperCAmelCase			     =  config_class(out_features=['stage1', 'stage3']  )
              self.assertEqual(config.out_features     ,	['stage1', 'stage3']  )
              self.assertEqual(config.out_indices     ,	[1, 3]  )

              # Only out_indices set
              _UpperCAmelCase			     =  config_class(out_indices=[0, 2]  )
              self.assertEqual(config.out_features     ,	[config.stage_names[0], config.stage_names[2]]  )
              self.assertEqual(config.out_indices     ,	[0, 2]  )

              # Error raised when out_indices do not correspond to out_features
              with self.assertRaises(a__  ):
                     _UpperCAmelCase			     =  config_class(out_features=['stage1', 'stage2']     ,	out_indices=[0, 2]  )






       def 				__A			( self  ):
              _UpperCAmelCase     ,				_UpperCAmelCase			     =  self.model_tester.prepare_config_and_inputs_for_common()

              for model_class in self.all_model_classes:
                     _UpperCAmelCase			     =  model_class(a__  )
                     _UpperCAmelCase			     =  inspect.signature(model.forward  )
                     # signature.parameters is an OrderedDict => so arg_names order is deterministic
                     _UpperCAmelCase			     =  [*signature.parameters.keys()]
                     _UpperCAmelCase			     =  ['pixel_values']
                     self.assertListEqual(arg_names[:1]     ,	a__  )






       def 				__A			( self  ):
              _UpperCAmelCase     ,				_UpperCAmelCase			     =  self.model_tester.prepare_config_and_inputs_for_common()

              for model_class in self.all_model_classes:
                     _UpperCAmelCase			     =  model_class(a__  )
                     self.assertEqual(len(model.channels  )     ,	len(config.out_features  )  )
                     _UpperCAmelCase			     =  model.num_features
                     _UpperCAmelCase			     =  [config.stage_names.index(a__  ) for feat in config.out_features]
                     _UpperCAmelCase			     =  [num_features[idx] for idx in out_indices]
                     self.assertListEqual(model.channels     ,	a__  )

                     _UpperCAmelCase			     =  copy.deepcopy(a__  )
                     _UpperCAmelCase			     =  None
                     _UpperCAmelCase			     =  model_class(a__  )
                     self.assertEqual(len(model.channels  )     ,	1  )
                     self.assertListEqual(model.channels     ,	[num_features[-1]]  )

                     _UpperCAmelCase			     =  copy.deepcopy(a__  )
                     _UpperCAmelCase			     =  None
                     _UpperCAmelCase			     =  model_class(a__  )
                     self.assertEqual(len(model.channels  )     ,	1  )
                     self.assertListEqual(model.channels     ,	[num_features[-1]]  )






       def 				__A			( self  ):
              _UpperCAmelCase     ,				_UpperCAmelCase			     =  self.model_tester.prepare_config_and_inputs_for_common()

              for model_class in self.all_model_classes:
                     _UpperCAmelCase			     =  model_class(a__  )
                     model.to(a__  )
                     model.eval()
                     _UpperCAmelCase			     =  model(**a__  )

                     self.assertEqual(len(result.feature_maps  )     ,	len(config.out_features  )  )
                     self.assertEqual(len(model.channels  )     ,	len(config.out_features  )  )
                     self.assertEqual(len(result.feature_maps  )     ,	len(config.out_indices  )  )
                     self.assertEqual(len(model.channels  )     ,	len(config.out_indices  )  )

                     # Check output of last stage is taken if out_features=None, out_indices=None
                     _UpperCAmelCase			     =  copy.deepcopy(a__  )
                     _UpperCAmelCase			     =  None
                     _UpperCAmelCase			     =  model_class(a__  )
                     model.to(a__  )
                     model.eval()
                     _UpperCAmelCase			     =  model(**a__  )

                     self.assertEqual(len(result.feature_maps  )     ,	1  )
                     self.assertEqual(len(model.channels  )     ,	1  )

                     _UpperCAmelCase			     =  copy.deepcopy(a__  )
                     _UpperCAmelCase			     =  None
                     _UpperCAmelCase			     =  model_class(a__  )
                     model.to(a__  )
                     model.eval()
                     _UpperCAmelCase			     =  model(**a__  )

                     self.assertEqual(len(result.feature_maps  )     ,	1  )
                     self.assertEqual(len(model.channels  )     ,	1  )

                     # Check backbone can be initialized with fresh weights
                     _UpperCAmelCase			     =  copy.deepcopy(a__  )
                     _UpperCAmelCase			     =  False
                     _UpperCAmelCase			     =  model_class(a__  )
                     model.to(a__  )
                     model.eval()
                     _UpperCAmelCase			     =  model(**a__  )






       def 				__A			( self  ):
              _UpperCAmelCase     ,				_UpperCAmelCase			     =  self.model_tester.prepare_config_and_inputs_for_common()

              for backbone_class in self.all_model_classes:
                     _UpperCAmelCase			     =  backbone_class(a__  )

                     self.assertTrue(hasattr(a__     ,	'backbone_type'  )  )
                     self.assertTrue(hasattr(a__     ,	'stage_names'  )  )
                     self.assertTrue(hasattr(a__     ,	'num_features'  )  )
                     self.assertTrue(hasattr(a__     ,	'out_indices'  )  )
                     self.assertTrue(hasattr(a__     ,	'out_features'  )  )
                     self.assertTrue(hasattr(a__     ,	'out_feature_channels'  )  )
                     self.assertTrue(hasattr(a__     ,	'channels'  )  )

                     self.assertIsInstance(backbone.backbone_type     ,	a__  )
                     # Verify num_features has been initialized in the backbone init
                     self.assertIsNotNone(backbone.num_features  )
                     self.assertTrue(len(backbone.channels  ) == len(backbone.out_indices  )  )
                     self.assertTrue(len(backbone.stage_names  ) == len(backbone.num_features  )  )
                     self.assertTrue(len(backbone.channels  ) <= len(backbone.num_features  )  )
                     self.assertTrue(len(backbone.out_feature_channels  ) == len(backbone.stage_names  )  )






       def 				__A			( self  ):
              _UpperCAmelCase     ,				_UpperCAmelCase			     =  self.model_tester.prepare_config_and_inputs_for_common()
              _UpperCAmelCase			     =  inputs_dict['pixel_values'].shape[0]

              for backbone_class in self.all_model_classes:
                     _UpperCAmelCase			     =  backbone_class(a__  )
                     backbone.to(a__  )
                     backbone.eval()

                     _UpperCAmelCase			     =  backbone(**a__  )

                     # Test default outputs and verify feature maps
                     self.assertIsInstance(outputs.feature_maps     ,	a__  )
                     self.assertTrue(len(outputs.feature_maps  ) == len(backbone.channels  )  )
                     for feature_map, n_channels in zip(outputs.feature_maps     ,	backbone.channels  ):
                            self.assertTrue(feature_map.shape[:2]     ,	(batch_size, n_channels)  )
                     self.assertIsNone(outputs.hidden_states  )
                     self.assertIsNone(outputs.attentions  )

                     # Test output_hidden_states=True
                     _UpperCAmelCase			     =  backbone(**a__     ,	output_hidden_states=a__  )
                     self.assertIsNotNone(outputs.hidden_states  )
                     self.assertTrue(len(outputs.hidden_states  )     ,	len(backbone.stage_names  )  )
                     for hidden_state, n_channels in zip(outputs.hidden_states     ,	backbone.channels  ):
                            self.assertTrue(hidden_state.shape[:2]     ,	(batch_size, n_channels)  )

                     # Test output_attentions=True
                     if self.has_attentions:
                            _UpperCAmelCase			     =  backbone(**a__     ,	output_attentions=a__  )
                            self.assertIsNotNone(outputs.attentions  )






