

'''simple docstring'''

from __future__ import annotations

import random
from collections.abc import Iterable


class   lowerCAmelCase     :







       def __init__(							self			: Any						,      __lowercase			: list[str]      ):







            """simple docstring"""







            __lowercase					={literal: None for literal in literals}







       def __str__(							self			: Optional[Any]      ):







            """simple docstring"""







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







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







            """simple docstring"""







            return len(self.literals      )







       def 			snake_case   (							self			: List[Any]						,      __lowercase			: dict[str, bool | None]      ):







            """simple docstring"""







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







       def 			snake_case   (							self			: List[str]						,      __lowercase			: dict[str, bool | None]      ):







            """simple docstring"""







            for literal in self.literals:
                 __lowercase					=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   lowerCAmelCase     :







       def __init__(							self			: Any						,      __lowercase			: Iterable[Clause]      ):







            """simple docstring"""







            __lowercase					=list(__lowercase      )







       def __str__(							self			: int      ):







            """simple docstring"""







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






def 				__UpperCamelCase							(	):






     '''simple docstring'''





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

def 				__UpperCamelCase							(	):






     '''simple docstring'''





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

def 				__UpperCamelCase							(	lowercase__						:  Formula ):






     '''simple docstring'''





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

def 				__UpperCamelCase							(	lowercase__						:  list[Clause],					lowercase__						:  list[str],					lowercase__						:  dict[str, bool | None] ):






     '''simple docstring'''





     __lowercase					=[]
     __lowercase					={}
     __lowercase					=[]

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

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

def 				__UpperCamelCase							(	lowercase__						:  list[Clause],					lowercase__						:  dict[str, bool | None] ):






     '''simple docstring'''





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

     return unit_symbols, assignment

def 				__UpperCamelCase							(	lowercase__						:  list[Clause],					lowercase__						:  list[str],					lowercase__						:  dict[str, bool | None] ):






     '''simple docstring'''





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

     if check_clause_all_true:
          return True, model

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

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

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

     return dpll_algorithm(lowercase__,					lowercase__,					lowercase__ ) or dpll_algorithm(lowercase__,					lowercase__,					lowercase__ )


if __name__ == "__main__":
       import doctest

       doctest.testmod()

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

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

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





'''simple docstring'''

from typing import Dict, List, Optional, Union

import numpy as np

from ...image_processing_utils import BaseImageProcessor, BatchFeature, get_size_dict
from ...image_transforms import center_crop, normalize, rescale, resize, to_channel_dimension_format
from ...image_utils import (
    IMAGENET_DEFAULT_MEAN,
    IMAGENET_DEFAULT_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    get_image_size,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_vision_available, logging


if is_vision_available():
       import PIL


UpperCAmelCase				   =  logging.get_logger(__name__)


class   lowerCAmelCase     (      A   ):
       lowerCAmelCase_		= ["pixel_values"]







       def __init__(							self			: Dict						,      __lowercase			: bool = True						,      __lowercase			: Dict[str, int] = None						,      __lowercase			: bool = True						,      __lowercase			: Dict[str, int] = None						,      __lowercase			: PILImageResampling = PILImageResampling.BICUBIC						,      __lowercase			: bool = True						,      __lowercase			: Union[int, float] = 1 / 255						,      __lowercase			: bool = True						,      __lowercase			: Optional[Union[float, List[float]]] = None						,      __lowercase			: Optional[Union[float, List[float]]] = None						,      **__lowercase			: Any						,      ):







            """simple docstring"""







            super().__init__(**__lowercase      )
            __lowercase					=crop_size if crop_size is not None else {'height': 256, 'width': 256}
            __lowercase					=get_size_dict(__lowercase						,      param_name='crop_size'      )
            __lowercase					=size if size is not None else {'height': 224, 'width': 224}
            __lowercase					=get_size_dict(__lowercase      )

            __lowercase					=do_center_crop
            __lowercase					=crop_size
            __lowercase					=do_resize
            __lowercase					=size
            __lowercase					=resample
            __lowercase					=do_rescale
            __lowercase					=rescale_factor
            __lowercase					=do_normalize
            __lowercase					=image_mean if image_mean is not None else IMAGENET_DEFAULT_MEAN
            __lowercase					=image_std if image_std is not None else IMAGENET_DEFAULT_STD







       def 			snake_case   (							self			: int						,      __lowercase			: np.ndarray						,      __lowercase			: Dict[str, int]						,      __lowercase			: Optional[int] = None						,      __lowercase			: Optional[Union[str, ChannelDimension]] = None						,      **__lowercase			: Optional[Any]						,      ):







            """simple docstring"""







            __lowercase					=self.size if size is None else size
            __lowercase					=get_size_dict(__lowercase      )
            __lowercase					=get_size_dict(__lowercase						,      param_name='crop_size'      )

            __lowercase		,     __lowercase					=get_image_size(__lowercase      )
            __lowercase					=min(__lowercase						,      __lowercase      )
            __lowercase					=(size['height'] / crop_size['height']) * min_dim
            __lowercase					=(size['width'] / crop_size['width']) * min_dim
            return center_crop(__lowercase						,      size=(cropped_height, cropped_width)						,      data_format=__lowercase						,      **__lowercase      )







       def 			snake_case   (							self			: str						,      __lowercase			: np.ndarray						,      __lowercase			: Dict[str, int]						,      __lowercase			: PILImageResampling = PIL.Image.BICUBIC						,      __lowercase			: Optional[Union[str, ChannelDimension]] = None						,      **__lowercase			: Optional[int]						,      ):







            """simple docstring"""







            __lowercase					=get_size_dict(__lowercase      )
            if "height" not in size or "width" not in size:
                 raise ValueError(f'''The size dictionary must contain the keys \'height\' and \'width\'. Got {size.keys()}'''      )
            return resize(
                __lowercase						,      size=(size['height'], size['width'])						,      resample=__lowercase						,      data_format=__lowercase						,      **__lowercase      )







       def 			snake_case   (							self			: Dict						,      __lowercase			: np.ndarray						,      __lowercase			: Union[int, float]						,      __lowercase			: Optional[Union[str, ChannelDimension]] = None						,      **__lowercase			: Dict						,      ):







            """simple docstring"""







            return rescale(__lowercase						,      scale=__lowercase						,      data_format=__lowercase						,      **__lowercase      )







       def 			snake_case   (							self			: Union[str, Any]						,      __lowercase			: np.ndarray						,      __lowercase			: Union[float, List[float]]						,      __lowercase			: Union[float, List[float]]						,      __lowercase			: Optional[Union[str, ChannelDimension]] = None						,      **__lowercase			: int						,      ):







            """simple docstring"""







            return normalize(__lowercase						,      mean=__lowercase						,      std=__lowercase						,      data_format=__lowercase						,      **__lowercase      )







       def 			snake_case   (							self			: Dict						,      __lowercase			: ImageInput						,      __lowercase			: Optional[bool] = None						,      __lowercase			: Optional[Dict[str, int]] = None						,      __lowercase			: Optional[bool] = None						,      __lowercase			: Optional[Dict[str, int]] = None						,      __lowercase			: PILImageResampling = None						,      __lowercase			: Optional[bool] = None						,      __lowercase			: Optional[float] = None						,      __lowercase			: Optional[bool] = None						,      __lowercase			: Optional[Union[float, List[float]]] = None						,      __lowercase			: Optional[Union[float, List[float]]] = None						,      __lowercase			: Optional[Union[str, TensorType]] = None						,      __lowercase			: ChannelDimension = ChannelDimension.FIRST						,      **__lowercase			: Optional[int]						,      ):







            """simple docstring"""







            __lowercase					=do_center_crop if do_center_crop is not None else self.do_center_crop
            __lowercase					=crop_size if crop_size is not None else self.crop_size
            __lowercase					=get_size_dict(__lowercase						,      param_name='crop_size'      )
            __lowercase					=do_resize if do_resize is not None else self.do_resize
            __lowercase					=size if size is not None else self.size
            __lowercase					=get_size_dict(__lowercase      )
            __lowercase					=resample if resample is not None else self.resample
            __lowercase					=do_rescale if do_rescale is not None else self.do_rescale
            __lowercase					=rescale_factor if rescale_factor is not None else self.rescale_factor
            __lowercase					=do_normalize if do_normalize is not None else self.do_normalize
            __lowercase					=image_mean if image_mean is not None else self.image_mean
            __lowercase					=image_std if image_std is not None else self.image_std

            __lowercase					=make_list_of_images(__lowercase      )

            if not valid_images(__lowercase      ):
                 raise ValueError(
                     'Invalid image type. Must be of type PIL.Image.Image, numpy.ndarray, '
                     'torch.Tensor, tf.Tensor or jax.ndarray.'      )

            if do_center_crop and crop_size is None:
                 raise ValueError('If `do_center_crop` is set to `True`, `crop_size` must be provided.'      )

            if do_resize and size is None:
                 raise ValueError('Size must be specified if do_resize is True.'      )

            if do_rescale and rescale_factor is None:
                 raise ValueError('Rescale factor must be specified if do_rescale is True.'      )

            if do_normalize and (image_mean is None or image_std is None):
                 raise ValueError('Image mean and image standard deviation must be specified if do_normalize is True.'      )

            # All transformations expect numpy arrays.
            __lowercase					=[to_numpy_array(__lowercase      ) for image in images]

            if do_center_crop:
                 __lowercase					=[self.center_crop(__lowercase						,      __lowercase						,      size=__lowercase      ) for image in images]

            if do_resize:
                 __lowercase					=[self.resize(image=__lowercase						,      size=__lowercase						,      resample=__lowercase      ) for image in images]

            if do_rescale:
                 __lowercase					=[self.rescale(image=__lowercase						,      scale=__lowercase      ) for image in images]

            if do_normalize:
                 __lowercase					=[self.normalize(image=__lowercase						,      mean=__lowercase						,      std=__lowercase      ) for image in images]

            __lowercase					=[to_channel_dimension_format(__lowercase						,      __lowercase      ) for image in images]

            __lowercase					={'pixel_values': images}
            return BatchFeature(data=__lowercase						,      tensor_type=__lowercase      )


