






'''simple docstring'''

from __future__ import annotations

import random
from collections.abc import Iterable
class 							lowercase_    :







    def __init__(	self       ,     UpperCamelCase__				)				->       None:





     """simple docstring"""

     UpperCAmelCase_				       =					{literal: None for literal in literals}







    def __str__(	self				)				->       str:





     """simple docstring"""

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







    def __len__(	self				)				->       int:





     """simple docstring"""

     return len(self.literals				)







    def   lowerCamelCase_    (	self       ,     UpperCamelCase__				)				->       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   lowerCamelCase_    (	self       ,     UpperCamelCase__				)				->       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(UpperCamelCase__				)
     for value in self.literals.values():
      if value in (True, None):
       return value
     return any(self.literals.values()				)


class 							lowercase_    :







    def __init__(	self       ,     UpperCamelCase__				)				->       None:





     """simple docstring"""

     UpperCAmelCase_				       =					list(UpperCamelCase__				)







    def __str__(	self				)				->       str:





     """simple docstring"""

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



def lowerCamelCase__						(       ):
 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 lowerCamelCase__						(       ):
 UpperCAmelCase_				       =					set()
 UpperCAmelCase_				       =					random.randint(1       ,			10       )
 while len(A_       ) < no_of_clauses:
  clauses.add(generate_clause()       )
 return Formula(A_       )



def lowerCamelCase__						(       A_       ):
 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 lowerCamelCase__						(       A_       ,			A_       ,			A_       ):
 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 lowerCamelCase__						(       A_       ,			A_       ):
 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 lowerCamelCase__						(       A_       ,			A_       ,			A_       ):
 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()

      __snake_case       :   Optional[int]  		=    generate_formula()
      print(F'''The formula {formula} is''', end=''' ''')

      __snake_case       :   Tuple  		=    generate_parameters(formula)
      __snake_case       :   Union[str, Any]  		=    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,
    convert_to_rgb,
    get_resize_output_image_size,
    normalize,
    rescale,
    resize,
    to_channel_dimension_format,
)
from ...image_utils import (
    OPENAI_CLIP_MEAN,
    OPENAI_CLIP_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_vision_available, logging


__snake_case       :   Any  		=    logging.get_logger(__name__)


if is_vision_available():
      import PIL
class 							lowercase_    (     _A						):
    a_             =   ["""pixel_values"""]







    def __init__(	self       ,     UpperCamelCase__ = True       ,     UpperCamelCase__ = None       ,     UpperCamelCase__ = PILImageResampling.BICUBIC       ,     UpperCamelCase__ = True       ,     UpperCamelCase__ = None       ,     UpperCamelCase__ = True       ,     UpperCamelCase__ = 1 / 2_5_5       ,     UpperCamelCase__ = True       ,     UpperCamelCase__ = None       ,     UpperCamelCase__ = None       ,     UpperCamelCase__ = True       ,     **UpperCamelCase__       ,     )				->       None:





     """simple docstring"""

     super().__init__(**UpperCamelCase__				)
     UpperCAmelCase_				       =					size if size is not None else {"shortest_edge": 2_2_4}
     UpperCAmelCase_				       =					get_size_dict(UpperCamelCase__       ,     default_to_square=UpperCamelCase__				)
     UpperCAmelCase_				       =					crop_size if crop_size is not None else {"height": 2_2_4, "width": 2_2_4}
     UpperCAmelCase_				       =					get_size_dict(UpperCamelCase__				)

     UpperCAmelCase_				       =					do_resize
     UpperCAmelCase_				       =					size
     UpperCAmelCase_				       =					resample
     UpperCAmelCase_				       =					do_center_crop
     UpperCAmelCase_				       =					crop_size
     UpperCAmelCase_				       =					do_rescale
     UpperCAmelCase_				       =					rescale_factor
     UpperCAmelCase_				       =					do_normalize
     UpperCAmelCase_				       =					image_mean if image_mean is not None else OPENAI_CLIP_MEAN
     UpperCAmelCase_				       =					image_std if image_std is not None else OPENAI_CLIP_STD
     UpperCAmelCase_				       =					do_convert_rgb







    def   lowerCamelCase_    (	self       ,     UpperCamelCase__       ,     UpperCamelCase__       ,     UpperCamelCase__ = PILImageResampling.BICUBIC       ,     UpperCamelCase__ = None       ,     **UpperCamelCase__       ,     )				->       np.ndarray:





     """simple docstring"""

     UpperCAmelCase_				       =					get_size_dict(UpperCamelCase__       ,     default_to_square=UpperCamelCase__				)
     UpperCAmelCase_				       =					get_resize_output_image_size(
         UpperCamelCase__       ,     size=(size["height"], size["width"])       ,     default_to_square=UpperCamelCase__				)
     return resize(UpperCamelCase__       ,     size=UpperCamelCase__       ,     resample=UpperCamelCase__       ,     data_format=UpperCamelCase__       ,     **UpperCamelCase__				)







    def   lowerCamelCase_    (	self       ,     UpperCamelCase__       ,     UpperCamelCase__       ,     UpperCamelCase__ = None       ,     **UpperCamelCase__       ,     )				->       np.ndarray:





     """simple docstring"""

     UpperCAmelCase_				       =					get_size_dict(UpperCamelCase__				)
     return center_crop(UpperCamelCase__       ,     size=(size["height"], size["width"])       ,     data_format=UpperCamelCase__       ,     **UpperCamelCase__				)







    def   lowerCamelCase_    (	self       ,     UpperCamelCase__       ,     UpperCamelCase__       ,     UpperCamelCase__ = None       ,     **UpperCamelCase__       ,     )				->       int:





     """simple docstring"""

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







    def   lowerCamelCase_    (	self       ,     UpperCamelCase__       ,     UpperCamelCase__       ,     UpperCamelCase__       ,     UpperCamelCase__ = None       ,     **UpperCamelCase__       ,     )				->       np.ndarray:





     """simple docstring"""

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







    def   lowerCamelCase_    (	self       ,     UpperCamelCase__       ,     UpperCamelCase__ = None       ,     UpperCamelCase__ = None       ,     UpperCamelCase__ = None       ,     UpperCamelCase__ = None       ,     UpperCamelCase__ = None       ,     UpperCamelCase__ = None       ,     UpperCamelCase__ = None       ,     UpperCamelCase__ = None       ,     UpperCamelCase__ = None       ,     UpperCamelCase__ = None       ,     UpperCamelCase__ = None       ,     UpperCamelCase__ = None       ,     UpperCamelCase__ = ChannelDimension.FIRST       ,     **UpperCamelCase__       ,     )				->       PIL.Image.Image:





     """simple docstring"""

     UpperCAmelCase_				       =					do_resize if do_resize is not None else self.do_resize
     UpperCAmelCase_				       =					size if size is not None else self.size
     UpperCAmelCase_				       =					get_size_dict(UpperCamelCase__       ,     default_to_square=UpperCamelCase__				)
     UpperCAmelCase_				       =					resample if resample is not None else self.resample
     UpperCAmelCase_				       =					do_center_crop if do_center_crop is not None else self.do_center_crop
     UpperCAmelCase_				       =					crop_size if crop_size is not None else self.crop_size
     UpperCAmelCase_				       =					get_size_dict(UpperCamelCase__				)
     UpperCAmelCase_				       =					do_rescale if do_rescale is not None else self.do_rescale
     UpperCAmelCase_				       =					rescale_factor if rescale_factor is not None else self.rescale_factor
     UpperCAmelCase_				       =					do_normalize if do_normalize is not None else self.do_normalize
     UpperCAmelCase_				       =					image_mean if image_mean is not None else self.image_mean
     UpperCAmelCase_				       =					image_std if image_std is not None else self.image_std
     UpperCAmelCase_				       =					do_convert_rgb if do_convert_rgb is not None else self.do_convert_rgb

     UpperCAmelCase_				       =					make_list_of_images(UpperCamelCase__				)

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

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

     if do_center_crop and crop_size is None:
      raise ValueError("Crop size must be specified if do_center_crop 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 std must be specified if do_normalize is True."				)

     # PIL RGBA images are converted to RGB
     if do_convert_rgb:
      UpperCAmelCase_				       =					[convert_to_rgb(UpperCamelCase__				) for image in images]

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

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

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

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

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

     UpperCAmelCase_				       =					[to_channel_dimension_format(UpperCamelCase__       ,     UpperCamelCase__				) for image in images]

     UpperCAmelCase_				       =					{"pixel_values": images}
     return BatchFeature(data=UpperCamelCase__       ,     tensor_type=UpperCamelCase__				)
