



"""simple docstring"""






from __future__ import annotations

import random
from collections.abc import Iterable




class    __snake_case:




    def __init__(   self    ,							A_			):





      '''simple docstring'''



      _SCREAMING_SNAKE_CASE        =			{literal: None for literal in literals}




    def __str__(   self			):





      '''simple docstring'''



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




    def __len__(   self			):





      '''simple docstring'''



      return len(self.literals			)




    def   A   (   self    ,							A_			):





      '''simple docstring'''



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




    def   A   (   self    ,							A_			):





      '''simple docstring'''



      for literal in self.literals:
        _SCREAMING_SNAKE_CASE        =			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    __snake_case:




    def __init__(   self    ,							A_			):





      '''simple docstring'''



      _SCREAMING_SNAKE_CASE        =			list(A_			)




    def __str__(   self			):





      '''simple docstring'''



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



def 							A__ (     ):


  '''simple docstring'''


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


def 							A__ (     ):


  '''simple docstring'''


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


def 							A__ (     UpperCamelCase__    ):


  '''simple docstring'''


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


def 							A__ (     UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__    ):


  '''simple docstring'''


  _SCREAMING_SNAKE_CASE        =			[]
  _SCREAMING_SNAKE_CASE        =			{}
  _SCREAMING_SNAKE_CASE        =			[]

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

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


def 							A__ (     UpperCamelCase__       ,							UpperCamelCase__    ):


  '''simple docstring'''


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

  return unit_symbols, assignment


def 							A__ (     UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__    ):


  '''simple docstring'''


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

  if check_clause_all_true:
    return True, model

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

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

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

  return dpll_algorithm(UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__    ) or dpll_algorithm(UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__    )


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    lowerCamelCase				:     List[str]								=  generate_formula()
    print(F'''The formula {formula} is''', end=""" """)

    lowerCamelCase			,						lowerCamelCase				:     Optional[int]								=  generate_parameters(formula)
    lowerCamelCase			,						lowerCamelCase				:     Tuple								=  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
import torch

from diffusers import DDPMPipeline, DDPMScheduler, UNetaDModel
from diffusers.utils.testing_utils import enable_full_determinism, require_torch_gpu, slow, torch_device


enable_full_determinism()




class    __snake_case(					unittest.TestCase       ):




    @property
    def   A   (   self			):





      '''simple docstring'''



      torch.manual_seed(0			)
      _SCREAMING_SNAKE_CASE        =			UNetaDModel(
          block_out_channels=(32, 64)    ,							layers_per_block=2    ,							sample_size=32    ,							in_channels=3    ,							out_channels=3    ,							down_block_types=('''DownBlock2D''', '''AttnDownBlock2D''')    ,							up_block_types=('''AttnUpBlock2D''', '''UpBlock2D''')    ,							)
      return model




    def   A   (   self			):





      '''simple docstring'''



      _SCREAMING_SNAKE_CASE        =			'''cpu'''
      _SCREAMING_SNAKE_CASE        =			self.dummy_uncond_unet
      _SCREAMING_SNAKE_CASE        =			DDPMScheduler()

      _SCREAMING_SNAKE_CASE        =			DDPMPipeline(unet=A_    ,							scheduler=A_			)
      ddpm.to(A_			)
      ddpm.set_progress_bar_config(disable=A_			)

      _SCREAMING_SNAKE_CASE        =			torch.Generator(device=A_			).manual_seed(0			)
      _SCREAMING_SNAKE_CASE        =			ddpm(generator=A_    ,							num_inference_steps=2    ,							output_type='''numpy'''			).images

      _SCREAMING_SNAKE_CASE        =			torch.Generator(device=A_			).manual_seed(0			)
      _SCREAMING_SNAKE_CASE        =			ddpm(generator=A_    ,							num_inference_steps=2    ,							output_type='''numpy'''    ,							return_dict=A_			)[0]

      _SCREAMING_SNAKE_CASE        =			image[0, -3:, -3:, -1]
      _SCREAMING_SNAKE_CASE        =			image_from_tuple[0, -3:, -3:, -1]

      assert image.shape == (1, 32, 32, 3)
      _SCREAMING_SNAKE_CASE        =			np.array(
          [9.956e-01, 5.785e-01, 4.675e-01, 9.930e-01, 0.0, 1.000, 1.199e-03, 2.648e-04, 5.101e-04]			)

      assert np.abs(image_slice.flatten() - expected_slice			).max() < 1e-2
      assert np.abs(image_from_tuple_slice.flatten() - expected_slice			).max() < 1e-2




    def   A   (   self			):





      '''simple docstring'''



      _SCREAMING_SNAKE_CASE        =			self.dummy_uncond_unet
      _SCREAMING_SNAKE_CASE        =			DDPMScheduler(prediction_type='''sample'''			)

      _SCREAMING_SNAKE_CASE        =			DDPMPipeline(unet=A_    ,							scheduler=A_			)
      ddpm.to(A_			)
      ddpm.set_progress_bar_config(disable=A_			)

      _SCREAMING_SNAKE_CASE        =			torch.manual_seed(0			)
      _SCREAMING_SNAKE_CASE        =			ddpm(generator=A_    ,							num_inference_steps=2    ,							output_type='''numpy'''			).images

      _SCREAMING_SNAKE_CASE        =			torch.manual_seed(0			)
      _SCREAMING_SNAKE_CASE        =			ddpm(generator=A_    ,							num_inference_steps=2    ,							output_type='''numpy'''			)[0]

      _SCREAMING_SNAKE_CASE        =			image[0, -3:, -3:, -1]
      _SCREAMING_SNAKE_CASE        =			image_eps[0, -3:, -3:, -1]

      assert image.shape == (1, 32, 32, 3)
      _SCREAMING_SNAKE_CASE        =			1e-2 if torch_device != '''mps''' else 3e-2
      assert np.abs(image_slice.flatten() - image_eps_slice.flatten()			).max() < tolerance




@slow
@require_torch_gpu
class    __snake_case(					unittest.TestCase       ):




    def   A   (   self			):





      '''simple docstring'''



      _SCREAMING_SNAKE_CASE        =			'''google/ddpm-cifar10-32'''

      _SCREAMING_SNAKE_CASE        =			UNetaDModel.from_pretrained(A_			)
      _SCREAMING_SNAKE_CASE        =			DDPMScheduler.from_pretrained(A_			)

      _SCREAMING_SNAKE_CASE        =			DDPMPipeline(unet=A_    ,							scheduler=A_			)
      ddpm.to(A_			)
      ddpm.set_progress_bar_config(disable=A_			)

      _SCREAMING_SNAKE_CASE        =			torch.manual_seed(0			)
      _SCREAMING_SNAKE_CASE        =			ddpm(generator=A_    ,							output_type='''numpy'''			).images

      _SCREAMING_SNAKE_CASE        =			image[0, -3:, -3:, -1]

      assert image.shape == (1, 32, 32, 3)
      _SCREAMING_SNAKE_CASE        =			np.array([0.4_200, 0.3_588, 0.1_939, 0.3_847, 0.3_382, 0.2_647, 0.4_155, 0.3_582, 0.3_385]			)
      assert np.abs(image_slice.flatten() - expected_slice			).max() < 1e-2
