






"""simple docstring"""



from __future__ import annotations

import random
from collections.abc import Iterable

class 			a	:







    def __init__(     self				,						_lowerCamelCase			):
      lowercase				       =			{literal: None for literal in literals}







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







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







    def      UpperCamelCase_ (     self				,						_lowerCamelCase			):
      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      UpperCamelCase_ (     self				,						_lowerCamelCase			):
      for literal in self.literals:
        lowercase				       =			literal.rstrip('\''			) if literal.endswith('\''			) else literal + '\''
        if symbol in self.literals:
          return True

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


class 			a	:







    def __init__(     self				,						_lowerCamelCase			):
      lowercase				       =			list(_lowerCamelCase			)







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


def 		_SCREAMING_SNAKE_CASE					(       ):





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





  '''simple docstring'''





  lowercase				       =			set()
  lowercase				       =			random.randint(1						,   10       )
  while len(__snake_case       ) < no_of_clauses:
    clauses.add(generate_clause()       )
  return Formula(__snake_case       )
def 		_SCREAMING_SNAKE_CASE					(       __snake_case     :    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(__snake_case       )
  return clauses, symbols_set
def 		_SCREAMING_SNAKE_CASE					(       __snake_case     :    list[Clause]						,   __snake_case     :    list[str]						,   __snake_case     :    dict[str, bool | None]       ):





  '''simple docstring'''





  lowercase				       =			[]
  lowercase				       =			{}
  lowercase				       =			[]

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

  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(__snake_case       )
  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 		_SCREAMING_SNAKE_CASE					(       __snake_case     :    list[Clause]						,   __snake_case     :    dict[str, bool | None]       ):





  '''simple docstring'''





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

  return unit_symbols, assignment
def 		_SCREAMING_SNAKE_CASE					(       __snake_case     :    list[Clause]						,   __snake_case     :    list[str]						,   __snake_case     :    dict[str, bool | None]       ):





  '''simple docstring'''





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

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

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

  return dpll_algorithm(__snake_case						,   __snake_case						,   __snake_case       ) or dpll_algorithm(__snake_case						,   __snake_case						,   __snake_case       )


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    _UpperCamelCase						:    Tuple		=						generate_formula()
    print(F'''The formula {formula} is''', end=' ')

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

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




'''simple docstring'''







from typing import List, Optional, Tuple, Union

import torch

from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput


class       lowerCAmelCase			(					__UpperCAmelCase      ):




		def __init__(					self       ,    UpperCamelCase       ,    UpperCamelCase   ):
								super().__init__()
								self.register_modules(unet=UpperCamelCase       ,    scheduler=UpperCamelCase   )




		@torch.no_grad()
		def __call__(					self       ,    UpperCamelCase = 1       ,    UpperCamelCase = None       ,    UpperCamelCase = 1_000       ,    UpperCamelCase = "pil"       ,    UpperCamelCase = True       ,    ):
								# Sample gaussian noise to begin loop
								if isinstance(self.unet.config.sample_size       ,    UpperCamelCase   ):
														_SCREAMING_SNAKE_CASE					=			(
														    batch_size,
														    self.unet.config.in_channels,
														    self.unet.config.sample_size,
														    self.unet.config.sample_size,
														)
								else:
														_SCREAMING_SNAKE_CASE					=			(batch_size, self.unet.config.in_channels, *self.unet.config.sample_size)

								if self.device.type == "mps":
														# randn does not work reproducibly on mps
														_SCREAMING_SNAKE_CASE					=			randn_tensor(UpperCamelCase       ,    generator=UpperCamelCase   )
														_SCREAMING_SNAKE_CASE					=			image.to(self.device   )
								else:
														_SCREAMING_SNAKE_CASE					=			randn_tensor(UpperCamelCase       ,    generator=UpperCamelCase       ,    device=self.device   )

								# set step values
								self.scheduler.set_timesteps(UpperCamelCase   )

								for t in self.progress_bar(self.scheduler.timesteps   ):
														# 1. predict noise model_output
														_SCREAMING_SNAKE_CASE					=			self.unet(UpperCamelCase       ,    UpperCamelCase   ).sample

														# 2. compute previous image: x_t -> x_t-1
														_SCREAMING_SNAKE_CASE					=			self.scheduler.step(UpperCamelCase       ,    UpperCamelCase       ,    UpperCamelCase       ,    generator=UpperCamelCase   ).prev_sample

								_SCREAMING_SNAKE_CASE					=			(image / 2 + 0.5).clamp(0       ,    1   )
								_SCREAMING_SNAKE_CASE					=			image.cpu().permute(0       ,    2       ,    3       ,    1   ).numpy()
								if output_type == "pil":
														_SCREAMING_SNAKE_CASE					=			self.numpy_to_pil(UpperCamelCase   )

								if not return_dict:
														return (image,)

								return ImagePipelineOutput(images=UpperCamelCase   )