






from __future__ import annotations

import random
from collections.abc import Iterable
class 							A_      :






 '''simple docstring'''




 def __init__(		self							,					_A)	->						None:

     """simple docstring"""



     _UpperCAmelCase			: dict[str, bool | None]     					=			{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 	snake_case__			(		self							,					_A)	->						None:

     """simple docstring"""



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


 def 	snake_case__			(		self							,					_A)	->						bool | None:

     """simple docstring"""



     for literal in self.literals:
         _UpperCAmelCase			: Tuple     					=			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 							A_      :






 '''simple docstring'''




 def __init__(		self							,					_A)	->						None:

     """simple docstring"""



     _UpperCAmelCase			: Dict     					=			list(_A)


 def __str__(		self)	->						str:

     """simple docstring"""



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



def        _lowerCamelCase		(  ) ->   Clause:
    _UpperCAmelCase			: Optional[Any]     					=			[]
    _UpperCAmelCase			: List[str]     					=			random.randint(1						,						5	)
    _UpperCAmelCase			: Any     					=			'''A'''
    _UpperCAmelCase			: Optional[Any]     					=			0
    while i < no_of_literals:
        _UpperCAmelCase			: Dict     					=			random.randint(1						,						5	)
        _UpperCAmelCase			: Union[str, Any]     					=			base_var + str(__A	)
        _UpperCAmelCase			: str     					=			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		(  ) ->   Formula:
    _UpperCAmelCase			: set[Clause]     					=			set()
    _UpperCAmelCase			: Dict     					=			random.randint(1						,						10	)
    while len(__A	) < no_of_clauses:
        clauses.add(generate_clause()	)
    return Formula(__A	)

def        _lowerCamelCase		(  __A      :							Formula	) ->   tuple[list[Clause], list[str]]:
    _UpperCAmelCase			: List[Any]     					=			formula.clauses
    _UpperCAmelCase			: Any     					=			[]
    for clause in formula.clauses:
        for literal in clause.literals:
            _UpperCAmelCase			: Any     					=			literal[:2]
            if symbol not in symbols_set:
                symbols_set.append(__A	)
    return clauses, symbols_set

def        _lowerCamelCase		(  __A      :							list[Clause]						,						__A      :							list[str]						,						__A      :							dict[str, bool | None]	) ->   tuple[list[str], dict[str, bool | None]]:
    _UpperCAmelCase			: Any     					=			[]
    _UpperCAmelCase			: dict[str, bool | None]     					=			{}
    _UpperCAmelCase			: List[str]     					=			[]

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

    for s in symbols:
        _UpperCAmelCase			: str     					=			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			: int     					=			None
    for s in pure_symbols:
        _UpperCAmelCase			: Any     					=			s + '''\''''
        if s in literals:
            _UpperCAmelCase			: int     					=			True
        elif sym in literals:
            _UpperCAmelCase			: str     					=			False
    return pure_symbols, assignment

def        _lowerCamelCase		(  __A      :							list[Clause]						,						__A      :							dict[str, bool | None]	) ->   tuple[list[str], dict[str, bool | None]]:
    _UpperCAmelCase			: List[str]     					=			[]
    for clause in clauses:
        if len(__A	) == 1:
            unit_symbols.append(list(clause.literals.keys()	)[0]	)
        else:
            _UpperCAmelCase			: List[str]     					=			0, 0
            for literal, value in clause.literals.items():
                if value is False:
                    f_count += 1
                elif value is None:
                    _UpperCAmelCase			: int     					=			literal
                    n_count += 1
            if f_count == len(__A	) - 1 and n_count == 1:
                unit_symbols.append(__A	)
    _UpperCAmelCase			: dict[str, bool | None]     					=			{}
    for i in unit_symbols:
        _UpperCAmelCase			: Union[str, Any]     					=			i[:2]
        _UpperCAmelCase			: List[str]     					=			len(__A	) == 2
    _UpperCAmelCase			: int     					=			[i[:2] for i in unit_symbols]

    return unit_symbols, assignment

def        _lowerCamelCase		(  __A      :							list[Clause]						,						__A      :							list[str]						,						__A      :							dict[str, bool | None]	) ->   tuple[bool | None, dict[str, bool | None] | None]:
    _UpperCAmelCase			: Dict     					=			True
    for clause in clauses:
        _UpperCAmelCase			: str     					=			clause.evaluate(__A	)
        if clause_check is False:
            return False, None
        elif clause_check is None:
            _UpperCAmelCase			: Any     					=			False
            continue

    if check_clause_all_true:
        return True, model

    try:
        _UpperCAmelCase			: Union[str, Any]     					=			find_pure_symbols(__A						,						__A						,						__A	)
    except RecursionError:
        print('''raises a RecursionError and is'''	)
        return None, {}
    _UpperCAmelCase			: Optional[int]     					=			None
    if len(__A	) > 0:
        _UpperCAmelCase			: str     					=			pure_symbols[0], assignment[pure_symbols[0]]

    if p:
        _UpperCAmelCase			: Any     					=			model
        _UpperCAmelCase			: Optional[int]     					=			value
        _UpperCAmelCase			: str     					=			list(__A	)
        if p in tmp_symbols:
            tmp_symbols.remove(__A	)
        return dpll_algorithm(__A						,						__A						,						__A	)

    _UpperCAmelCase			: Union[str, Any]     					=			find_unit_clauses(__A						,						__A	)
    _UpperCAmelCase			: Tuple     					=			None
    if len(__A	) > 0:
        _UpperCAmelCase			: List[Any]     					=			unit_symbols[0], assignment[unit_symbols[0]]
    if p:
        _UpperCAmelCase			: int     					=			model
        _UpperCAmelCase			: Any     					=			value
        _UpperCAmelCase			: str     					=			list(__A	)
        if p in tmp_symbols:
            tmp_symbols.remove(__A	)
        return dpll_algorithm(__A						,						__A						,						__A	)
    _UpperCAmelCase			: Any     					=			symbols[0]
    _UpperCAmelCase			: str     					=			symbols[1:]
    _UpperCAmelCase			: int     					=			model, model
    _UpperCAmelCase			: List[Any]     					=			True, False

    return dpll_algorithm(__A						,						__A						,						__A	) or dpll_algorithm(__A						,						__A						,						__A	)


if __name__ == "__main__":
 import doctest

 doctest.testmod()

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

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

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












from typing import List, Optional, Tuple, Union

import torch

from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput
class 							A_      (  __lowercase     ):






 '''simple docstring'''




 def __init__(		self							,					_A							,					_A)	->						Dict:

     """simple docstring"""



     super().__init__()
     self.register_modules(unet=_A							,					scheduler=_A)


 @torch.no_grad()
 def __call__(		self							,					_A = 1							,					_A = None							,					_A = 1000							,					_A = "pil"							,					_A = True							,					)	->						Union[ImagePipelineOutput, Tuple]:

     """simple docstring"""



     if isinstance(self.unet.config.sample_size							,					_A):
         _UpperCAmelCase			: List[str]     					=			(
             batch_size,
             self.unet.config.in_channels,
             self.unet.config.sample_size,
             self.unet.config.sample_size,
         )
     else:
         _UpperCAmelCase			: Union[str, Any]     					=			(batch_size, self.unet.config.in_channels, *self.unet.config.sample_size)

     if self.device.type == "mps":
         # randn does not work reproducibly on mps
         _UpperCAmelCase			: int     					=			randn_tensor(_A							,					generator=_A)
         _UpperCAmelCase			: Tuple     					=			image.to(self.device)
     else:
         _UpperCAmelCase			: Any     					=			randn_tensor(_A							,					generator=_A							,					device=self.device)

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

     for t in self.progress_bar(self.scheduler.timesteps):
         # 1. predict noise model_output
         _UpperCAmelCase			: Optional[Any]     					=			self.unet(_A							,					_A).sample

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

     _UpperCAmelCase			: Optional[int]     					=			(image / 2 + 0.5).clamp(0							,					1)
     _UpperCAmelCase			: int     					=			image.cpu().permute(0							,					2							,					3							,					1).numpy()
     if output_type == "pil":
         _UpperCAmelCase			: str     					=			self.numpy_to_pil(_A)

     if not return_dict:
         return (image,)

     return ImagePipelineOutput(images=_A)




