code: 
  
  
  import math
  
  class 						A__      :
  
  
  
  
  
  
  
      """simple docstring"""
  
      def __init__( self    ,      __snake_case    ,      __snake_case    ,      __snake_case    ,      __snake_case					):
           snake_case					=       x
           snake_case					=       y
           snake_case					=       step_size
           snake_case					=       function_to_optimize
      def 	a_    ( self					):
           return self.function(self.x    ,      self.y					)
      def 	a_    ( self					):
           snake_case					=       self.step_size
           return [
               SearchProblem(__snake_case    ,      __snake_case    ,      __snake_case    ,      self.function					)
               for x, y in (
                   (self.x - step_size, self.y - step_size),
                   (self.x - step_size, self.y),
                   (self.x - step_size, self.y + step_size),
                   (self.x, self.y - step_size),
                   (self.x, self.y + step_size),
                   (self.x + step_size, self.y - step_size),
                   (self.x + step_size, self.y),
                   (self.x + step_size, self.y + step_size),
               )
           ]
      def __hash__( self					):
           return hash(str(self					)					)
      def __eq__( self    ,      __snake_case					):
           if isinstance(__snake_case    ,      __snake_case					):
                return hash(str(self					)					) == hash(str(__snake_case					)					)
           return False
  
  
  
  
      def __str__( self					):
           return F'''x: {self.x} y: {self.y}'''
  
  
  
  
  
  
  def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_ = True							,UpperCamelCase_ = math.inf							,UpperCamelCase_ = -math.inf							,UpperCamelCase_ = math.inf							,UpperCamelCase_ = -math.inf							,UpperCamelCase_ = False							,UpperCamelCase_ = 1_00_00							,):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       snake_case					=       search_prob
       snake_case					=       []  # list to store the current score at each iteration
       snake_case					=       0
       snake_case					=       False
       snake_case					=       set()
       while not solution_found and iterations < max_iter:
            visited.add(UpperCamelCase_       )
            iterations += 1
            snake_case					=       current_state.score()
            scores.append(UpperCamelCase_       )
            snake_case					=       current_state.get_neighbors()
            snake_case					=       -math.inf
            snake_case					=       math.inf
            snake_case					=       None  # to hold the next best neighbor
            for neighbor in neighbors:
                 if neighbor in visited:
                      continue  # do not want to visit the same state again
                 if (
                     neighbor.x > max_x
                     or neighbor.x < min_x
                     or neighbor.y > max_y
                     or neighbor.y < min_y
                 ):
                      continue  # neighbor outside our bounds
                 snake_case					=       neighbor.score() - current_score
                 if find_max:  # finding max
                      # going to direction with greatest ascent
                      if change > max_change and change > 0:
                           snake_case					=       change
                           snake_case					=       neighbor
                 else:  # finding min
                      # to direction with greatest descent
                      if change < min_change and change < 0:
                           snake_case					=       change
                           snake_case					=       neighbor
            if next_state is not None:
                 # we found at least one neighbor which improved the current state
                 snake_case					=       next_state
            else:
                 # since we have no neighbor that improves the solution we stop the search
                 snake_case					=       True
  
       if visualization:
            from matplotlib import pyplot as plt
  
            plt.plot(range(UpperCamelCase_       )							,UpperCamelCase_       )
            plt.xlabel('''Iterations'''       )
            plt.ylabel('''Function values'''       )
            plt.show()
  
       return current_state
  
  
  if __name__ == "__main__":
   import doctest
  
   doctest.testmod()
   def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_       ):
  
  
  
        """simple docstring"""
  
  
  
  
  
  
        return (x**2) + (y**2)
  
   # starting the problem with initial coordinates (3, 4)
   _SCREAMING_SNAKE_CASE    :				Dict       =					SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
   _SCREAMING_SNAKE_CASE    :				Union[str, Any]       =					hill_climbing(prob, find_max=False)
   print(
       "The minimum score for f(x, y) = x^2 + y^2 found via hill climbing: "
       f'''{local_min.score()}'''
   )
  
   # starting the problem with initial coordinates (12, 47)
   _SCREAMING_SNAKE_CASE    :				List[str]       =					SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
   _SCREAMING_SNAKE_CASE    :				Tuple       =					hill_climbing(
       prob, find_max=False, max_x=1_00, min_x=5, max_y=50, min_y=-5, visualization=True
   )
   print(
       "The minimum score for f(x, y) = x^2 + y^2 with the domain 100 > x > 5 "
       f'''and 50 > y > - 5 found via hill climbing: {local_min.score()}'''
   )
   def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_       ):
  
  
  
        """simple docstring"""
  
  
  
  
  
  
        return (3 * x**2) - (6 * y)
  
   _SCREAMING_SNAKE_CASE    :				Dict       =					SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
   _SCREAMING_SNAKE_CASE    :				List[str]       =					hill_climbing(prob, find_max=True)
  
   print(
       "The maximum score for f(x, y) = x^2 + y^2 found via hill climbing: "
       f'''{local_min.score()}'''
   )
  
  
  
  
  
style_context: 
  
  
  from ..utils import deprecate
  from .attention_processor import (  # noqa: F401
      Attention,
      AttentionProcessor,
      AttnAddedKVProcessor,
      AttnProcessor2_0,
      LoRAAttnProcessor,
      LoRALinearLayer,
      LoRAXFormersAttnProcessor,
      SlicedAttnAddedKVProcessor,
      SlicedAttnProcessor,
      XFormersAttnProcessor,
  )
  from .attention_processor import AttnProcessor as AttnProcessorRename  # noqa: F401
  
  
  deprecate(
      "cross_attention",
      "0.20.0",
      "Importing from cross_attention is deprecated. Please import from diffusers.models.attention_processor instead.",
      standard_warn=False,
  )
  
  
  _SCREAMING_SNAKE_CASE    :				Optional[int]       =					AttentionProcessor
  
  class 						A__      (					snake_case__			):
  
  
  
  
  
  
  
      """simple docstring"""
  
      def __init__( self    ,      *__snake_case    ,      **__snake_case					):
           snake_case					=       F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"					)					)} instead.'''
           deprecate('''cross_attention'''    ,      '''0.20.0'''    ,      __snake_case    ,      standard_warn=__snake_case					)
           super().__init__(*__snake_case    ,      **__snake_case					)
  
  
  
  
  
  
  class 						A__      (					snake_case__			):
  
  
  
  
  
  
  
      """simple docstring"""
  
      def __init__( self    ,      *__snake_case    ,      **__snake_case					):
           snake_case					=       F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"					)					)} instead.'''
           deprecate('''cross_attention'''    ,      '''0.20.0'''    ,      __snake_case    ,      standard_warn=__snake_case					)
           super().__init__(*__snake_case    ,      **__snake_case					)
  
  
  
  
  
  
  class 						A__      (					snake_case__			):
  
  
  
  
  
  
  
      """simple docstring"""
  
      def __init__( self    ,      *__snake_case    ,      **__snake_case					):
           snake_case					=       F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"					)					)} instead.'''
           deprecate('''cross_attention'''    ,      '''0.20.0'''    ,      __snake_case    ,      standard_warn=__snake_case					)
           super().__init__(*__snake_case    ,      **__snake_case					)
  
  
  
  
  
  
  class 						A__      (					snake_case__			):
  
  
  
  
  
  
  
      """simple docstring"""
  
      def __init__( self    ,      *__snake_case    ,      **__snake_case					):
           snake_case					=       F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"					)					)} instead.'''
           deprecate('''cross_attention'''    ,      '''0.20.0'''    ,      __snake_case    ,      standard_warn=__snake_case					)
           super().__init__(*__snake_case    ,      **__snake_case					)
  
  
  
  
  
  
  class 						A__      (					snake_case__			):
  
  
  
  
  
  
  
      """simple docstring"""
  
      def __init__( self    ,      *__snake_case    ,      **__snake_case					):
           snake_case					=       F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"					)					)} instead.'''
           deprecate('''cross_attention'''    ,      '''0.20.0'''    ,      __snake_case    ,      standard_warn=__snake_case					)
           super().__init__(*__snake_case    ,      **__snake_case					)
  
  
  
  
  
  
  class 						A__      (					snake_case__			):
  
  
  
  
  
  
  
      """simple docstring"""
  
      def __init__( self    ,      *__snake_case    ,      **__snake_case					):
           snake_case					=       F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"					)					)} instead.'''
           deprecate('''cross_attention'''    ,      '''0.20.0'''    ,      __snake_case    ,      standard_warn=__snake_case					)
           super().__init__(*__snake_case    ,      **__snake_case					)
  
  
  
  
  
  
  class 						A__      (					snake_case__			):
  
  
  
  
  
  
  
      """simple docstring"""
  
      def __init__( self    ,      *__snake_case    ,      **__snake_case					):
           snake_case					=       F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"					)					)} instead.'''
           deprecate('''cross_attention'''    ,      '''0.20.0'''    ,      __snake_case    ,      standard_warn=__snake_case					)
           super().__init__(*__snake_case    ,      **__snake_case					)
  
  
  
  
  
  
  class 						A__      (					snake_case__			):
  
  
  
  
  
  
  
      """simple docstring"""
  
      def __init__( self    ,      *__snake_case    ,      **__snake_case					):
           snake_case					=       F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"					)					)} instead.'''
           deprecate('''cross_attention'''    ,      '''0.20.0'''    ,      __snake_case    ,      standard_warn=__snake_case					)
           super().__init__(*__snake_case    ,      **__snake_case					)
  
  
  
  
  