



a_								=   '''
# Transformers installation
! pip install transformers datasets evaluate
# To install from source instead of the last release, comment the command above and uncomment the following one.
# ! pip install git+https://github.com/huggingface/transformers.git
'''

a_								=   [{'''type''': '''code''', '''content''': INSTALL_CONTENT}]
a_								=   {
    '''{processor_class}''': '''FakeProcessorClass''',
    '''{model_class}''': '''FakeModelClass''',
    '''{object_class}''': '''FakeObjectClass''',
}











import math



class 	__lowerCAmelCase       :




 def __init__(  self		,			__UpperCAmelCase		,			__UpperCAmelCase		,			__UpperCAmelCase		,			__UpperCAmelCase			):



    '''simple docstring'''
    __lowerCamelCase  							=      x
    __lowerCamelCase  							=      y
    __lowerCamelCase  							=      step_size
    __lowerCamelCase  							=      function_to_optimize




 def     lowerCamelCase (  self			):



    '''simple docstring'''
    return self.function(self.x		,			self.y			)




 def     lowerCamelCase (  self			):



    '''simple docstring'''
    __lowerCamelCase  							=      self.step_size
    return [
        SearchProblem(__UpperCAmelCase		,			__UpperCAmelCase		,			__UpperCAmelCase		,			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			):



    '''simple docstring'''
    return hash(str(self			)			)




 def __eq__(  self		,			__UpperCAmelCase			):



    '''simple docstring'''
    if isinstance(__UpperCAmelCase		,			__UpperCAmelCase			):
       return hash(str(self			)			) == hash(str(__UpperCAmelCase			)			)
    return False




 def __str__(  self			):



    '''simple docstring'''
    return F"""x: {self.x} y: {self.y}"""





def 						a__     (						_UpperCamelCase     :	Tuple	,_UpperCamelCase     :	bool = True	,_UpperCamelCase     :	float = math.inf	,_UpperCamelCase     :	float = -math.inf	,_UpperCamelCase     :	float = math.inf	,_UpperCamelCase     :	float = -math.inf	,_UpperCamelCase     :	bool = False	,_UpperCamelCase     :	int = 1_00_00	,):
   __lowerCamelCase  							=      search_prob
   __lowerCamelCase  							=      []  # list to store the current score at each iteration
   __lowerCamelCase  							=      0
   __lowerCamelCase  							=      False
   __lowerCamelCase  							=      set()
   while not solution_found and iterations < max_iter:
      visited.add(_UpperCamelCase							)
      iterations += 1
      __lowerCamelCase  							=      current_state.score()
      scores.append(_UpperCamelCase							)
      __lowerCamelCase  							=      current_state.get_neighbors()
      __lowerCamelCase  							=      -math.inf
      __lowerCamelCase  							=      math.inf
      __lowerCamelCase  							=      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
         __lowerCamelCase  							=      neighbor.score() - current_score
         if find_max:  # finding max
            # going to direction with greatest ascent
            if change > max_change and change > 0:
               __lowerCamelCase  							=      change
               __lowerCamelCase  							=      neighbor
         else:  # finding min
            # to direction with greatest descent
            if change < min_change and change < 0:
               __lowerCamelCase  							=      change
               __lowerCamelCase  							=      neighbor
      if next_state is not None:
         # we found at least one neighbor which improved the current state
         __lowerCamelCase  							=      next_state
      else:
         # since we have no neighbor that improves the solution we stop the search
         __lowerCamelCase  							=      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 						a__     (						_UpperCamelCase     :	Union[str, Any]	,_UpperCamelCase     :	Union[str, Any]							):
     return (x**2) + (y**2)

  # starting the problem with initial coordinates (3, 4)
  a_								=   SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
  a_								=   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)
  a_								=   SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
  a_								=   hill_climbing(
      prob, find_max=False, max_x=100, 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 						a__     (						_UpperCamelCase     :	int	,_UpperCamelCase     :	Dict							):
     return (3 * x**2) - (6 * y)

  a_								=   SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
  a_								=   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()}"
  )






