"""simple docstring"""







import math






class      _SCREAMING_SNAKE_CASE							:



   '''simple docstring'''



   def __init__(	self ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE	):


      '''simple docstring'''

      __lowerCamelCase    		=					x
      __lowerCamelCase    		=					y
      __lowerCamelCase    		=					step_size
      __lowerCamelCase    		=					function_to_optimize







   def    _A				(	self	):


      '''simple docstring'''

      return self.function(self.x ,				self.y	)







   def    _A				(	self	):


      '''simple docstring'''

      __lowerCamelCase    		=					self.step_size
      return [
          SearchProblem(_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_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	):


      '''simple docstring'''

      return hash(str(self	)	)







   def __eq__(	self ,				_SCREAMING_SNAKE_CASE	):


      '''simple docstring'''

      if isinstance(_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE	):
         return hash(str(self	)	) == hash(str(_SCREAMING_SNAKE_CASE	)	)
      return False







   def __str__(	self	):


      '''simple docstring'''

      return F'''x: {self.x} y: {self.y}'''



def       A__    (	lowercase_     :	str      , lowercase_     :	Tuple = True      , lowercase_     :	List[Any] = math.inf      , lowercase_     :	Optional[Any] = -math.inf      , lowercase_     :	Optional[int] = math.inf      , lowercase_     :	Dict = -math.inf      , lowercase_     :	Any = False      , lowercase_     :	Optional[int] = 10000      , )  ->							SearchProblem:
   __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(lowercase_						)
      iterations += 1
      __lowerCamelCase    		=					current_state.score()
      scores.append(lowercase_						)
      __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(lowercase_						)      , lowercase_						)
      plt.xlabel('Iterations'						)
      plt.ylabel('Function values'						)
      plt.show()

   return current_state


if __name__ == "__main__":
     import doctest

     doctest.testmod()



     def       A__    (	lowercase_     :	str      , lowercase_     :	Tuple						)  ->							int:
        return (x**2) + (y**2)

     # starting the problem with initial coordinates (3, 4)
     _SCREAMING_SNAKE_CASE	:		List[str]   =   SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
     _SCREAMING_SNAKE_CASE	:		str   =   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[Any]   =   SearchProblem(x=1_2, y=4_7, step_size=1, function_to_optimize=test_fa)
     _SCREAMING_SNAKE_CASE	:		Tuple   =   hill_climbing(
         prob, find_max=False, max_x=1_0_0, min_x=5, max_y=5_0, 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__    (	lowercase_     :	Optional[Any]      , lowercase_     :	Tuple						)  ->							Optional[int]:
        return (3 * x**2) - (6 * y)

     _SCREAMING_SNAKE_CASE	:		Any   =   SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
     _SCREAMING_SNAKE_CASE	:		Union[str, Any]   =   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()}"
     )












def        __SCREAMING_SNAKE_CASE (	lowercase_   )							->						str:

    """simple docstring"""


    return " ".join(sorted(set(sentence.split()   )   )   )


if __name__ == "__main__":
 import doctest

 doctest.testmod()






