


'''simple docstring'''






import math




class 			a  :
 def __init__(			self   ,					__magic_name__   ,					__magic_name__   ,					__magic_name__   ,					__magic_name__    )       ->				str:
      _a         =				x
      _a         =				y
      _a         =				step_size
      _a         =				function_to_optimize
 def 				__UpperCAmelCase		(			self    )       ->				int:
      return self.function(self.x   ,					self.y    )
 def 				__UpperCAmelCase		(			self    )       ->				Tuple:
      _a         =				self.step_size
      return [
          SearchProblem(__magic_name__   ,					__magic_name__   ,					__magic_name__   ,					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    )       ->				Union[str, Any]:
      return hash(str(self    )    )
 def __eq__(			self   ,					__magic_name__    )       ->				List[Any]:
      if isinstance(__magic_name__   ,					__magic_name__    ):
           return hash(str(self    )    ) == hash(str(__magic_name__    )    )
      return False




 def __str__(			self    )       ->				Tuple:
      return f'x: {self.x} y: {self.y}'






def 						_A					(lowerCAmelCase__	:Tuple					,    lowerCAmelCase__	:bool = True					,    lowerCAmelCase__	:float = math.inf					,    lowerCAmelCase__	:float = -math.inf					,    lowerCAmelCase__	:float = math.inf					,    lowerCAmelCase__	:float = -math.inf					,    lowerCAmelCase__	:bool = False					,    lowerCAmelCase__	:int = 1_00_00					,    ) ->	SearchProblem:




     '''simple docstring'''



     _a         =				search_prob
     _a         =				[]  # list to store the current score at each iteration
     _a         =				0
     _a         =				False
     _a         =				set()
     while not solution_found and iterations < max_iter:
          visited.add(lowerCAmelCase__		)
          iterations += 1
          _a         =				current_state.score()
          scores.append(lowerCAmelCase__		)
          _a         =				current_state.get_neighbors()
          _a         =				-math.inf
          _a         =				math.inf
          _a         =				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
               _a         =				neighbor.score() - current_score
               if find_max:  # finding max
                    # going to direction with greatest ascent
                    if change > max_change and change > 0:
                         _a         =				change
                         _a         =				neighbor
               else:  # finding min
                    # to direction with greatest descent
                    if change < min_change and change < 0:
                         _a         =				change
                         _a         =				neighbor
          if next_state is not None:
               # we found at least one neighbor which improved the current state
               _a         =				next_state
          else:
               # since we have no neighbor that improves the solution we stop the search
               _a         =				True

     if visualization:
          from matplotlib import pyplot as plt

          plt.plot(range(lowerCAmelCase__		)					,    lowerCAmelCase__		)
          plt.xlabel('Iterations'		)
          plt.ylabel('Function values'		)
          plt.show()

     return current_state


if __name__ == "__main__":
 import doctest

 doctest.testmod()






 def 						_A					(lowerCAmelCase__	:List[Any]					,    lowerCAmelCase__	:Union[str, Any]		) ->	int:




      '''simple docstring'''



      return (x**2) + (y**2)

 # starting the problem with initial coordinates (3, 4)
 a_       :     Any 							=     SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
 a_       :     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)
 a_       :     Optional[Any] 							=     SearchProblem(x=1_2, y=4_7, step_size=1, function_to_optimize=test_fa)
 a_       :     List[str] 							=     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					(lowerCAmelCase__	:List[Any]					,    lowerCAmelCase__	:Optional[int]		) ->	Tuple:




      '''simple docstring'''



      return (3 * x**2) - (6 * y)

 a_       :     Any 							=     SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
 a_       :     Tuple 							=     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()}'''
 )





'''simple docstring'''






import os






def 						_A					() ->	int:




     '''simple docstring'''



     _a         =				os.path.dirname(os.path.realpath(lowerCAmelCase__		)		)
     _a         =				os.path.join(lowerCAmelCase__					,    'triangle.txt'		)

     with open(lowerCAmelCase__		) as in_file:
          _a         =				[[int(lowerCAmelCase__		) for i in line.split()] for line in in_file]

     while len(lowerCAmelCase__		) != 1:
          _a         =				triangle.pop()
          _a         =				triangle[-1]
          for j in range(len(lowerCAmelCase__		) - 1		):
               curr_row[j] += max(last_row[j]					,    last_row[j + 1]		)
     return triangle[0][0]


if __name__ == "__main__":
 print(solution())

