'''simple docstring'''




import math

class      lowerCamelCase_     :
						'''simple docstring'''

						def __init__(	self						:    Dict						, A						:    int						, A						:    int						, A						:    int						, A						:    Optional[Any]	):
													_UpperCAmelCase					:  Dict											=   x
													_UpperCAmelCase					:  Tuple											=   y
													_UpperCAmelCase					:  List[Any]											=   step_size
													_UpperCAmelCase					:  int											=   function_to_optimize




						def 					_A     (	self						:    Any	):
													return self.function(self.x						, self.y	)




						def 					_A     (	self						:    int	):
													_UpperCAmelCase					:  Union[str, Any]											=   self.step_size
													return [
													    SearchProblem(_A						, _A						, _A						, 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						:    Tuple						, A						:    int	):




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





						def __str__(	self						:    Optional[Any]	):
													return F"""x: {self.x} y: {self.y}"""

def      UpperCamelCase_							( _UpperCAmelCase  :				Any      ,     _UpperCAmelCase  :				List[str] = True      ,     _UpperCAmelCase  :				Tuple = math.inf      ,     _UpperCAmelCase  :				Optional[int] = -math.inf      ,     _UpperCAmelCase  :				int = math.inf      ,     _UpperCAmelCase  :				Dict = -math.inf      ,     _UpperCAmelCase  :				Optional[int] = False      ,     _UpperCAmelCase  :				Optional[Any] = 10_000      ,     )   ->   List[str]:


							"""simple docstring"""







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


									"""simple docstring"""







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

		# starting the problem with initial coordinates (3, 4)
		__SCREAMING_SNAKE_CASE	:					Any					=  SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
		__SCREAMING_SNAKE_CASE	:					Optional[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	:					Dict					=  SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
		__SCREAMING_SNAKE_CASE	:					int					=  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      UpperCamelCase_							( _UpperCAmelCase  :				Dict      ,     _UpperCAmelCase  :				List[str]   )   ->   Optional[Any]:


									"""simple docstring"""







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

		__SCREAMING_SNAKE_CASE	:					Optional[int]					=  SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
		__SCREAMING_SNAKE_CASE	:					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()}'
		)


'''simple docstring'''




def      UpperCamelCase_							( _UpperCAmelCase  :				Optional[int]      ,     _UpperCAmelCase  :				List[Any]   )   ->   List[str]:


       """simple docstring"""







       if len(str(_UpperCAmelCase   )   ) == 1 or len(str(_UpperCAmelCase   )   ) == 1:
              return a * b

       _UpperCAmelCase					:  Any											=   max(len(str(_UpperCAmelCase   )   )      ,     len(str(_UpperCAmelCase   )   )   )
       _UpperCAmelCase					:  Any											=   ma // 2

       _UpperCAmelCase				,  _UpperCAmelCase					:  Union[str, Any]											=   divmod(_UpperCAmelCase      ,     10**ma   )
       _UpperCAmelCase				,  _UpperCAmelCase					:  int											=   divmod(_UpperCAmelCase      ,     10**ma   )

       _UpperCAmelCase					:  List[str]											=   karatsuba(_UpperCAmelCase      ,     _UpperCAmelCase   )
       _UpperCAmelCase					:  int											=   karatsuba((aa + aa)      ,     (ba + ba)   )
       _UpperCAmelCase					:  Any											=   karatsuba(_UpperCAmelCase      ,     _UpperCAmelCase   )

       return (z * 10 ** (2 * ma)) + ((y - z - x) * 10 ** (ma)) + (x)

def      UpperCamelCase_							( )   ->   List[str]:


       """simple docstring"""







       print(karatsuba(15_463      ,     23_489   )   )


if __name__ == "__main__":
  main()

