

'''simple docstring'''




import math






class     UpperCamelCase_     :







						"""simple docstring"""


						def __init__(     self      :       Any							, _lowerCamelCase      :       str							, _lowerCamelCase      :       Dict							, _lowerCamelCase      :       int							, _lowerCamelCase      :       List[str]    ):





											"""simple docstring"""







											A_ :     Union[str, Any] =							x
											A_ :     List[str] =							y
											A_ :     Union[str, Any] =							step_size
											A_ :     Tuple =							function_to_optimize







						def       _a    (     self      :       List[str]    ):





											"""simple docstring"""







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







						def       _a    (     self      :       List[str]    ):





											"""simple docstring"""







											A_ :     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      :       Any    ):





											"""simple docstring"""







											return hash(str(self    )    )







						def __eq__(     self      :       Tuple							, _lowerCamelCase      :       List[str]    ):





											"""simple docstring"""







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







						def __str__(     self      :       Optional[int]    ):





											"""simple docstring"""







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






def 						snake_case__    ( lowerCamelCase__				:   Union[str, Any]			,		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_0_0_0_0			,		)   ->   Union[str, Any]:
					A_ :     Optional[Any] =							search_prob
					A_ :     List[Any] =							[]  # list to store the current score at each iteration
					A_ :     Any =							0
					A_ :     int =							False
					A_ :     Tuple =							set()
					while not solution_found and iterations < max_iter:
										visited.add(_SCREAMING_SNAKE_CASE			)
										iterations += 1
										A_ :     Optional[Any] =							current_state.score()
										scores.append(_SCREAMING_SNAKE_CASE			)
										A_ :     List[Any] =							current_state.get_neighbors()
										A_ :     Optional[Any] =							-math.inf
										A_ :     str =							math.inf
										A_ :     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
															A_ :     List[Any] =							neighbor.score() - current_score
															if find_max:  # finding max
																				# going to direction with greatest ascent
																				if change > max_change and change > 0:
																									A_ :     Dict =							change
																									A_ :     str =							neighbor
															else:  # finding min
																				# to direction with greatest descent
																				if change < min_change and change < 0:
																									A_ :     List[str] =							change
																									A_ :     Tuple =							neighbor
										if next_state is not None:
															# we found at least one neighbor which improved the current state
															A_ :     Tuple =							next_state
										else:
															# since we have no neighbor that improves the solution we stop the search
															A_ :     int =							True

					if visualization:
										from matplotlib import pyplot as plt

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

					return current_state


if __name__ == "__main__":
							import doctest

							doctest.testmod()




							def 						snake_case__    ( lowerCamelCase__				:   Union[str, Any]			,		lowerCamelCase__				:   Union[str, Any]			)   ->   Any:
												return (x**2) + (y**2)

							# starting the problem with initial coordinates (3, 4)
							snake_case__          =						SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
							snake_case__          =						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)
							snake_case__          =						SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
							snake_case__          =						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 						snake_case__    ( lowerCamelCase__				:   Any			,		lowerCamelCase__				:   Optional[Any]			)   ->   Union[str, Any]:
												return (3 * x**2) - (6 * y)

							snake_case__          =						SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
							snake_case__          =						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 						snake_case__    ( lowerCamelCase__				:   float			)   ->   float:
					return -num if num < 0 else num




def 						snake_case__    ( lowerCamelCase__				:   list[int]			)   ->   int:
					if len(lowerCamelCase__			) == 0:
										raise ValueError('''abs_min() arg is an empty sequence'''			)
					A_ :     Any =							x[0]
					for i in x:
										if abs_val(lowerCamelCase__			) < abs_val(lowerCamelCase__			):
															A_ :     Tuple =							i
					return j




def 						snake_case__    ( lowerCamelCase__				:   list[int]			)   ->   int:
					if len(lowerCamelCase__			) == 0:
										raise ValueError('''abs_max() arg is an empty sequence'''			)
					A_ :     List[str] =							x[0]
					for i in x:
										if abs(lowerCamelCase__			) > abs(lowerCamelCase__			):
															A_ :     Any =							i
					return j




def 						snake_case__    ( lowerCamelCase__				:   list[int]			)   ->   int:
					if len(lowerCamelCase__			) == 0:
										raise ValueError('''abs_max_sort() arg is an empty sequence'''			)
					return sorted(lowerCamelCase__			,		key=lowerCamelCase__			)[-1]




def 						snake_case__    ( )   ->   Optional[Any]:
					assert abs_val(0			) == 0
					assert abs_val(3_4			) == 3_4
					assert abs_val(-1_0_0_0_0_0_0_0_0_0_0_0			) == 1_0_0_0_0_0_0_0_0_0_0_0

					A_ :     Dict =							[-3, -1, 2, -1_1]
					assert abs_max(lowerCamelCase__			) == -1_1
					assert abs_max_sort(lowerCamelCase__			) == -1_1
					assert abs_min(lowerCamelCase__			) == -1


if __name__ == "__main__":
							import doctest

							doctest.testmod()

							test_abs_val()
							print(abs_val(-34))  # --> 34



