



"""simple docstring"""
import math


class 							lowerCamelCase_:





					'''simple docstring'''



					def __init__(			self ,				lowerCamelCase__ ,				lowerCamelCase__ ,				lowerCamelCase__ ,				lowerCamelCase__      ):
									_lowerCamelCase					     = x
									_lowerCamelCase					     = y
									_lowerCamelCase					     = step_size
									_lowerCamelCase					     = function_to_optimize

					def 	snake_case__					(			self      ):
									return self.function(self.x ,				self.y      )

					def 	snake_case__					(			self      ):
									_lowerCamelCase					     = self.step_size
									return [
									    SearchProblem(lowerCamelCase__ ,				lowerCamelCase__ ,				lowerCamelCase__ ,				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      ):
									return hash(str(self      )      )

					def __eq__(			self ,				lowerCamelCase__      ):
									if isinstance(lowerCamelCase__ ,				lowerCamelCase__      ):
													return hash(str(self      )      ) == hash(str(lowerCamelCase__      )      )
									return False





					def __str__(			self      ):
									return F"""x: {self.x} y: {self.y}"""



def 				lowerCAmelCase_(      lowercase_   :							Any  ,      lowercase_   :							bool = True  ,      lowercase_   :							float = math.inf  ,      lowercase_   :							float = -math.inf  ,      lowercase_   :							float = math.inf  ,      lowercase_   :							float = -math.inf  ,      lowercase_   :							bool = False  ,      lowercase_   :							int = 1_00_00  ,      )		->				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 				lowerCAmelCase_(      lowercase_   :							Union[str, Any]  ,      lowercase_   :							List[Any]							)		->				List[Any]:
							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     :  List[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     :  Optional[int]										=					SearchProblem(x=1_2, y=4_7, step_size=1, function_to_optimize=test_fa)
			__SCREAMING_SNAKE_CASE     :  Union[str, Any]										=					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 				lowerCAmelCase_(      lowercase_   :							Optional[int]  ,      lowercase_   :							Dict							)		->				List[Any]:
							return (3 * x**2) - (6 * y)

			__SCREAMING_SNAKE_CASE     :  List[str]										=					SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
			__SCREAMING_SNAKE_CASE     :  Dict										=					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"""
from .stack import Stack



def 				lowerCAmelCase_(      lowercase_   :							str							)		->				bool:
				_lowerCamelCase					     = Stack()
				_lowerCamelCase					     = {'''(''': ''')''', '''[''': ''']''', '''{''': '''}'''}
				for bracket in parentheses:
								if bracket in bracket_pairs:
												stack.push(lowercase_							)
								elif bracket in (")", "]", "}"):
												if stack.is_empty() or bracket_pairs[stack.pop()] != bracket:
																return False
				return stack.is_empty()


if __name__ == "__main__":
			from doctest import testmod

			testmod()

			__SCREAMING_SNAKE_CASE     :  Optional[Any]										=					['''((()))''', '''((())''', '''(()))''']
			print('''Balanced parentheses demonstration:\n''')
			for example in examples:
						__SCREAMING_SNAKE_CASE     :  Any										=					'''''' if balanced_parentheses(example) else '''not '''
						print(F"""{example} is {not_str}balanced""")
