


'''simple docstring'''
import math






class 		UpperCamelCase_		:





						"""simple docstring"""




						def __init__( self				:					Dict	,				_lowerCamelCase				:					Tuple	,				_lowerCamelCase				:					List[str]	,				_lowerCamelCase				:					Tuple	,				_lowerCamelCase				:					Union[str, Any]  )							->					List[Any]:
										__magic_name__	  = x
										__magic_name__	  = y
										__magic_name__	  = step_size
										__magic_name__	  = function_to_optimize
						def 					__A					( self				:					str  )							->					str:
										return self.function(self.x	,				self.y  )
						def 					__A					( self				:					List[str]  )							->					str:
										__magic_name__	  = self.step_size
										return [
										    SearchProblem(__snake_case	,				__snake_case	,				__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				:					int  )							->					Any:
										return hash(str(self  )  )
						def __eq__( self				:					Tuple	,				_lowerCamelCase				:					Union[str, Any]  )							->					Dict:
										if isinstance(__snake_case	,				__snake_case  ):
														return hash(str(self  )  ) == hash(str(__snake_case  )  )
										return False

						def __str__( self				:					Optional[Any]  )							->					List[Any]:
										return f'x: {self.x} y: {self.y}'





def      __snake_case       (       lowerCamelCase_ :				str	,  lowerCamelCase_ :				Any = True	,  lowerCamelCase_ :				Any = math.inf	,  lowerCamelCase_ :				int = -math.inf	,  lowerCamelCase_ :				List[Any] = math.inf	,  lowerCamelCase_ :				Optional[int] = -math.inf	,  lowerCamelCase_ :				List[str] = False	,  lowerCamelCase_ :				Optional[int] = 1_0000	,  ):
				'''simple docstring'''




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




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

						# starting the problem with initial coordinates (3, 4)
						__magic_name__   :   Dict  							=SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
						__magic_name__   :   Union[str, 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)
						__magic_name__   :   List[str]  							=SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
						__magic_name__   :   Tuple  							=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_ :				Optional[Any]	,  lowerCamelCase_ :				Tuple						):
										'''simple docstring'''




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

						__magic_name__   :   Dict  							=SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
						__magic_name__   :   List[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'''
from __future__ import annotations




def      __snake_case       (       lowerCamelCase_ :				list[list[int]]	,  lowerCamelCase_ :				list[list[int]]						):
				'''simple docstring'''




				assert len(lowerCamelCase_						) == len(lowerCamelCase_						)

				__magic_name__	  = len(lowerCamelCase_						)
				__magic_name__	  = list(range(lowerCamelCase_						)						)
				__magic_name__	  = [-1] * n  # who the donor has donated to
				__magic_name__	  = [-1] * n  # who the recipient has received from
				__magic_name__	  = [0] * n

				while unmatched_donors:
								__magic_name__	  = unmatched_donors[0]
								__magic_name__	  = donor_pref[donor]
								__magic_name__	  = donor_preference[num_donations[donor]]
								num_donations[donor] += 1
								__magic_name__	  = recipient_pref[recipient]
								__magic_name__	  = rec_record[recipient]

								if prev_donor != -1:
												if rec_preference.index(lowerCamelCase_						) > rec_preference.index(lowerCamelCase_						):
																__magic_name__	  = donor
																__magic_name__	  = recipient
																unmatched_donors.append(lowerCamelCase_						)
																unmatched_donors.remove(lowerCamelCase_						)
								else:
												__magic_name__	  = donor
												__magic_name__	  = recipient
												unmatched_donors.remove(lowerCamelCase_						)
				return donor_record



