
import math
import random
from typing import Any

from .hill_climbing import SearchProblem







def     A__   (  lowerCamelCase       ,      lowerCamelCase = True       ,      lowerCamelCase = math.inf       ,      lowerCamelCase = -math.inf       ,      lowerCamelCase = math.inf       ,      lowerCamelCase = -math.inf       ,      lowerCamelCase = False       ,      lowerCamelCase = 1_00       ,      lowerCamelCase = 0.01       ,      lowerCamelCase = 1       ,      )					->		Any:
				UpperCamelCase_:							List[str]		=  False
				UpperCamelCase_:							Any		=  search_prob
				UpperCamelCase_:							Union[str, Any]		=  start_temperate
				UpperCamelCase_:							Dict		=  []
				UpperCamelCase_:							Union[str, Any]		=  0
				UpperCamelCase_:							Any		=  None

				while not search_end:
								UpperCamelCase_:							str		=  current_state.score()
								if best_state is None or current_score > best_state.score():
												UpperCamelCase_:							Any		=  current_state
								scores.append(a__  )
								iterations += 1
								UpperCamelCase_:							int		=  None
								UpperCamelCase_:							Optional[Any]		=  current_state.get_neighbors()
								while (
								    next_state is None and neighbors
								):  # till we do not find a neighbor that we can move to
												UpperCamelCase_:							Union[str, Any]		=  random.randint(0       ,      len(a__  ) - 1  )  # picking a random neighbor
												UpperCamelCase_:							Tuple		=  neighbors.pop(a__  )
												UpperCamelCase_:							List[Any]		=  picked_neighbor.score() - current_score

												if (
												    picked_neighbor.x > max_x
												    or picked_neighbor.x < min_x
												    or picked_neighbor.y > max_y
												    or picked_neighbor.y < min_y
												):
																continue  # neighbor outside our bounds

												if not find_max:
																UpperCamelCase_:							List[Any]		=  change * -1  # in case we are finding minimum
												if change > 0:  # improves the solution
																UpperCamelCase_:							int		=  picked_neighbor
												else:
																UpperCamelCase_:							List[str]		=  (math.e) ** (
																    change / current_temp
																)  # probability generation function
																if random.random() < probability:  # random number within probability
																				UpperCamelCase_:							List[Any]		=  picked_neighbor
								UpperCamelCase_:							List[Any]		=  current_temp - (current_temp * rate_of_decrease)

								if current_temp < threshold_temp or next_state is None:
												# temperature below threshold, or could not find a suitable neighbor
												UpperCamelCase_:							Optional[int]		=  True
								else:
												UpperCamelCase_:							Optional[Any]		=  next_state

				if visualization:
								from matplotlib import pyplot as plt

								plt.plot(range(a__  )       ,      a__  )
								plt.xlabel("""Iterations"""  )
								plt.ylabel("""Function values"""  )
								plt.show()
				return best_state


if __name__ == "__main__":







							def     A__   (  lowerCamelCase       ,      lowerCamelCase  )					->		Dict:
											return (x**2) + (y**2)

							# starting the problem with initial coordinates (12, 47)
							lowerCamelCase_  :	Tuple 				=					SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
							lowerCamelCase_  :	List[str] 				=					simulated_annealing(
							    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()}"""
							)

							# starting the problem with initial coordinates (12, 47)
							lowerCamelCase_  :	str 				=					SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
							lowerCamelCase_  :	List[str] 				=					simulated_annealing(
							    prob, find_max=True, max_x=1_00, min_x=5, max_y=50, min_y=-5, visualization=True
							)
							print(
							    """The maximum 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       ,      lowerCamelCase  )					->		Union[str, Any]:
											return (3 * x**2) - (6 * y)

							lowerCamelCase_  :	str 				=					SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
							lowerCamelCase_  :	List[str] 				=					simulated_annealing(prob, find_max=False, visualization=True)
							print(
							    """The minimum score for f(x, y) = 3*x^2 - 6*y found via hill climbing: """
							    F"""{local_min.score()}"""
							)

							lowerCamelCase_  :	Tuple 				=					SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
							lowerCamelCase_  :	List[str] 				=					simulated_annealing(prob, find_max=True, visualization=True)





							print(
							    """The maximum score for f(x, y) = 3*x^2 - 6*y found via hill climbing: """
							    F"""{local_min.score()}"""
							)








def     A__   (  lowerCamelCase       ,      lowerCamelCase  )					->		list:
				UpperCamelCase_:							Optional[int]		=  word.split()

				def justify(lowerCamelCase       ,      lowerCamelCase       ,      lowerCamelCase  ) -> str:
								UpperCamelCase_:							Tuple		=  max_width - width
								UpperCamelCase_:							Optional[Any]		=  len(lowerCamelCase  )
								if len(lowerCamelCase  ) == 1:
												# if there is only word in line
												# just insert overall_spaces_count for the remainder of line
												return line[0] + " " * overall_spaces_count
								else:
												UpperCamelCase_:							List[Any]		=  words_count - 1
												# num_spaces_between_words_list[i] : tells you to insert
												# num_spaces_between_words_list[i] spaces
												# after word on line[i]
												UpperCamelCase_:							Optional[Any]		=  spaces_to_insert_between_words * [
												    overall_spaces_count // spaces_to_insert_between_words
												]
												UpperCamelCase_:							List[str]		=  (
												    overall_spaces_count % spaces_to_insert_between_words
												)
												# distribute spaces via round robin to the left words
												for i in range(lowerCamelCase  ):
																num_spaces_between_words_list[i] += 1
												UpperCamelCase_:							Dict		=  []
												for i in range(lowerCamelCase  ):
																# add the word
																aligned_words_list.append(line[i]  )
																# add the spaces to insert
																aligned_words_list.append(num_spaces_between_words_list[i] * """ """  )
												# just add the last word to the sentence
												aligned_words_list.append(line[-1]  )
												# join the aligned words list to form a justified line
												return "".join(lowerCamelCase  )

				UpperCamelCase_:							Optional[int]		=  []
				UpperCamelCase_:							list[str]		=  []
				UpperCamelCase_:							List[str]		=  0
				for word in words:
								if width + len(lowerCamelCase  ) + len(lowerCamelCase  ) <= max_width:
												# keep adding words until we can fill out max_width
												# width = sum of length of all words (without overall_spaces_count)
												# len(word) = length of current word
												# len(line) = number of overall_spaces_count to insert between words
												line.append(lowerCamelCase  )
												width += len(lowerCamelCase  )
								else:
												# justify the line and add it to result
												answer.append(justify(lowerCamelCase       ,      lowerCamelCase       ,      lowerCamelCase  )  )
												# reset new line and new width
												UpperCamelCase_,				UpperCamelCase_:							List[str]		=  [word], len(lowerCamelCase  )
				UpperCamelCase_:							List[str]		=  max_width - width - len(lowerCamelCase  )
				answer.append(""" """.join(lowerCamelCase  ) + (remaining_spaces + 1) * """ """  )
				return answer


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

							testmod()






