




import math
import random
from typing import Any

from .hill_climbing import SearchProblem







def 			lowerCamelCase_		(       UpperCamelCase__				:      Tuple ,     UpperCamelCase__				:      bool = True ,     UpperCamelCase__				:      float = math.inf ,     UpperCamelCase__				:      float = -math.inf ,     UpperCamelCase__				:      float = math.inf ,     UpperCamelCase__				:      float = -math.inf ,     UpperCamelCase__				:      bool = False ,     UpperCamelCase__				:      float = 100 ,     UpperCamelCase__				:      float = 0.01 ,     UpperCamelCase__				:      float = 1 ,     )     ->       Any:





				"""simple docstring"""


				__lowerCamelCase		       =    False
				__lowerCamelCase		       =    search_prob
				__lowerCamelCase		       =    start_temperate
				__lowerCamelCase		       =    []
				__lowerCamelCase		       =    0
				__lowerCamelCase		       =    None

				while not search_end:
								__lowerCamelCase		       =    current_state.score()
								if best_state is None or current_score > best_state.score():
												__lowerCamelCase		       =    current_state
								scores.append(UpperCamelCase__      )
								iterations += 1
								__lowerCamelCase		       =    None
								__lowerCamelCase		       =    current_state.get_neighbors()
								while (
								    next_state is None and neighbors
								):  # till we do not find a neighbor that we can move to
												__lowerCamelCase		       =    random.randint(0 ,     len(UpperCamelCase__      ) - 1      )  # picking a random neighbor
												__lowerCamelCase		       =    neighbors.pop(UpperCamelCase__      )
												__lowerCamelCase		       =    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:
																__lowerCamelCase		       =    change * -1  # in case we are finding minimum
												if change > 0:  # improves the solution
																__lowerCamelCase		       =    picked_neighbor
												else:
																__lowerCamelCase		       =    (math.e) ** (
																    change / current_temp
																)  # probability generation function
																if random.random() < probability:  # random number within probability
																				__lowerCamelCase		       =    picked_neighbor
								__lowerCamelCase		       =    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
												__lowerCamelCase		       =    True
								else:
												__lowerCamelCase		       =    next_state

				if visualization:
								from matplotlib import pyplot as plt

								plt.plot(range(UpperCamelCase__      ) ,     UpperCamelCase__      )
								plt.xlabel('Iterations'      )
								plt.ylabel('Function values'      )
								plt.show()
				return best_state


if __name__ == "__main__":







					def 			lowerCamelCase_		(       UpperCamelCase__				:      Optional[Any] ,     UpperCamelCase__				:      Tuple      )     ->       Tuple:





									"""simple docstring"""


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

					# starting the problem with initial coordinates (12, 47)
					__A        =    SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
					__A        =    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)
					__A        =    SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
					__A        =    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 			lowerCamelCase_		(       UpperCamelCase__				:      List[str] ,     UpperCamelCase__				:      Tuple      )     ->       List[Any]:





									"""simple docstring"""


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

					__A        =    SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
					__A        =    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()}'''
					)

					__A        =    SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
					__A        =    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()}'''
					)








class     __lowerCAmelCase :

			"""simple docstring"""







			def __init__(      self							)    ->      Any:



							'''simple docstring'''
							__lowerCamelCase		       =    0
							__lowerCamelCase		       =    0
							__lowerCamelCase		       =    {}


			def       lowercase_    (      self			,						lowerCamelCase__							)    ->      Tuple:



							'''simple docstring'''
							if vertex not in self.adjacency:
											__lowerCamelCase		       =    {}
											self.num_vertices += 1


			def       lowercase_    (      self			,						lowerCamelCase__			,						lowerCamelCase__			,						lowerCamelCase__							)    ->      str:



							'''simple docstring'''
							self.add_vertex(lowerCamelCase__							)
							self.add_vertex(lowerCamelCase__							)

							if head == tail:
											return

							__lowerCamelCase		       =    weight
							__lowerCamelCase		       =    weight


			def       lowercase_    (      self							)    ->      List[str]:



							'''simple docstring'''
							__lowerCamelCase		       =    self.get_edges()
							for edge in edges:
											__lowerCamelCase       ,						__lowerCamelCase       ,						__lowerCamelCase		       =    edge
											edges.remove((tail, head, weight)							)
							for i in range(len(lowerCamelCase__							)							):
											__lowerCamelCase		       =    list(edges[i]							)

							edges.sort(key=lambda lowerCamelCase__							: e[2]							)
							for i in range(len(lowerCamelCase__							) - 1							):
											if edges[i][2] >= edges[i + 1][2]:
															__lowerCamelCase		       =    edges[i][2] + 1
							for edge in edges:
											__lowerCamelCase       ,						__lowerCamelCase       ,						__lowerCamelCase		       =    edge
											__lowerCamelCase		       =    weight
											__lowerCamelCase		       =    weight


			def __str__(      self							)    ->      Union[str, Any]:



							'''simple docstring'''
							__lowerCamelCase		       =    ''
							for tail in self.adjacency:
											for head in self.adjacency[tail]:
															__lowerCamelCase		       =    self.adjacency[head][tail]
															string += f"""{head} -> {tail} == {weight}\n"""
							return string.rstrip('\n'							)


			def       lowercase_    (      self							)    ->      Optional[Any]:



							'''simple docstring'''
							__lowerCamelCase		       =    []
							for tail in self.adjacency:
											for head in self.adjacency[tail]:
															output.append((tail, head, self.adjacency[head][tail])							)
							return output


			def       lowercase_    (      self							)    ->      List[Any]:



							'''simple docstring'''
							return self.adjacency.keys()


			@staticmethod
			def       lowercase_    (      lowerCamelCase__=None			,						lowerCamelCase__=None							)    ->      str:



							'''simple docstring'''
							__lowerCamelCase		       =    Graph()
							if vertices is None:
											__lowerCamelCase		       =    []
							if edges is None:
											__lowerCamelCase		       =    []
							for vertex in vertices:
											g.add_vertex(lowerCamelCase__							)
							for edge in edges:
											g.add_edge(*lowerCamelCase__							)
							return g







			class     __lowerCAmelCase :

						"""simple docstring"""







						def __init__(      self							)    ->      Tuple:



										'''simple docstring'''
										__lowerCamelCase		       =    {}
										__lowerCamelCase		       =    {}


						def __len__(      self							)    ->      Tuple:



										'''simple docstring'''
										return len(self.parent							)


						def       lowercase_    (      self			,						lowerCamelCase__							)    ->      List[Any]:



										'''simple docstring'''
										if item in self.parent:
														return self.find(lowerCamelCase__							)

										__lowerCamelCase		       =    item
										__lowerCamelCase		       =    0
										return item


						def       lowercase_    (      self			,						lowerCamelCase__							)    ->      List[str]:



										'''simple docstring'''
										if item not in self.parent:
														return self.make_set(lowerCamelCase__							)
										if item != self.parent[item]:
														__lowerCamelCase		       =    self.find(self.parent[item]							)
										return self.parent[item]






						def       lowercase_    (      self			,						lowerCamelCase__			,						lowerCamelCase__							)    ->      int:



										'''simple docstring'''
										__lowerCamelCase		       =    self.find(lowerCamelCase__							)
										__lowerCamelCase		       =    self.find(lowerCamelCase__							)

										if roota == roota:
														return roota

										if self.rank[roota] > self.rank[roota]:
														__lowerCamelCase		       =    roota
														return roota

										if self.rank[roota] < self.rank[roota]:
														__lowerCamelCase		       =    roota
														return roota

										if self.rank[roota] == self.rank[roota]:
														self.rank[roota] += 1
														__lowerCamelCase		       =    roota
														return roota
										return None




			@staticmethod
			def       lowercase_    (      lowerCamelCase__							)    ->      str:



							'''simple docstring'''
							__lowerCamelCase		       =    graph.num_vertices

							__lowerCamelCase		       =    Graph.UnionFind()
							__lowerCamelCase		       =    []
							while num_components > 1:
											__lowerCamelCase		       =    {}
											for vertex in graph.get_vertices():
															__lowerCamelCase		       =    -1

											__lowerCamelCase		       =    graph.get_edges()
											for edge in edges:
															__lowerCamelCase       ,						__lowerCamelCase       ,						__lowerCamelCase		       =    edge
															edges.remove((tail, head, weight)							)
											for edge in edges:
															__lowerCamelCase       ,						__lowerCamelCase       ,						__lowerCamelCase		       =    edge
															__lowerCamelCase		       =    union_find.find(lowerCamelCase__							)
															__lowerCamelCase		       =    union_find.find(lowerCamelCase__							)
															if seta != seta:
																			if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
																							__lowerCamelCase		       =    [head, tail, weight]

																			if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
																							__lowerCamelCase		       =    [head, tail, weight]
											for vertex in cheap_edge:
															if cheap_edge[vertex] != -1:
																			__lowerCamelCase       ,						__lowerCamelCase       ,						__lowerCamelCase		       =    cheap_edge[vertex]
																			if union_find.find(lowerCamelCase__							) != union_find.find(lowerCamelCase__							):
																							union_find.union(lowerCamelCase__			,						lowerCamelCase__							)
																							mst_edges.append(cheap_edge[vertex]							)
																							__lowerCamelCase		       =    num_components - 1
							__lowerCamelCase		       =    Graph.build(edges=lowerCamelCase__							)
							return mst


