



import math
import random
from typing import Any

from .hill_climbing import SearchProblem



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_  ,					SCREAMING_SNAKE_CASE_ = True  ,					SCREAMING_SNAKE_CASE_ = math.inf  ,					SCREAMING_SNAKE_CASE_ = -math.inf  ,					SCREAMING_SNAKE_CASE_ = math.inf  ,					SCREAMING_SNAKE_CASE_ = -math.inf  ,					SCREAMING_SNAKE_CASE_ = False  ,					SCREAMING_SNAKE_CASE_ = 100  ,					SCREAMING_SNAKE_CASE_ = 0.01  ,					SCREAMING_SNAKE_CASE_ = 1  ,					) ->    List[Any]:
			lowercase__   					=			False
			lowercase__   					=			search_prob
			lowercase__   					=			start_temperate
			lowercase__   					=			[]
			lowercase__   					=			0
			lowercase__   					=			None

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

			if visualization:
						from matplotlib import pyplot as plt

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


if __name__ == "__main__":



							def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_  ,					SCREAMING_SNAKE_CASE_					) ->    Optional[int]:
										return (x**2) + (y**2)

							# starting the problem with initial coordinates (12, 47)
							lowercase_						=       SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
							lowercase_						=       simulated_annealing(
							    prob, find_max=False, max_x=100, 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)
							lowercase_						=       SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
							lowercase_						=       simulated_annealing(
							    prob, find_max=True, max_x=100, 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	(       SCREAMING_SNAKE_CASE_  ,					SCREAMING_SNAKE_CASE_					) ->    Any:
										return (3 * x**2) - (6 * y)

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

							lowercase_						=       SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
							lowercase_						=       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 __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_  ,					SCREAMING_SNAKE_CASE_					):
			lowercase__   					=			1  # To kept the Calculated Value
			# Since C(n, k) = C(n, n-k)
			if k > (n - k):
						lowercase__   					=			n - k
			# Calculate C(n,k)
			for i in range(SCREAMING_SNAKE_CASE_					):
						result *= n - i
						result //= i + 1
			return result



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_					):
			return binomial_coefficient(2 * node_count  ,					SCREAMING_SNAKE_CASE_					) // (node_count + 1)



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_					):
			if n < 0:
						raise ValueError("factorial() not defined for negative values"					)
			lowercase__   					=			1
			for i in range(1  ,					n + 1					):
						result *= i
			return result



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_					):
			return catalan_number(SCREAMING_SNAKE_CASE_					) * factorial(SCREAMING_SNAKE_CASE_					)


if __name__ == "__main__":
							lowercase_						=       int(input("""Enter the number of nodes: """).strip() or 0)
							if node_count <= 0:
														raise ValueError("""We need some nodes to work with.""")
							print(
							    F'Given {node_count} nodes, there are {binary_tree_count(node_count)} '
							    F'binary trees and {catalan_number(node_count)} binary search trees.'
							)




