

import math
import random
from typing import Any

from .hill_climbing import SearchProblem

def 							__SCREAMING_SNAKE_CASE							(			lowerCAmelCase:					Optional[Any]					, lowerCAmelCase:					bool = True					, lowerCAmelCase:					float = math.inf					, lowerCAmelCase:					float = -math.inf					, lowerCAmelCase:					float = math.inf					, lowerCAmelCase:					float = -math.inf					, lowerCAmelCase:					bool = False					, lowerCAmelCase:					float = 100					, lowerCAmelCase:					float = 0.01					, lowerCAmelCase:					float = 1					, )				->    Any:
				_UpperCAmelCase    :						str							=      False
				_UpperCAmelCase    :						Optional[int]							=      search_prob
				_UpperCAmelCase    :						Dict							=      start_temperate
				_UpperCAmelCase    :						Dict							=      []
				_UpperCAmelCase    :						List[Any]							=      0
				_UpperCAmelCase    :						int							=      None

				while not search_end:
								_UpperCAmelCase    :						str							=      current_state.score()
								if best_state is None or current_score > best_state.score():
												_UpperCAmelCase    :						Tuple							=      current_state
								scores.append(lowerCAmelCase	)
								iterations += 1
								_UpperCAmelCase    :						Union[str, Any]							=      None
								_UpperCAmelCase    :						Optional[int]							=      current_state.get_neighbors()
								while (
								    next_state is None and neighbors
								):  # till we do not find a neighbor that we can move to
												_UpperCAmelCase    :						int							=      random.randint(0					, len(lowerCAmelCase	) - 1	)  # picking a random neighbor
												_UpperCAmelCase    :						List[Any]							=      neighbors.pop(lowerCAmelCase	)
												_UpperCAmelCase    :						str							=      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    :						List[str]							=      picked_neighbor
												else:
																_UpperCAmelCase    :						Union[str, Any]							=      (math.e) ** (
																    change / current_temp
																)  # probability generation function
																if random.random() < probability:  # random number within probability
																				_UpperCAmelCase    :						Optional[Any]							=      picked_neighbor
								_UpperCAmelCase    :						int							=      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    :						List[str]							=      True
								else:
												_UpperCAmelCase    :						Union[str, Any]							=      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 							__SCREAMING_SNAKE_CASE							(			lowerCAmelCase:					Optional[Any]					, lowerCAmelCase:					Any	)				->    str:
									return (x**2) + (y**2)

					# starting the problem with initial coordinates (12, 47)
					SCREAMING_SNAKE_CASE_            = SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
					SCREAMING_SNAKE_CASE_            = 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)
					SCREAMING_SNAKE_CASE_            = SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
					SCREAMING_SNAKE_CASE_            = 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 							__SCREAMING_SNAKE_CASE							(			lowerCAmelCase:					Dict					, lowerCAmelCase:					Dict	)				->    Optional[int]:
									return (3 * x**2) - (6 * y)

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

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







from __future__ import annotations

from decimal import Decimal
from math import *  # noqa: F403

from sympy import diff

def 							__SCREAMING_SNAKE_CASE							(			lowerCAmelCase:					str					, lowerCAmelCase:					float | Decimal					, lowerCAmelCase:					float = 10**-10	)				->    float:
				_UpperCAmelCase    :						Optional[int]							=      a
				while True:
								_UpperCAmelCase    :						Tuple							=      Decimal(lowerCAmelCase	) - (
								    Decimal(eval(lowerCAmelCase	)	) / Decimal(eval(str(diff(lowerCAmelCase	)	)	)	)  # noqa: S307
								)
								# This number dictates the accuracy of the answer
								if abs(eval(lowerCAmelCase	)	) < precision:  # noqa: S307
												return float(lowerCAmelCase	)


# Let's Execute
if __name__ == "__main__":
					# Find root of trigonometric function
					# Find value of pi
					print(F'''The root of sin(x) = 0 is {newton_raphson("sin(x)", 2)}''')
					# Find root of polynomial
					print(F'''The root of x**2 - 5*x + 2 = 0 is {newton_raphson("x**2 - 5*x + 2", 0.4)}''')
					# Find Square Root of 5
					print(F'''The root of log(x) - 1 = 0 is {newton_raphson("log(x) - 1", 2)}''')
					# Exponential Roots
					print(F'''The root of exp(x) - 1 = 0 is {newton_raphson("exp(x) - 1", 0)}''')


