





import math
import random
from typing import Any

from .hill_climbing import SearchProblem






def      lowerCamelCase_						(				_UpperCamelCase ,				_UpperCamelCase = True ,				_UpperCamelCase = math.inf ,				_UpperCamelCase = -math.inf ,				_UpperCamelCase = math.inf ,				_UpperCamelCase = -math.inf ,				_UpperCamelCase = False ,				_UpperCamelCase = 100 ,				_UpperCamelCase = 0.01 ,				_UpperCamelCase = 1 ,				)		->						Any:






				"""simple docstring"""


				snake_case_						:    Any				=  False
				snake_case_						:    Tuple				=  search_prob
				snake_case_						:    Any				=  start_temperate
				snake_case_						:    Dict				=  []
				snake_case_						:    Union[str, Any]				=  0
				snake_case_						:    List[Any]				=  None

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






					"""simple docstring"""


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

	# starting the problem with initial coordinates (12, 47)
	lowerCAmelCase_    =				SearchProblem(x=1_2, y=4_7, step_size=1, function_to_optimize=test_fa)
	lowerCAmelCase_    =				simulated_annealing(
	    prob, find_max=False, max_x=1_0_0, min_x=5, max_y=5_0, 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_    =				SearchProblem(x=1_2, y=4_7, step_size=1, function_to_optimize=test_fa)
	lowerCAmelCase_    =				simulated_annealing(
	    prob, find_max=True, max_x=1_0_0, min_x=5, max_y=5_0, 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 ,				_UpperCamelCase )		->						List[str]:






					"""simple docstring"""


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

	lowerCAmelCase_    =				SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
	lowerCAmelCase_    =				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_    =				SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
	lowerCAmelCase_    =				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 math import factorial

lowerCAmelCase_    =				{str(digit): factorial(digit) for digit in range(1_0)}






def      lowerCamelCase_						(				_UpperCamelCase )		->						int:






				"""simple docstring"""


				if not isinstance(_UpperCamelCase ,				_UpperCamelCase ):
								raise TypeError('''Parameter number must be int''' )

				if number < 0:
								raise ValueError('''Parameter number must be greater than or equal to 0''' )

				# Converts number in string to iterate on its digits and adds its factorial.
				return sum(DIGIT_FACTORIAL[digit] for digit in str(_UpperCamelCase ) )






def      lowerCamelCase_						(				_UpperCamelCase = 60 ,				_UpperCamelCase = 1_000_000 )		->						int:






				"""simple docstring"""


				if not isinstance(_UpperCamelCase ,				_UpperCamelCase ) or not isinstance(_UpperCamelCase ,				_UpperCamelCase ):
								raise TypeError('''Parameters chain_length and number_limit must be int''' )

				if chain_length <= 0 or number_limit <= 0:
								raise ValueError(
								    '''Parameters chain_length and number_limit must be greater than 0''' )

				# the counter for the chains with the exact desired length
				snake_case_						:    Optional[Any]				=  0
				# the cached sizes of the previous chains
				snake_case_						:    dict[int, int]				=  {}

				for start_chain_element in range(1 ,				_UpperCamelCase ):
								# The temporary set will contain the elements of the chain
								snake_case_						:    List[str]				=  set()
								snake_case_						:    List[Any]				=  0

								# Stop computing the chain when you find a cached size, a repeating item or the
								# length is greater then the desired one.
								snake_case_						:    Any				=  start_chain_element
								while (
								    chain_element not in chain_sets_lengths
								    and chain_element not in chain_set
								    and chain_set_length <= chain_length
								):
												chain_set.add(_UpperCamelCase )
												chain_set_length += 1
												snake_case_						:    List[Any]				=  digit_factorial_sum(_UpperCamelCase )

								if chain_element in chain_sets_lengths:
												chain_set_length += chain_sets_lengths[chain_element]

								snake_case_						:    List[str]				=  chain_set_length

								# If chain contains the exact amount of elements increase the counter
								if chain_set_length == chain_length:
												chains_counter += 1

				return chains_counter


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	print(F'''{solution()}''')
