






import math
import random
from typing import Any

from .hill_climbing import SearchProblem

def   __lowercase       (			snake_case,	snake_case = True,	snake_case = math.inf,	snake_case = -math.inf,	snake_case = math.inf,	snake_case = -math.inf,	snake_case = False,	snake_case = 1_0_0,	snake_case = 0.01,	snake_case = 1,	):







				"""simple docstring"""






				__magic_name__		:Optional[int]   =   False
				__magic_name__		:Optional[Any]   =   search_prob
				__magic_name__		:Dict   =   start_temperate
				__magic_name__		:Tuple   =   []
				__magic_name__		:List[str]   =   0
				__magic_name__		:Any   =   None

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

				if visualization:
								from matplotlib import pyplot as plt

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


if __name__ == "__main__":

					def   __lowercase       (			snake_case,	snake_case			):







									"""simple docstring"""






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

					# starting the problem with initial coordinates (12, 47)
					SCREAMING_SNAKE_CASE__   :      Union[str, Any]				=		SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
					SCREAMING_SNAKE_CASE__   :      Optional[Any]				=		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)
					SCREAMING_SNAKE_CASE__   :      Tuple				=		SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
					SCREAMING_SNAKE_CASE__   :      List[Any]				=		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   __lowercase       (			snake_case,	snake_case			):







									"""simple docstring"""






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

					SCREAMING_SNAKE_CASE__   :      Optional[Any]				=		SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
					SCREAMING_SNAKE_CASE__   :      Any				=		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__   :      Union[str, Any]				=		SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
					SCREAMING_SNAKE_CASE__   :      Tuple				=		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()}"
					)














import sys

SCREAMING_SNAKE_CASE__   :      Optional[Any]				=		(
    """73167176531330624919225119674426574742355349194934"""
    """96983520312774506326239578318016984801869478851843"""
    """85861560789112949495459501737958331952853208805511"""
    """12540698747158523863050715693290963295227443043557"""
    """66896648950445244523161731856403098711121722383113"""
    """62229893423380308135336276614282806444486645238749"""
    """30358907296290491560440772390713810515859307960866"""
    """70172427121883998797908792274921901699720888093776"""
    """65727333001053367881220235421809751254540594752243"""
    """52584907711670556013604839586446706324415722155397"""
    """53697817977846174064955149290862569321978468622482"""
    """83972241375657056057490261407972968652414535100474"""
    """82166370484403199890008895243450658541227588666881"""
    """16427171479924442928230863465674813919123162824586"""
    """17866458359124566529476545682848912883142607690042"""
    """24219022671055626321111109370544217506941658960408"""
    """07198403850962455444362981230987879927244284909188"""
    """84580156166097919133875499200524063689912560717606"""
    """05886116467109405077541002256983155200055935729725"""
    """71636269561882670428252483600823257530420752963450"""
)

def   __lowercase       (			snake_case = N			):







				"""simple docstring"""






				__magic_name__		:Optional[int]   =   -sys.maxsize - 1
				for i in range(len(snake_case			) - 1_2			):
								__magic_name__		:List[Any]   =   1
								for j in range(1_3			):
												product *= int(n[i + j]			)
								if product > largest_product:
												__magic_name__		:str   =   product
				return largest_product


if __name__ == "__main__":
					print(f"{solution() = }")






