
'''simple docstring'''



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_ = 1_00    ,      SCREAMING_SNAKE_CASE_ = 0.01    ,      SCREAMING_SNAKE_CASE_ = 1    ,      )     ->     Any:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE      =				False
   _SCREAMING_SNAKE_CASE      =				search_prob
   _SCREAMING_SNAKE_CASE      =				start_temperate
   _SCREAMING_SNAKE_CASE      =				[]
   _SCREAMING_SNAKE_CASE      =				0
   _SCREAMING_SNAKE_CASE      =				None

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

   if visualization:
      from matplotlib import pyplot as plt

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


if __name__ == "__main__":
     def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						)     ->     str:




        """simple docstring"""
        return (x**2) + (y**2)

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




        """simple docstring"""
        return (3 * x**2) - (6 * y)

     UpperCamelCase__      :		List[Any]       							=  SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
     UpperCamelCase__      :		int       							=  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()}"""
     )

     UpperCamelCase__      :		Union[str, Any]       							=  SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
     UpperCamelCase__      :		Dict       							=  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()}"""
     )








'''simple docstring'''



import sys

UpperCamelCase__      :		int       							=  (
    "73167176531330624919225119674426574742355349194934"
    "96983520312774506326239578318016984801869478851843"
    "85861560789112949495459501737958331952853208805511"
    "12540698747158523863050715693290963295227443043557"
    "66896648950445244523161731856403098711121722383113"
    "62229893423380308135336276614282806444486645238749"
    "30358907296290491560440772390713810515859307960866"
    "70172427121883998797908792274921901699720888093776"
    "65727333001053367881220235421809751254540594752243"
    "52584907711670556013604839586446706324415722155397"
    "53697817977846174064955149290862569321978468622482"
    "83972241375657056057490261407972968652414535100474"
    "82166370484403199890008895243450658541227588666881"
    "16427171479924442928230863465674813919123162824586"
    "17866458359124566529476545682848912883142607690042"
    "24219022671055626321111109370544217506941658960408"
    "07198403850962455444362981230987879927244284909188"
    "84580156166097919133875499200524063689912560717606"
    "05886116467109405077541002256983155200055935729725"
    "71636269561882670428252483600823257530420752963450"
)
def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_ = N						)     ->     int:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE      =				-sys.maxsize - 1
   for i in range(len(SCREAMING_SNAKE_CASE_						) - 12						):
      _SCREAMING_SNAKE_CASE      =				1
      for j in range(13						):
         product *= int(n[i + j]						)
      if product > largest_product:
         _SCREAMING_SNAKE_CASE      =				product
   return largest_product


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






