



from __future__ import annotations

from collections.abc import Callable
from typing import Any, Generic, TypeVar

lowerCamelCase__    :		List[Any]          =   TypeVar("""T""")



class       _snake_case   (	Generic[T]							):


 def __init__(					self					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   lowercase__  :   Any | T    		=      None

   lowercase__  :   int    		=      len(SCREAMING_SNAKE_CASE_)
   lowercase__  :   list[T]    		=      [any_type for _ in range(self.N)] + arr
   lowercase__  :   List[str]    		=      fnc
   self.build()


 def      lowercase__     (					self):


   '''simple docstring'''




   for p in range(self.N - 1					,  0					,  -1):
     lowercase__  :   List[str]    		=      self.fn(self.st[p * 2]					,  self.st[p * 2 + 1])


 def      lowercase__     (					self					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   p += self.N
   lowercase__  :   List[str]    		=      v
   while p > 1:
     lowercase__  :   str    		=      p // 2
     lowercase__  :   Optional[Any]    		=      self.fn(self.st[p * 2]					,  self.st[p * 2 + 1])



 def      lowercase__     (					self					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_):  # noqa: E741


   '''simple docstring'''




   lowercase__  :   int    		=      l + self.N, r + self.N

   lowercase__  :   T | None    		=      None
   while l <= r:
     if l % 2 == 1:
       lowercase__  :   str    		=      self.st[l] if res is None else self.fn(SCREAMING_SNAKE_CASE_					,  self.st[l])
     if r % 2 == 0:
       lowercase__  :   str    		=      self.st[r] if res is None else self.fn(SCREAMING_SNAKE_CASE_					,  self.st[r])
     lowercase__  :   str    		=      (l + 1) // 2, (r - 1) // 2
   return res


if __name__ == "__main__":
     from functools import reduce

     lowerCamelCase__    :		Tuple          =   [1, 1_0, -2, 9, -3, 8, 4, -7, 5, 6, 1_1, -1_2]

     lowerCamelCase__    :		Union[str, Any]          =   {
         0: 7,
         1: 2,
         2: 6,
         3: -1_4,
         4: 5,
         5: 4,
         6: 7,
         7: -1_0,
         8: 9,
         9: 1_0,
         1_0: 1_2,
         1_1: 1,
     }

     lowerCamelCase__    :		Dict          =   SegmentTree(test_array, min)
     lowerCamelCase__    :		int          =   SegmentTree(test_array, max)
     lowerCamelCase__    :		str          =   SegmentTree(test_array, lambda a, b: a + b)

     def 		UpperCamelCase	(      )		->	None:


       '''simple docstring'''






       for i in range(len(lowercase_   )   ):
         for j in range(lowercase_ , len(lowercase_   )   ):
           lowercase__  :   int    		=      reduce(lowercase_ , test_array[i : j + 1]   )
           lowercase__  :   Optional[Any]    		=      reduce(lowercase_ , test_array[i : j + 1]   )
           lowercase__  :   Any    		=      reduce(lambda lowercase_ , lowercase_   : a + b , test_array[i : j + 1]   )
           assert min_range == min_segment_tree.query(lowercase_ , lowercase_   )
           assert max_range == max_segment_tree.query(lowercase_ , lowercase_   )
           assert sum_range == sum_segment_tree.query(lowercase_ , lowercase_   )

     test_all_segments()

     for index, value in test_updates.items():
          lowerCamelCase__    :		List[Any]          =   value
          min_segment_tree.update(index, value)
          max_segment_tree.update(index, value)
          sum_segment_tree.update(index, value)
          test_all_segments()








import math
import random
from typing import Any

from .hill_climbing import SearchProblem

def 		UpperCamelCase	(      lowercase_ , lowercase_ = True , lowercase_ = math.inf , lowercase_ = -math.inf , lowercase_ = math.inf , lowercase_ = -math.inf , lowercase_ = False , lowercase_ = 1_00 , lowercase_ = 0.01 , lowercase_ = 1 , )		->	Any:


  '''simple docstring'''






  lowercase__  :   Any    		=      False
  lowercase__  :   Union[str, Any]    		=      search_prob
  lowercase__  :   int    		=      start_temperate
  lowercase__  :   Union[str, Any]    		=      []
  lowercase__  :   List[str]    		=      0
  lowercase__  :   Optional[int]    		=      None

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

  if visualization:
    from matplotlib import pyplot as plt

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


if __name__ == "__main__":

     def 		UpperCamelCase	(      lowercase_ , lowercase_   )		->	str:


       '''simple docstring'''






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

     # starting the problem with initial coordinates (12, 47)
     lowerCamelCase__    :		str          =   SearchProblem(x=1_2, y=4_7, step_size=1, function_to_optimize=test_fa)
     lowerCamelCase__    :		List[Any]          =   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__    :		List[Any]          =   SearchProblem(x=1_2, y=4_7, step_size=1, function_to_optimize=test_fa)
     lowerCamelCase__    :		Optional[int]          =   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 		UpperCamelCase	(      lowercase_ , lowercase_   )		->	Union[str, Any]:


       '''simple docstring'''






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

     lowerCamelCase__    :		Tuple          =   SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
     lowerCamelCase__    :		Union[str, 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()}'''
     )

     lowerCamelCase__    :		Dict          =   SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
     lowerCamelCase__    :		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()}'''
     )






