'''simple docstring'''

import math
import random
from typing import Any

from .hill_climbing import SearchProblem
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase = True		,     UpperCAmelCase = math.inf		,     UpperCAmelCase = -math.inf		,     UpperCAmelCase = math.inf		,     UpperCAmelCase = -math.inf		,     UpperCAmelCase = False		,     UpperCAmelCase = 100		,     UpperCAmelCase = 0.0_1		,     UpperCAmelCase = 1		,     ):
 lowercase__				:    Optional[Any]  =					False
 lowercase__				:    str  =					search_prob
 lowercase__				:    Any  =					start_temperate
 lowercase__				:    Dict  =					[]
 lowercase__				:    str  =					0
 lowercase__				:    Optional[Any]  =					None

 while not search_end:
  lowercase__				:    Dict  =					current_state.score()
  if best_state is None or current_score > best_state.score():
   lowercase__				:    Dict  =					current_state
  scores.append(UpperCAmelCase     )
  iterations += 1
  lowercase__				:    List[str]  =					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__				:    Any  =					random.randint(0		,     len(UpperCAmelCase     ) - 1     )  # picking a random neighbor
   lowercase__				:    Optional[int]  =					neighbors.pop(UpperCAmelCase     )
   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__				:    int  =					change * -1  # in case we are finding minimum
   if change > 0:  # improves the solution
    lowercase__				:    Tuple  =					picked_neighbor
   else:
    lowercase__				:    Any  =					(math.e) ** (
        change / current_temp
    )  # probability generation function
    if random.random() < probability:  # random number within probability
     lowercase__				:    str  =					picked_neighbor
  lowercase__				:    Optional[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
   lowercase__				:    List[str]  =					True
  else:
   lowercase__				:    int  =					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 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase     ):
   return (x**2) + (y**2)

  # starting the problem with initial coordinates (12, 47)
  __a: str          =   SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
  __a: int          =   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)
  __a: Optional[int]          =   SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
  __a: int          =   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 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase     ):
   return (3 * x**2) - (6 * y)

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

  __a: Optional[Any]          =   SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
  __a: Union[str, Any]          =   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'''

from __future__ import annotations

from random import random



class 			UpperCAmelCase  :





       '''simple docstring'''



       def __init__(						self	,   __lowerCAmelCase = None )  ->  str:
        lowercase__				:    Any  =					value
        lowercase__				:    Union[str, Any]  =					random()
        lowercase__				:    Node | None  =					None
        lowercase__				:    Node | None  =					None

       def __repr__(						self )  ->  str:
        from pprint import pformat

        if self.left is None and self.right is None:
         return F"""'{self.value}: {self.prior:.5}'"""
        else:
         return pformat(
             {F"""{self.value}: {self.prior:.5}""": (self.left, self.right)}	,   indent=1 )


       def __str__(						self )  ->  str:
        lowercase__				:    Any  =					str(self.value ) + ''' '''
        lowercase__				:    str  =					str(self.left or '''''' )
        lowercase__				:    List[str]  =					str(self.right or '''''' )
        return value + left + right


def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase     ):
 if root is None:  # None tree is split into 2 Nones
  return None, None
 elif root.value is None:
  return None, None
 else:
  if value < root.value:
   lowercase__ ,							lowercase__				:    int  =					split(root.left		,     UpperCAmelCase     )
   return left, root
  else:
   lowercase__ ,							lowercase__				:    Optional[Any]  =					split(root.right		,     UpperCAmelCase     )
   return root, right
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase     ):
 if (not left) or (not right):  # If one node is None, return the other
  return left or right
 elif left.prior < right.prior:
  lowercase__				:    Any  =					merge(left.right		,     UpperCAmelCase     )
  return left
 else:
  lowercase__				:    Dict  =					merge(UpperCAmelCase		,     right.left     )
  return right
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase     ):
 lowercase__				:    Dict  =					Node(UpperCAmelCase     )
 lowercase__ ,							lowercase__				:    Tuple  =					split(UpperCAmelCase		,     UpperCAmelCase     )
 return merge(merge(UpperCAmelCase		,     UpperCAmelCase     )		,     UpperCAmelCase     )
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase     ):
 lowercase__ ,							lowercase__				:    Dict  =					split(UpperCAmelCase		,     value - 1     )
 lowercase__ ,							lowercase__				:    int  =					split(UpperCAmelCase		,     UpperCAmelCase     )
 return merge(UpperCAmelCase		,     UpperCAmelCase     )
def 			__UpperCamelCase       (   UpperCAmelCase     ):
 if not root:  # None
  return
 else:
  inorder(root.left     )
  print(root.value		,     end=''','''     )
  inorder(root.right     )
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase     ):
 for arg in args.split():
  if arg[0] == "+":
   lowercase__				:    Tuple  =					insert(UpperCAmelCase		,     int(arg[1:]     )     )

  elif arg[0] == "-":
   lowercase__				:    Union[str, Any]  =					erase(UpperCAmelCase		,     int(arg[1:]     )     )

  else:
   print('''Unknown command'''     )

 return root
def 			__UpperCamelCase       (   ):
 lowercase__				:    Tuple  =					None
 print(
     '''enter numbers to create a tree, + value to add value into treap, '''
     '''- value to erase all nodes with value. \'q\' to quit. '''     )

 lowercase__				:    Dict  =					input()
 while args != "q":
  lowercase__				:    Any  =					interact_treap(UpperCAmelCase		,     UpperCAmelCase     )
  print(UpperCAmelCase     )
  lowercase__				:    List[Any]  =					input()

 print('''good by!'''     )


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()

