'''simple docstring'''





import math
import random
from typing import Any

from .hill_climbing import SearchProblem





def 	lowerCAmelCase_				(					snake_case_       : Any					,    snake_case_       : bool = True					,    snake_case_       : float = math.inf					,    snake_case_       : float = -math.inf					,    snake_case_       : float = math.inf					,    snake_case_       : float = -math.inf					,    snake_case_       : bool = False					,    snake_case_       : float = 1_00					,    snake_case_       : float = 0.01					,    snake_case_       : float = 1					,    )    ->      Any:


     '''simple docstring'''




     UpperCAmelCase_           =   False
     UpperCAmelCase_           =   search_prob
     UpperCAmelCase_           =   start_temperate
     UpperCAmelCase_           =   []
     UpperCAmelCase_           =   0
     UpperCAmelCase_           =   None

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


         '''simple docstring'''




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

    # starting the problem with initial coordinates (12, 47)
    SCREAMING_SNAKE_CASE_:     List[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[str]  =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 	lowerCAmelCase_				(					snake_case_       : int					,    snake_case_       : Union[str, Any]			)    ->      Optional[Any]:


         '''simple docstring'''




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

    SCREAMING_SNAKE_CASE_:     str  =SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
    SCREAMING_SNAKE_CASE_:     Tuple  =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_:     List[str]  =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()}"
    )








'''simple docstring'''




from __future__ import annotations

from bisect import bisect_left
from functools import total_ordering
from heapq import merge

@total_ordering
class 		UpperCAmelCase_      (  __lowercase		):





     def __lt__( self       :      Optional[int]    ,      UpperCAmelCase__       :      List[str]    )				->  List[Any]:
        return self[-1] < other[-1]





     def __eq__( self       :      str    ,      UpperCAmelCase__       :      List[str]    )				->  Tuple:
        return self[-1] == other[-1]





def 	a_					( lowerCamelCase	:     list				):
   lowerCAmelCase     =			[]
   # sort into stacks
   for element in collection:
      lowerCAmelCase     =			Stack([element]				)
      lowerCAmelCase     =			bisect_left(lowerCamelCase	, lowerCamelCase				)
      if i != len(lowerCamelCase				):
         stacks[i].append(lowerCamelCase				)
      else:
         stacks.append(lowerCamelCase				)

    # use a heap-based merge to merge stack efficiently
   lowerCAmelCase     =			merge(*(reversed(lowerCamelCase				) for stack in stacks)				)
   return collection


if __name__ == "__main__":
       __snake_case    						=input("""Enter numbers separated by a comma:\n""").strip()
       __snake_case    						=[int(item) for item in user_input.split(""",""")]
       print(patience_sort(unsorted))





