






from __future__ import annotations

import math
from collections.abc import Callable







def 			A__							(      _a  :					Callable[[int | float], int | float]		,  _a  :					int | float		,  _a  :					int | float		,  _a  :					int = 100		,  ):





 '''simple docstring'''







 snake_case__  :    Dict							       =x_start
 snake_case__  :    str							       =fnc(_a	)
 snake_case__  :    Optional[Any]							       =0.0

 for _ in range(_a	):
  # Approximates curve as a sequence of linear lines and sums their length
  snake_case__  :    Optional[Any]							       =(x_end - x_start) / steps + xa
  snake_case__  :    Any							       =fnc(_a	)
  length += math.hypot(xa - xa		,  fxa - fxa	)

  # Increment step
  snake_case__  :    Dict							       =xa
  snake_case__  :    List[Any]							       =fxa

 return length


if __name__ == "__main__":







       def 			A__							(      _a  :					Tuple	):





        '''simple docstring'''







        return math.sin(10 * x	)

       print("""f(x) = sin(10 * x)""")
       print("""The length of the curve from x = -10 to x = 10 is:""")
       __lowerCamelCase	:		Dict										=   10
       while i <= 10_00_00:
              print(F"With {i} steps: {line_length(f, -10, 10, i)}")
              i *= 10













import math







def 			A__							(      _a  :					list		,  _a  :					int = 0		,  _a  :					int = 0	):





 '''simple docstring'''







 snake_case__  :    Tuple							       =end or len(_a	)
 for i in range(_a		,  _a	):
  snake_case__  :    int							       =i
  snake_case__  :    int							       =array[i]
  while temp_index != start and temp_index_value < array[temp_index - 1]:
   snake_case__  :    Dict							       =array[temp_index - 1]
   temp_index -= 1
  snake_case__  :    Dict							       =temp_index_value
 return array







def 			A__							(      _a  :					list		,  _a  :					int		,  _a  :					int	):  # Max Heap





 '''simple docstring'''







 snake_case__  :    Tuple							       =index
 snake_case__  :    Dict							       =2 * index + 1  # Left Node
 snake_case__  :    Union[str, Any]							       =2 * index + 2  # Right Node

 if left_index < heap_size and array[largest] < array[left_index]:
  snake_case__  :    Dict							       =left_index

 if right_index < heap_size and array[largest] < array[right_index]:
  snake_case__  :    List[Any]							       =right_index

 if largest != index:
  snake_case__       ,   snake_case__  :    List[Any]							       =array[largest], array[index]
  heapify(_a		,  _a		,  _a	)







def 			A__							(      _a  :					list	):





 '''simple docstring'''







 snake_case__  :    List[str]							       =len(_a	)

 for i in range(n // 2		,  -1		,  -1	):
  heapify(_a		,  _a		,  _a	)

 for i in range(n - 1		,  0		,  -1	):
  snake_case__       ,   snake_case__  :    Tuple							       =array[0], array[i]
  heapify(_a		,  0		,  _a	)

 return array







def 			A__							(      _a  :					list		,  _a  :					int		,  _a  :					int		,  _a  :					int	):





 '''simple docstring'''







 if (array[first_index] > array[middle_index]) != (
     array[first_index] > array[last_index]
 ):
  return array[first_index]
 elif (array[middle_index] > array[first_index]) != (
     array[middle_index] > array[last_index]
 ):
  return array[middle_index]
 else:
  return array[last_index]







def 			A__							(      _a  :					list		,  _a  :					int		,  _a  :					int		,  _a  :					int	):





 '''simple docstring'''







 snake_case__  :    Dict							       =low
 snake_case__  :    Union[str, Any]							       =high
 while True:
  while array[i] < pivot:
   i += 1
  j -= 1
  while pivot < array[j]:
   j -= 1
  if i >= j:
   return i
  snake_case__       ,   snake_case__  :    List[Any]							       =array[j], array[i]
  i += 1







def 			A__							(      _a  :					list	):





 '''simple docstring'''







 if len(_a	) == 0:
  return array
 snake_case__  :    Optional[int]							       =2 * math.ceil(math.loga(len(_a	)	)	)
 snake_case__  :    Tuple							       =16
 return intro_sort(_a		,  0		,  len(_a	)		,  _a		,  _a	)







def 			A__							(      _a  :					list		,  _a  :					int		,  _a  :					int		,  _a  :					int		,  _a  :					int	):





 '''simple docstring'''







 while end - start > size_threshold:
  if max_depth == 0:
   return heap_sort(_a	)
  max_depth -= 1
  snake_case__  :    Dict							       =median_of_a(_a		,  _a		,  start + ((end - start) // 2) + 1		,  end - 1	)
  snake_case__  :    List[str]							       =partition(_a		,  _a		,  _a		,  _a	)
  intro_sort(_a		,  _a		,  _a		,  _a		,  _a	)
  snake_case__  :    Union[str, Any]							       =p
 return insertion_sort(_a		,  _a		,  _a	)


if __name__ == "__main__":
       import doctest

       doctest.testmod()

       __lowerCamelCase	:		Optional[int]										=   input("""Enter numbers separated by a comma : """).strip()
       __lowerCamelCase	:		Dict										=   [float(item) for item in user_input.split(""",""")]
       print(sort(unsorted))





