

"""simple docstring"""






from __future__ import annotations

import math
from collections.abc import Callable





def 	lowercase      (   __UpperCamelCase      ,   __UpperCamelCase      ,   __UpperCamelCase      ,   __UpperCamelCase = 100      ,   ) ->      float:
 __magic_name__     =      x_start
 __magic_name__     =      fnc(__UpperCamelCase						)
 __magic_name__     =      0.0

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

  # Increment step
  __magic_name__     =      xa
  __magic_name__     =      fxa

 return length


if __name__ == "__main__":





    def 	lowercase      (   __UpperCamelCase						) ->      int:
     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										=		10
    while i <= 10_00_00:
        print(f"""With {i} steps: {line_length(f, -10, 10, i)}""")
        i *= 10




"""simple docstring"""






from __future__ import annotations

from random import choice





def 	lowercase      (   __UpperCamelCase						) ->      Any:
 return choice(__UpperCamelCase						)





def 	lowercase      (   __UpperCamelCase      ,   __UpperCamelCase						) ->      int:
 __magic_name__     =      random_pivot(__UpperCamelCase						)

 # partition based on pivot
 # linear time
 __magic_name__     =      [e for e in lst if e < pivot]
 __magic_name__     =      [e for e in lst if e > pivot]

 # if we get lucky, pivot might be the element we want.
 # we can easily see this:
 # small (elements smaller than k)
 # + pivot (kth element)
 # + big (elements larger than k)
 if len(__UpperCamelCase						) == k - 1:
  return pivot
 # pivot is in elements bigger than k
 elif len(__UpperCamelCase						) < k - 1:
  return kth_number(__UpperCamelCase      ,   k - len(__UpperCamelCase						) - 1						)
 # pivot is in elements smaller than k
 else:
  return kth_number(__UpperCamelCase      ,   __UpperCamelCase						)


if __name__ == "__main__":
 import doctest

 doctest.testmod()

