






from random import randint
from tempfile import TemporaryFile

import numpy as np
def 		lowercase__  (				_UpperCamelCase       ,							_UpperCamelCase       ,							_UpperCamelCase) ->			List[str]:
      """simple docstring"""

      UpperCamelCase					       =  0
      if start < end:
            UpperCamelCase					       =  randint(_UpperCamelCase       ,							_UpperCamelCase)
            UpperCamelCase					       =  a[end]
            UpperCamelCase					       =  a[pivot]
            UpperCamelCase					       =  temp

            UpperCamelCase       ,  UpperCamelCase					       =  _in_place_partition(_UpperCamelCase       ,							_UpperCamelCase       ,							_UpperCamelCase)
            count += _in_place_quick_sort(_UpperCamelCase       ,							_UpperCamelCase       ,							p - 1)
            count += _in_place_quick_sort(_UpperCamelCase       ,							p + 1       ,							_UpperCamelCase)
      return count
def 		lowercase__  (				_UpperCamelCase       ,							_UpperCamelCase       ,							_UpperCamelCase) ->			Union[str, Any]:
      """simple docstring"""

      UpperCamelCase					       =  0
      UpperCamelCase					       =  randint(_UpperCamelCase       ,							_UpperCamelCase)
      UpperCamelCase					       =  a[end]
      UpperCamelCase					       =  a[pivot]
      UpperCamelCase					       =  temp
      UpperCamelCase					       =  start - 1
      for index in range(_UpperCamelCase       ,							_UpperCamelCase):
            count += 1
            if a[index] < a[end]:  # check if current val is less than pivot value
                  UpperCamelCase					       =  new_pivot_index + 1
                  UpperCamelCase					       =  a[new_pivot_index]
                  UpperCamelCase					       =  a[index]
                  UpperCamelCase					       =  temp

      UpperCamelCase					       =  a[new_pivot_index + 1]
      UpperCamelCase					       =  a[end]
      UpperCamelCase					       =  temp
      return new_pivot_index + 1, count


__magic_name__   :  int        =							TemporaryFile()
__magic_name__   :  List[Any]        =							100  # 1000 elements are to be sorted


__magic_name__     ,   __magic_name__   :  List[Any]        =							0, 1  # mean and standard deviation
__magic_name__   :  Dict        =							np.random.normal(mu, sigma, p)
np.save(outfile, X)
print('''The array is''')
print(X)


outfile.seek(0)  # using the same array
__magic_name__   :  Optional[Any]        =							np.load(outfile)
__magic_name__   :  Dict        =							len(M) - 1
__magic_name__   :  Union[str, Any]        =							_in_place_quick_sort(M, 0, r)

print(
    '''No of Comparisons for 100 elements selected from a standard normal distribution'''
    '''is :'''
)
print(z)











from __future__ import annotations

from collections.abc import MutableSequence





class 					A__     :

     '''simple docstring'''






     def __init__( self      :    Dict   ,						_SCREAMING_SNAKE_CASE      :    int   ,						_SCREAMING_SNAKE_CASE      :    MutableSequence[float] ):






           """simple docstring"""




           if len(_SCREAMING_SNAKE_CASE ) != degree + 1:
                 raise ValueError(
                     'The number of coefficients should be equal to the degree + 1.' )

           UpperCamelCase					       =  list(_SCREAMING_SNAKE_CASE )
           UpperCamelCase					       =  degree







     def __add__( self      :    Any   ,						_SCREAMING_SNAKE_CASE      :    Polynomial ):






           """simple docstring"""




           if self.degree > polynomial_a.degree:
                 UpperCamelCase					       =  self.coefficients[:]
                 for i in range(polynomial_a.degree + 1 ):
                       coefficients[i] += polynomial_a.coefficients[i]
                 return Polynomial(self.degree   ,						_SCREAMING_SNAKE_CASE )
           else:
                 UpperCamelCase					       =  polynomial_a.coefficients[:]
                 for i in range(self.degree + 1 ):
                       coefficients[i] += self.coefficients[i]
                 return Polynomial(polynomial_a.degree   ,						_SCREAMING_SNAKE_CASE )







     def __sub__( self      :    Optional[int]   ,						_SCREAMING_SNAKE_CASE      :    Polynomial ):






           """simple docstring"""




           return self + polynomial_a * Polynomial(0   ,						[-1] )







     def __neg__( self      :    Any ):






           """simple docstring"""




           return Polynomial(self.degree   ,						[-c for c in self.coefficients] )







     def __mul__( self      :    Union[str, Any]   ,						_SCREAMING_SNAKE_CASE      :    Polynomial ):






           """simple docstring"""




           UpperCamelCase					       =  [0] * (self.degree + polynomial_a.degree + 1)
           for i in range(self.degree + 1 ):
                 for j in range(polynomial_a.degree + 1 ):
                       coefficients[i + j] += (
                           self.coefficients[i] * polynomial_a.coefficients[j]
                       )

           return Polynomial(self.degree + polynomial_a.degree   ,						_SCREAMING_SNAKE_CASE )







     def   _SCREAMING_SNAKE_CASE     ( self      :    Optional[int]   ,						_SCREAMING_SNAKE_CASE      :    int | float ):






           """simple docstring"""




           UpperCamelCase					       =  0
           for i in range(self.degree + 1 ):
                 result += self.coefficients[i] * (substitution**i)
           return result







     def __str__( self      :    Union[str, Any] ):






           """simple docstring"""




           UpperCamelCase					       =  ''
           for i in range(self.degree   ,						-1   ,						-1 ):
                 if self.coefficients[i] == 0:
                       continue
                 elif self.coefficients[i] > 0:
                       if polynomial:
                             polynomial += " + "
                 else:
                       polynomial += " - "

                 if i == 0:
                       polynomial += str(abs(self.coefficients[i] ) )
                 elif i == 1:
                       polynomial += str(abs(self.coefficients[i] ) ) + "x"
                 else:
                       polynomial += str(abs(self.coefficients[i] ) ) + "x^" + str(_SCREAMING_SNAKE_CASE )

           return polynomial







     def __repr__( self      :    str ):






           """simple docstring"""




           return self.__str__()







     def   _SCREAMING_SNAKE_CASE     ( self      :    Optional[Any] ):






           """simple docstring"""




           UpperCamelCase					       =  [0] * self.degree
           for i in range(self.degree ):
                 UpperCamelCase					       =  self.coefficients[i + 1] * (i + 1)
           return Polynomial(self.degree - 1   ,						_SCREAMING_SNAKE_CASE )







     def   _SCREAMING_SNAKE_CASE     ( self      :    Optional[int]   ,						_SCREAMING_SNAKE_CASE      :    int | float = 0 ):






           """simple docstring"""




           UpperCamelCase					       =  [0] * (self.degree + 2)
           UpperCamelCase					       =  constant
           for i in range(self.degree + 1 ):
                 UpperCamelCase					       =  self.coefficients[i] / (i + 1)
           return Polynomial(self.degree + 1   ,						_SCREAMING_SNAKE_CASE )







     def __eq__( self      :    Any   ,						_SCREAMING_SNAKE_CASE      :    object ):






           """simple docstring"""




           if not isinstance(_SCREAMING_SNAKE_CASE   ,						_SCREAMING_SNAKE_CASE ):
                 return False

           if self.degree != polynomial_a.degree:
                 return False

           for i in range(self.degree + 1 ):
                 if self.coefficients[i] != polynomial_a.coefficients[i]:
                       return False

           return True







     def __ne__( self      :    str   ,						_SCREAMING_SNAKE_CASE      :    object ):






           """simple docstring"""




           return not self.__eq__(_SCREAMING_SNAKE_CASE )



