

def   __UpperCAmelCase					(      __a :     List[Any]      )     ->	Any:

					"""simple docstring"""

					_a      :       Tuple   =						0
					_a      :       List[str]   =						len(__a      )

					for i in range(n - 1      ):
										for j in range(i + 1						,__a      ):
															if arr[i] > arr[j]:
																				num_inversions += 1

					return num_inversions



def   __UpperCAmelCase					(      __a :     Optional[Any]      )     ->	Union[str, Any]:

					"""simple docstring"""

					if len(__a      ) <= 1:
										return arr, 0
					_a      :       List[Any]   =						len(__a      ) // 2
					_a      :       List[str]   =						arr[0:mid]
					_a      :       Optional[int]   =						arr[mid:]

					_a ,   _a      :       str   =						count_inversions_recursive(__a      )
					_a ,   _a      :       Tuple   =						count_inversions_recursive(__a      )
					_a ,   _a      :       int   =						_count_cross_inversions(__a						,__a      )

					_a      :       Union[str, Any]   =						inversion_p + inversions_q + cross_inversions
					return c, num_inversions



def   __UpperCAmelCase					(      __a :     List[Any]						,__a :     Any      )     ->	Union[str, Any]:

					"""simple docstring"""

					_a      :       str   =						[]
					_a      :       Optional[int]   =						0
					while i < len(__a      ) and j < len(__a      ):
										if p[i] > q[j]:
															# if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
															# These are all inversions. The claim emerges from the
															# property that P is sorted.
															num_inversion += len(__a      ) - i
															r.append(q[j]      )
															j += 1
										else:
															r.append(p[i]      )
															i += 1

					if i < len(__a      ):
										r.extend(p[i:]      )
					else:
										r.extend(q[j:]      )

					return r, num_inversion



def   __UpperCAmelCase					(      )     ->	Any:

					"""simple docstring"""

					_a      :       Tuple   =						[10, 2, 1, 5, 5, 2, 11]

					# this arr has 8 inversions:
					# (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

					_a      :       Dict   =						count_inversions_bf(__a      )
					_a ,   _a      :       Dict   =						count_inversions_recursive(__a      )

					assert num_inversions_bf == num_inversions_recursive == 8

					print('''number of inversions = '''						,__a      )

					# testing an array with zero inversion (a sorted arr_1)

					arr_a.sort()
					_a      :       Optional[int]   =						count_inversions_bf(__a      )
					_a ,   _a      :       Union[str, Any]   =						count_inversions_recursive(__a      )

					assert num_inversions_bf == num_inversions_recursive == 0
					print('''number of inversions = '''						,__a      )

					# an empty list should also have zero inversions
					_a      :       Optional[int]   =						[]
					_a      :       List[Any]   =						count_inversions_bf(__a      )
					_a ,   _a      :       str   =						count_inversions_recursive(__a      )

					assert num_inversions_bf == num_inversions_recursive == 0
					print('''number of inversions = '''						,__a      )


if __name__ == "__main__":
			main()






from random import randint
from tempfile import TemporaryFile

import numpy as np



def   __UpperCAmelCase					(      __a :     Optional[Any]						,__a :     int						,__a :     Any      )     ->	int:

					"""simple docstring"""

					_a      :       int   =						0
					if start < end:
										_a      :       Tuple   =						randint(__a						,__a      )
										_a      :       Tuple   =						a[end]
										_a      :       List[str]   =						a[pivot]
										_a      :       Any   =						temp

										_a ,   _a      :       Optional[int]   =						_in_place_partition(__a						,__a						,__a      )
										count += _in_place_quick_sort(__a						,__a						,p - 1      )
										count += _in_place_quick_sort(__a						,p + 1						,__a      )
					return count



def   __UpperCAmelCase					(      __a :     List[Any]						,__a :     Tuple						,__a :     Dict      )     ->	Dict:

					"""simple docstring"""

					_a      :       Dict   =						0
					_a      :       Tuple   =						randint(__a						,__a      )
					_a      :       List[Any]   =						a[end]
					_a      :       str   =						a[pivot]
					_a      :       str   =						temp
					_a      :       Dict   =						start - 1
					for index in range(__a						,__a      ):
										count += 1
										if a[index] < a[end]:  # check if current val is less than pivot value
															_a      :       int   =						new_pivot_index + 1
															_a      :       Any   =						a[new_pivot_index]
															_a      :       Optional[int]   =						a[index]
															_a      :       str   =						temp

					_a      :       Union[str, Any]   =						a[new_pivot_index + 1]
					_a      :       Tuple   =						a[end]
					_a      :       Any   =						temp
					return new_pivot_index + 1, count


a__												=						TemporaryFile()
a__												=						100  # 1000 elements are to be sorted


a__						,     a__												=						0, 1  # mean and standard deviation
a__												=						np.random.normal(mu, sigma, p)
np.save(outfile, X)
print('''The array is''')
print(X)


outfile.seek(0)  # using the same array
a__												=						np.load(outfile)
a__												=						len(M) - 1
a__												=						_in_place_quick_sort(M, 0, r)

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







print(z)



