



"""simple docstring"""
from random import randint
from tempfile import TemporaryFile

import numpy as np

def    _snake_case		(		UpperCamelCase		:	str    ,	UpperCamelCase		:	Dict    ,	UpperCamelCase		:	List[str]		):
 UpperCAmelCase			:      Union[str, Any]			=			0
 if start < end:
  UpperCAmelCase			:      Optional[int]			=			randint(UpperCamelCase    ,	UpperCamelCase		)
  UpperCAmelCase			:      List[Any]			=			a[end]
  UpperCAmelCase			:      List[Any]			=			a[pivot]
  UpperCAmelCase			:      Dict			=			temp

  UpperCAmelCase			:      Any			=			_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    _snake_case		(		UpperCamelCase		:	Union[str, Any]    ,	UpperCamelCase		:	Optional[Any]    ,	UpperCamelCase		:	Optional[Any]		):
 UpperCAmelCase			:      Optional[int]			=			0
 UpperCAmelCase			:      Optional[int]			=			randint(UpperCamelCase    ,	UpperCamelCase		)
 UpperCAmelCase			:      Optional[int]			=			a[end]
 UpperCAmelCase			:      List[Any]			=			a[pivot]
 UpperCAmelCase			:      Any			=			temp
 UpperCAmelCase			:      Any			=			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			:      str			=			new_pivot_index + 1
   UpperCAmelCase			:      str			=			a[new_pivot_index]
   UpperCAmelCase			:      List[Any]			=			a[index]
   UpperCAmelCase			:      Optional[int]			=			temp

 UpperCAmelCase			:      Dict			=			a[new_pivot_index + 1]
 UpperCAmelCase			:      str			=			a[end]
 UpperCAmelCase			:      Any			=			temp
 return new_pivot_index + 1, count


A:     int										=	TemporaryFile()
A:     str										=	1_0_0  # 1000 elements are to be sorted


A:     Optional[int]										=	0, 1  # mean and standard deviation
A:     Tuple										=	np.random.normal(mu, sigma, p)
np.save(outfile, X)
print("The array is")
print(X)


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

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

print(z)





"""simple docstring"""
from __future__ import annotations

from decimal import Decimal

from numpy import array

def    _snake_case		(		UpperCamelCase		:	list[list[float]]		):
 UpperCAmelCase			:      str			=			Decimal

 # Check if the provided matrix has 2 rows and 2 columns
 # since this implementation only works for 2x2 matrices
 if len(UpperCamelCase		) == 2 and len(matrix[0]		) == 2 and len(matrix[1]		) == 2:
  # Calculate the determinant of the matrix
  UpperCAmelCase			:      Optional[int]			=			float(
      d(matrix[0][0]		) * d(matrix[1][1]		) - d(matrix[1][0]		) * d(matrix[0][1]		)		)
  if determinant == 0:
   raise ValueError("""This matrix has no inverse."""		)

  # Creates a copy of the matrix with swapped positions of the elements
  UpperCAmelCase			:      Optional[Any]			=			[[0.0, 0.0], [0.0, 0.0]]
  UpperCAmelCase			,	UpperCAmelCase			:      Any			=			matrix[1][1], matrix[0][0]
  UpperCAmelCase			,	UpperCAmelCase			:      Union[str, Any]			=			-matrix[1][0], -matrix[0][1]

  # Calculate the inverse of the matrix
  return [
      [(float(d(UpperCamelCase		)		) / determinant) or 0.0 for n in row] for row in swapped_matrix
  ]
 elif (
     len(UpperCamelCase		) == 3
     and len(matrix[0]		) == 3
     and len(matrix[1]		) == 3
     and len(matrix[2]		) == 3
 ):
  # Calculate the determinant of the matrix using Sarrus rule
  UpperCAmelCase			:      str			=			float(
      (
          (d(matrix[0][0]		) * d(matrix[1][1]		) * d(matrix[2][2]		))
          + (d(matrix[0][1]		) * d(matrix[1][2]		) * d(matrix[2][0]		))
          + (d(matrix[0][2]		) * d(matrix[1][0]		) * d(matrix[2][1]		))
      )
      - (
          (d(matrix[0][2]		) * d(matrix[1][1]		) * d(matrix[2][0]		))
          + (d(matrix[0][1]		) * d(matrix[1][0]		) * d(matrix[2][2]		))
          + (d(matrix[0][0]		) * d(matrix[1][2]		) * d(matrix[2][1]		))
      )		)
  if determinant == 0:
   raise ValueError("""This matrix has no inverse."""		)

  # Creating cofactor matrix
  UpperCAmelCase			:      Optional[int]			=			[
      [d(0.0		), d(0.0		), d(0.0		)],
      [d(0.0		), d(0.0		), d(0.0		)],
      [d(0.0		), d(0.0		), d(0.0		)],
  ]
  UpperCAmelCase			:      str			=			(d(matrix[1][1]		) * d(matrix[2][2]		)) - (
      d(matrix[1][2]		) * d(matrix[2][1]		)
  )
  UpperCAmelCase			:      List[str]			=			-(
      (d(matrix[1][0]		) * d(matrix[2][2]		)) - (d(matrix[1][2]		) * d(matrix[2][0]		))
  )
  UpperCAmelCase			:      Optional[int]			=			(d(matrix[1][0]		) * d(matrix[2][1]		)) - (
      d(matrix[1][1]		) * d(matrix[2][0]		)
  )
  UpperCAmelCase			:      Optional[int]			=			-(
      (d(matrix[0][1]		) * d(matrix[2][2]		)) - (d(matrix[0][2]		) * d(matrix[2][1]		))
  )
  UpperCAmelCase			:      str			=			(d(matrix[0][0]		) * d(matrix[2][2]		)) - (
      d(matrix[0][2]		) * d(matrix[2][0]		)
  )
  UpperCAmelCase			:      Union[str, Any]			=			-(
      (d(matrix[0][0]		) * d(matrix[2][1]		)) - (d(matrix[0][1]		) * d(matrix[2][0]		))
  )
  UpperCAmelCase			:      Dict			=			(d(matrix[0][1]		) * d(matrix[1][2]		)) - (
      d(matrix[0][2]		) * d(matrix[1][1]		)
  )
  UpperCAmelCase			:      Optional[Any]			=			-(
      (d(matrix[0][0]		) * d(matrix[1][2]		)) - (d(matrix[0][2]		) * d(matrix[1][0]		))
  )
  UpperCAmelCase			:      str			=			(d(matrix[0][0]		) * d(matrix[1][1]		)) - (
      d(matrix[0][1]		) * d(matrix[1][0]		)
  )

  # Transpose the cofactor matrix (Adjoint matrix)
  UpperCAmelCase			:      str			=			array(UpperCamelCase		)
  for i in range(3		):
   for j in range(3		):
    UpperCAmelCase			:      Any			=			cofactor_matrix[j][i]

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
  UpperCAmelCase			:      Tuple			=			array(UpperCamelCase		)
  for i in range(3		):
   for j in range(3		):
    inverse_matrix[i][j] /= d(UpperCamelCase		)

        # Calculate the inverse of the matrix
  return [[float(d(UpperCamelCase		)		) or 0.0 for n in row] for row in inverse_matrix]
 raise ValueError("""Please provide a matrix of size 2x2 or 3x3."""		)
