


"""simple docstring"""



from __future__ import annotations

import time
from collections.abc import Sequence
from random import randint

from matplotlib import pyplot as plt






def       lowerCamelCase					(a_						:int				,				a_						:str				,				a_						:Optional[int])     ->							List[Any]:






							if not arr:
														return None, None, 0
							if low == high:
														return low, high, arr[low]

							lowercase		:Union[str, Any]       							=				(low + high) // 2
							lowercase		:List[str]       							=				max_subarray(__SCREAMING_SNAKE_CASE				,				__SCREAMING_SNAKE_CASE				,				__SCREAMING_SNAKE_CASE)
							lowercase		:List[Any]       							=				max_subarray(__SCREAMING_SNAKE_CASE				,				mid + 1				,				__SCREAMING_SNAKE_CASE)
							lowercase		:Optional[int]       							=				max_cross_sum(__SCREAMING_SNAKE_CASE				,				__SCREAMING_SNAKE_CASE				,				__SCREAMING_SNAKE_CASE				,				__SCREAMING_SNAKE_CASE)
							if left_sum >= right_sum and left_sum >= cross_sum:
														return left_low, left_high, left_sum
							elif right_sum >= left_sum and right_sum >= cross_sum:
														return right_low, right_high, right_sum
							return cross_left, cross_right, cross_sum






def       lowerCamelCase					(a_						:Optional[Any]				,				a_						:Optional[Any]				,				a_						:List[str]				,				a_						:Any)     ->							Optional[int]:
							lowercase		:List[str]       							=				float('''-inf'''), -1
							lowercase		:List[str]       							=				float('''-inf'''), -1

							lowercase		:int | float       							=				0
							for i in range(__SCREAMING_SNAKE_CASE				,				low - 1				,				-1):
														summ += arr[i]
														if summ > left_sum:
																					lowercase		:List[str]       							=				summ
																					lowercase		:Optional[Any]       							=				i

							lowercase		:Tuple       							=				0
							for i in range(mid + 1				,				high + 1):
														summ += arr[i]
														if summ > right_sum:
																					lowercase		:Tuple       							=				summ
																					lowercase		:Optional[Any]       							=				i

							return max_left, max_right, (left_sum + right_sum)






def       lowerCamelCase					(a_						:Union[str, Any])     ->							Dict:
							lowercase		:Union[str, Any]       							=				[randint(1				,				__SCREAMING_SNAKE_CASE) for _ in range(__SCREAMING_SNAKE_CASE)]
							lowercase		:int       							=				time.time()
							max_subarray(__SCREAMING_SNAKE_CASE				,				0				,				input_size - 1)
							lowercase		:Optional[Any]       							=				time.time()
							return end - start






def       lowerCamelCase					()     ->							str:
							lowercase		:Dict       							=				[10, 100, 1000, 1_0000, 5_0000, 10_0000, 20_0000, 30_0000, 40_0000, 50_0000]
							lowercase		:Optional[Any]       							=				[time_max_subarray(__SCREAMING_SNAKE_CASE) for input_size in input_sizes]
							print('''No of Inputs\t\tTime Taken''')
							for input_size, runtime in zip(__SCREAMING_SNAKE_CASE				,				__SCREAMING_SNAKE_CASE):
														print(__SCREAMING_SNAKE_CASE				,				'''\t\t'''				,				__SCREAMING_SNAKE_CASE)
							plt.plot(__SCREAMING_SNAKE_CASE				,				__SCREAMING_SNAKE_CASE)
							plt.xlabel('''Number of Inputs''')
							plt.ylabel('''Time taken in seconds''')
							plt.show()


if __name__ == "__main__":
	from doctest import testmod

	testmod()





"""simple docstring"""



from __future__ import annotations

from decimal import Decimal

from numpy import array






def       lowerCamelCase					(a_						:list[list[float]])     ->							list[list[float]]:
       lowercase		:List[str]       							=				Decimal

       # Check if the provided matrix has 2 rows and 2 columns
       # since this implementation only works for 2x2 matrices
       if len(a_) == 2 and len(matrix[0]) == 2 and len(matrix[1]) == 2:
              # Calculate the determinant of the matrix
              lowercase		:List[str]       							=				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
              lowercase		:Optional[Any]       							=				[[0.0, 0.0], [0.0, 0.0]]
              lowercase							,  lowercase		:List[Any]       							=				matrix[1][1], matrix[0][0]
              lowercase							,  lowercase		:Union[str, Any]       							=				-matrix[1][0], -matrix[0][1]

              # Calculate the inverse of the matrix
              return [
                  [(float(d(a_)) / determinant) or 0.0 for n in row] for row in swapped_matrix
              ]
       elif (
           len(a_) == 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
              lowercase		:Any       							=				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
              lowercase		:Optional[Any]       							=				[
                  [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)],
              ]
              lowercase		:Optional[int]       							=				(d(matrix[1][1]) * d(matrix[2][2])) - (
                  d(matrix[1][2]) * d(matrix[2][1])
              )
              lowercase		:str       							=				-(
                  (d(matrix[1][0]) * d(matrix[2][2])) - (d(matrix[1][2]) * d(matrix[2][0]))
              )
              lowercase		:Union[str, Any]       							=				(d(matrix[1][0]) * d(matrix[2][1])) - (
                  d(matrix[1][1]) * d(matrix[2][0])
              )
              lowercase		:Union[str, Any]       							=				-(
                  (d(matrix[0][1]) * d(matrix[2][2])) - (d(matrix[0][2]) * d(matrix[2][1]))
              )
              lowercase		:Union[str, Any]       							=				(d(matrix[0][0]) * d(matrix[2][2])) - (
                  d(matrix[0][2]) * d(matrix[2][0])
              )
              lowercase		:List[str]       							=				-(
                  (d(matrix[0][0]) * d(matrix[2][1])) - (d(matrix[0][1]) * d(matrix[2][0]))
              )
              lowercase		:Union[str, Any]       							=				(d(matrix[0][1]) * d(matrix[1][2])) - (
                  d(matrix[0][2]) * d(matrix[1][1])
              )
              lowercase		:Union[str, Any]       							=				-(
                  (d(matrix[0][0]) * d(matrix[1][2])) - (d(matrix[0][2]) * d(matrix[1][0]))
              )
              lowercase		:Any       							=				(d(matrix[0][0]) * d(matrix[1][1])) - (
                  d(matrix[0][1]) * d(matrix[1][0])
              )

              # Transpose the cofactor matrix (Adjoint matrix)
              lowercase		:Union[str, Any]       							=				array(a_)
              for i in range(3):
                     for j in range(3):
                            lowercase		:Any       							=				cofactor_matrix[j][i]

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

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

