

from __future__ import annotations

from decimal import Decimal

from numpy import array




def 			UpperCAmelCase__				(			_A      : list[list[float]]							):





  '''simple docstring'''







  a__  =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
    a__  =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
    a__  =[[0.0, 0.0], [0.0, 0.0]]
    a__,      a__  =matrix[1][1], matrix[0][0]
    a__,      a__  =-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
    a__  =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
    a__  =[
        [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							)],
    ]
    a__  =(d(matrix[1][1]							) * d(matrix[2][2]							)) - (
        d(matrix[1][2]							) * d(matrix[2][1]							)
    )
    a__  =-(
        (d(matrix[1][0]							) * d(matrix[2][2]							)) - (d(matrix[1][2]							) * d(matrix[2][0]							))
    )
    a__  =(d(matrix[1][0]							) * d(matrix[2][1]							)) - (
        d(matrix[1][1]							) * d(matrix[2][0]							)
    )
    a__  =-(
        (d(matrix[0][1]							) * d(matrix[2][2]							)) - (d(matrix[0][2]							) * d(matrix[2][1]							))
    )
    a__  =(d(matrix[0][0]							) * d(matrix[2][2]							)) - (
        d(matrix[0][2]							) * d(matrix[2][0]							)
    )
    a__  =-(
        (d(matrix[0][0]							) * d(matrix[2][1]							)) - (d(matrix[0][1]							) * d(matrix[2][0]							))
    )
    a__  =(d(matrix[0][1]							) * d(matrix[1][2]							)) - (
        d(matrix[0][2]							) * d(matrix[1][1]							)
    )
    a__  =-(
        (d(matrix[0][0]							) * d(matrix[1][2]							)) - (d(matrix[0][2]							) * d(matrix[1][0]							))
    )
    a__  =(d(matrix[0][0]							) * d(matrix[1][1]							)) - (
        d(matrix[0][1]							) * d(matrix[1][0]							)
    )

    # Transpose the cofactor matrix (Adjoint matrix)
    a__  =array(_A							)
    for i in range(3							):
      for j in range(3							):
        a__  =cofactor_matrix[j][i]

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
    a__  =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.'''							)



def 			UpperCAmelCase__				(			_A      : dict							):





  '''simple docstring'''







  a__  =set()
  # To detect a back edge, keep track of vertices currently in the recursion stack
  a__  =set()
  return any(
      node not in visited and depth_first_search(_A	,      _A	,      _A	,      _A							)
      for node in graph							)




def 			UpperCAmelCase__				(			_A      : dict	,      _A      : int	,      _A      : set	,      _A      : set							):





  '''simple docstring'''







  visited.add(_A							)
  rec_stk.add(_A							)

  for node in graph[vertex]:
    if node not in visited:
      if depth_first_search(_A	,      _A	,      _A	,      _A							):
        return True
    elif node in rec_stk:
      return True

    # The node needs to be removed from recursion stack before function ends
  rec_stk.remove(_A							)
  return False


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

       testmod()
