
from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray



def        UpperCamelCase    (							lowerCAmelCase__ ,			lowerCAmelCase__ ,			lowerCAmelCase__ ,			lowerCAmelCase__ ,			):
					'''simple docstring'''
					lowercase	,						lowercase							=						coefficient_matrix.shape
					lowercase	,						lowercase							=						constant_matrix.shape

					if rowsa != colsa:
										lowercase							=						f'Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}'
										raise ValueError(lowerCAmelCase__		)

					if colsa != 1:
										lowercase							=						f'Constant matrix must be nx1 but received {rowsa}x{colsa}'
										raise ValueError(lowerCAmelCase__		)

					if rowsa != rowsa:
										lowercase							=						(
										    '''Coefficient and constant matrices dimensions must be nxn and nx1 but '''
										    f'received {rowsa}x{colsa} and {rowsa}x{colsa}'
										)
										raise ValueError(lowerCAmelCase__		)

					if len(lowerCAmelCase__		) != rowsa:
										lowercase							=						(
										    '''Number of initial values must be equal to number of rows in coefficient '''
										    f'matrix but received {len(lowerCAmelCase__		)} and {rowsa}'
										)
										raise ValueError(lowerCAmelCase__		)

					if iterations <= 0:
										raise ValueError('''Iterations must be at least 1'''		)

					lowercase							=						np.concatenate(
					    (coefficient_matrix, constant_matrix) ,			axis=1		)

					lowercase	,						lowercase							=						table.shape

					strictly_diagonally_dominant(lowerCAmelCase__		)

					# Iterates the whole matrix for given number of times
					for _ in range(lowerCAmelCase__		):
										lowercase							=						[]
										for row in range(lowerCAmelCase__		):
															lowercase							=						0
															for col in range(lowerCAmelCase__		):
																				if col == row:
																									lowercase							=						table[row][col]
																				elif col == cols - 1:
																									lowercase							=						table[row][col]
																				else:
																									temp += (-1) * table[row][col] * init_val[col]
															lowercase							=						(temp + val) / denom
															new_val.append(lowerCAmelCase__		)
										lowercase							=						new_val

					return [float(lowerCAmelCase__		) for i in new_val]



def        UpperCamelCase    (							lowerCAmelCase__		):
					'''simple docstring'''
					lowercase	,						lowercase							=						table.shape

					lowercase							=						True

					for i in range(0 ,			lowerCAmelCase__		):
										lowercase							=						0
										for j in range(0 ,			cols - 1		):
															if i == j:
																				continue
															else:
																				total += table[i][j]

										if table[i][i] <= total:
															raise ValueError('''Coefficient matrix is not strictly diagonally dominant'''		)

					return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
							import doctest

							doctest.testmod()





def    lowerCAmelCase_ (     __A,  __A							)     ->				None:







      '''simple docstring'''


      UpperCAmelCase__								=  len(__A							)
      print("The following activities are selected:"							)

      # The first activity is always selected
      UpperCAmelCase__								=  0
      print(__A,  end=","							)

      # Consider rest of the activities
      for j in range(__A							):
            # If this activity has start time greater than
            # or equal to the finish time of previously
            # selected activity, then select it
            if start[j] >= finish[i]:
                  print(__A,  end=","							)
                  UpperCAmelCase__								=  j


if __name__ == "__main__":
      import doctest

      doctest.testmod()

      UpperCamelCase__											=					[1, 3, 0, 5, 8, 5]
      UpperCamelCase__											=					[2, 4, 6, 7, 9, 9]
      print_max_activities(start, finish)



