





from __future__ import annotations

import numpy as np

def       A__(		__lowerCAmelCase ):
				_snake_case :			int  						=   np.shape(__lowerCAmelCase )
				if rows != columns:
								_snake_case :			Tuple  						=   (
								    '\'table\' has to be of square shaped array but got a '
								    F'''{rows}x{columns} array:\n{table}'''
								)
								raise ValueError(__lowerCAmelCase )

				_snake_case :			Union[str, Any]  						=   np.zeros((rows, columns) )
				_snake_case :			List[Any]  						=   np.zeros((rows, columns) )
				for i in range(__lowerCAmelCase ):
								for j in range(__lowerCAmelCase ):
												_snake_case :			Optional[int]  						=   sum(lower[i][k] * upper[k][j] for k in range(__lowerCAmelCase ) )
												if upper[j][j] == 0:
																raise ArithmeticError('No LU decomposition exists' )
												_snake_case :			Union[str, Any]  						=   (table[i][j] - total) / upper[j][j]
								_snake_case :			int  						=   1
								for j in range(__lowerCAmelCase	,			__lowerCAmelCase ):
												_snake_case :			Optional[Any]  						=   sum(lower[i][k] * upper[k][j] for k in range(__lowerCAmelCase ) )
												_snake_case :			List[str]  						=   table[i][j] - total
				return lower, upper


if __name__ == "__main__":
		import doctest

		doctest.testmod()













from __future__ import annotations

def       A__(		__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase ):
				_snake_case :			Dict  						=   list(range(len(__lowerCAmelCase ) ) )
				_snake_case :			Optional[int]  						=   [v / w for v, w in zip(__lowerCAmelCase	,			__lowerCAmelCase )]
				index.sort(key=lambda __lowerCAmelCase : ratio[i]	,			reverse=__lowerCAmelCase )

				_snake_case :			float  						=   0
				_snake_case :			list[float]  						=   [0] * len(__lowerCAmelCase )
				for i in index:
								if weight[i] <= capacity:
												_snake_case :			List[Any]  						=   1
												max_value += value[i]
												capacity -= weight[i]
								else:
												_snake_case :			Any  						=   capacity / weight[i]
												max_value += value[i] * capacity / weight[i]
												break

				return max_value, fractions


if __name__ == "__main__":
		import doctest

		doctest.testmod()






