


from typing import TypeVar

from .arrow_dataset import Dataset, _split_by_node_map_style_dataset
from .iterable_dataset import IterableDataset, _split_by_node_iterable_dataset


lowerCAmelCase					 =	TypeVar('''DatasetType''', Dataset, IterableDataset)







def  _lowerCamelCase(			lowercase__     ,				lowercase__     ,				lowercase__			)		->			DatasetType:

		'''simple docstring'''







		if isinstance(lowercase__     ,				lowercase__			):
				return _split_by_node_map_style_dataset(lowercase__     ,				rank=lowercase__     ,				world_size=lowercase__			)
		else:
				return _split_by_node_iterable_dataset(lowercase__     ,				rank=lowercase__     ,				world_size=lowercase__			)










def  _lowerCamelCase(			lowercase__			)		->			str:

		'''simple docstring'''







		if len(lowercase__			) == 0 or not all(len(lowercase__			) == 2 for pair in coordinates			):
				raise ValueError('The program cannot work out a fitting polynomial.'			)

		if len({tuple(lowercase__			) for pair in coordinates}			) != len(lowercase__			):
				raise ValueError('The program cannot work out a fitting polynomial.'			)

		__lowercase=    {x for x, _ in coordinates}
		if len(lowercase__			) == 1:
				return F'x={coordinates[0][0]}'

		if len(lowercase__			) != len(lowercase__			):
				raise ValueError('The program cannot work out a fitting polynomial.'			)

		__lowercase=    len(lowercase__			)

		__lowercase=    0
		__lowercase=    []
		# put the x and x to the power values in a matrix
		while count_of_line < x:
				__lowercase=    0
				__lowercase=    coordinates[count_of_line][0]
				__lowercase=    []
				while count_in_line < x:
						count_line.append(a ** (x - (count_in_line + 1))			)
						count_in_line += 1
				matrix.append(lowercase__			)
				count_of_line += 1

		__lowercase=    0
		# put the y values into a vector
		__lowercase=    []
		while count_of_line < x:
				vector.append(coordinates[count_of_line][1]			)
				count_of_line += 1

		__lowercase=    0

		while count < x:
				__lowercase=    0
				while zahlen < x:
						if count == zahlen:
								zahlen += 1
						if zahlen == x:
								break
						__lowercase=    matrix[zahlen][count] / matrix[count][count]
						for counting_columns, item in enumerate(matrix[count]			):
								# manipulating all the values in the matrix
								matrix[zahlen][counting_columns] -= item * bruch
						# manipulating the values in the vector
						vector[zahlen] -= vector[count] * bruch
						zahlen += 1
				count += 1

		__lowercase=    0
		# make solutions
		__lowercase=    []
		while count < x:
				solution.append(str(vector[count] / matrix[count][count]			)			)
				count += 1

		__lowercase=    0
		__lowercase=    'f(x)='

		while count < x:
				__lowercase=    solution[count].split('E'			)
				if len(lowercase__			) > 1:
						__lowercase=    F'{remove_e[0]}*10^{remove_e[1]}'
				solved += F'x^{x - (count + 1)}*{solution[count]}'
				if count + 1 != x:
						solved += "+"
				count += 1

		return solved


if __name__ == "__main__":
	print(points_to_polynomial([]))
	print(points_to_polynomial([[]]))
	print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
	print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
	print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
	print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
	print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
	print(points_to_polynomial([[1, 3], [2, 6], [3, 1_1]]))
	print(points_to_polynomial([[1, -3], [2, -6], [3, -1_1]]))
	print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))






