

def 				_UpperCAmelCase							(	a__):

			'''simple docstring'''



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

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

			a_	:	Optional[int]          =   {x for x, _ in coordinates}
			if len(a__) == 1:
						return f'''x={coordinates[0][0]}'''

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

			a_	:	Any          =   len(a__)

			a_	:	Any          =   0
			a_	:	list[list[float]]          =   []
			# put the x and x to the power values in a matrix
			while count_of_line < x:
						a_	:	str          =   0
						a_	:	List[str]          =   coordinates[count_of_line][0]
						a_	:	list[float]          =   []
						while count_in_line < x:
									count_line.append(a ** (x - (count_in_line + 1)))
									count_in_line += 1
						matrix.append(a__)
						count_of_line += 1

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

			a_	:	List[str]          =   0

			while count < x:
						a_	:	str          =   0
						while zahlen < x:
									if count == zahlen:
												zahlen += 1
									if zahlen == x:
												break
									a_	:	Optional[Any]          =   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

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

			a_	:	Dict          =   0
			a_	:	str          =   """f(x)="""

			while count < x:
						a_	:	list[str]          =   solution[count].split("""E""")
						if len(a__) > 1:
									a_	:	List[Any]          =   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, 11]]))
	print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
	print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))





from dataclasses import dataclass
from typing import Callable, Optional

import datasets



@dataclass
class 					A__(datasets.BuilderConfig       ):
						"""simple docstring"""






						_A						:							Optional[Callable]									= None
						_A						:							Optional[dict]									= None
						_A						:							Optional[datasets.Features]									= None





						def  UpperCamelCase__				(						self						)    ->   Tuple:
									assert self.generator is not None, "generator must be specified"

									if self.gen_kwargs is None:
												a_	:	Tuple          =   {}







class 					A__(datasets.GeneratorBasedBuilder       ):
						"""simple docstring"""






						_A						:							Dict									= GeneratorConfig





						def  UpperCamelCase__				(						self						)    ->   List[Any]:
									return datasets.DatasetInfo(features=self.config.features						)





						def  UpperCamelCase__				(						self     ,			_lowercase						)    ->   List[Any]:
									return [datasets.SplitGenerator(name=datasets.Split.TRAIN     ,			gen_kwargs=self.config.gen_kwargs						)]





						def  UpperCamelCase__				(						self     ,			**_lowercase						)    ->   Tuple:
									for idx, ex in enumerate(self.config.generator(**_lowercase						)						):
												yield idx, ex


