



"""simple docstring"""
def   A_    (     _lowercase      ):







						'''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."""      )

						snake_case_					:Dict		=     {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."""      )

						snake_case_					:Tuple		=     len(_lowercase      )

						snake_case_					:Union[str, Any]		=     0
						snake_case_					:list[list[float]]		=     []
						# put the x and x to the power values in a matrix
						while count_of_line < x:
												snake_case_					:List[Any]		=     0
												snake_case_					:Tuple		=     coordinates[count_of_line][0]
												snake_case_					:list[float]		=     []
												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

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

						snake_case_					:Dict		=     0

						while count < x:
												snake_case_					:int		=     0
												while zahlen < x:
																		if count == zahlen:
																								zahlen += 1
																		if zahlen == x:
																								break
																		snake_case_					:int		=     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

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

						snake_case_					:Union[str, Any]		=     0
						snake_case_					:Union[str, Any]		=     """f(x)="""

						while count < x:
												snake_case_					:list[str]		=     solution[count].split("""E"""      )
												if len(_lowercase      ) > 1:
																		snake_case_					: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]]))


"""simple docstring"""


from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available


__A					=			{
    'configuration_donut_swin': ['DONUT_SWIN_PRETRAINED_CONFIG_ARCHIVE_MAP', 'DonutSwinConfig'],
    'processing_donut': ['DonutProcessor'],
}

try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			__A					=			[
			    'DONUT_SWIN_PRETRAINED_MODEL_ARCHIVE_LIST',
			    'DonutSwinModel',
			    'DonutSwinPreTrainedModel',
			]

try:
			if not is_vision_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			__A					=			['DonutFeatureExtractor']
			__A					=			['DonutImageProcessor']


if TYPE_CHECKING:
			from .configuration_donut_swin import DONUT_SWIN_PRETRAINED_CONFIG_ARCHIVE_MAP, DonutSwinConfig
			from .processing_donut import DonutProcessor

			try:
						if not is_torch_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_donut_swin import (
						    DONUT_SWIN_PRETRAINED_MODEL_ARCHIVE_LIST,
						    DonutSwinModel,
						    DonutSwinPreTrainedModel,
						)

			try:
						if not is_vision_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .feature_extraction_donut import DonutFeatureExtractor
						from .image_processing_donut import DonutImageProcessor

else:
			import sys

			__A					=			_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)



