



"""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"""
# Copyright 2022 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

from pathlib import Path

from .config_args import default_config_file, load_config_from_file
from .config_utils import SubcommandHelpFormatter


__a           =							"Update an existing config file with the latest defaults while maintaining the old configuration."
def   A_    (     _lowercase      ):







						'''simple docstring'''


						snake_case_					:int		=     args.config_file
						if config_file is None and Path(_lowercase      ).exists():
												snake_case_					:str		=     default_config_file
						elif not Path(_lowercase      ).exists():
												raise ValueError(f"""The passed config file located at {config_file} doesn't exist."""      )
						snake_case_					:str		=     load_config_from_file(_lowercase      )

						if config_file.endswith(""".json"""      ):
												config.to_json_file(_lowercase      )
						else:
												config.to_yaml_file(_lowercase      )
						return config_file
def   A_    (     _lowercase,   _lowercase      ):







						'''simple docstring'''


						snake_case_					:Any		=     parser.add_parser("""update""",   parents=_lowercase,   help=_lowercase,   formatter_class=_lowercase      )
						parser.add_argument(
						    """--config_file""",   default=_lowercase,   help=(
						        """The path to the config file to update. Will default to a file named default_config.yaml in the cache """
						        """location, which is the content of the environment `HF_HOME` suffixed with 'accelerate', or if you don't have """
						        """such an environment variable, your cache directory ('~/.cache' or the content of `XDG_CACHE_HOME`) suffixed """
						        """with 'huggingface'."""
						    ),   )

						parser.set_defaults(func=_lowercase      )
						return parser

def   A_    (     _lowercase      ):







						'''simple docstring'''


						snake_case_					:str		=     update_config(_lowercase      )
						print(f"""Sucessfully updated the configuration file at {config_file}."""      )
