




"""simple docstring"""




from __future__ import annotations

from collections.abc import Callable

__UpperCAmelCase =				list[list[float | int]]
def   lowerCAmelCase						(					__UpperCamelCase							,    __UpperCamelCase      ):
 '''simple docstring'''





 UpperCAmelCase__					:  int					   =					len(a_      )
 UpperCAmelCase__					:  Matrix					   =					[[0 for _ in range(size + 1      )] for _ in range(a_      )]
 UpperCAmelCase__					:  int
 UpperCAmelCase__					:  int
 UpperCAmelCase__					:  int
 UpperCAmelCase__					:  int
 UpperCAmelCase__					:  int
 UpperCAmelCase__					:  float

 for row in range(a_      ):
  for col in range(a_      ):
   UpperCAmelCase__					:  Any					   =					matrix[row][col]

  UpperCAmelCase__					:  Optional[Any]					   =					vector[row][0]

 UpperCAmelCase__					:  int					   =					0
 UpperCAmelCase__					:  int					   =					0
 while row < size and col < size:
  # pivoting
  UpperCAmelCase__					:  int					   =					max((abs(augmented[rowa][col]      ), rowa) for rowa in range(a_							,    a_      )      )[
      1
  ]
  if augmented[pivot_row][col] == 0:
   col += 1
   continue
  else:
   UpperCAmelCase__					:  str					   =					augmented[pivot_row], augmented[row]

  for rowa in range(row + 1							,    a_      ):
   UpperCAmelCase__					:  Tuple					   =					augmented[rowa][col] / augmented[row][col]
   UpperCAmelCase__					:  Union[str, Any]					   =					0
   for cola in range(col + 1							,    size + 1      ):
    augmented[rowa][cola] -= augmented[row][cola] * ratio

  row += 1
  col += 1

 # back substitution
 for col in range(1							,    a_      ):
  for row in range(a_      ):
   UpperCAmelCase__					:  List[Any]					   =					augmented[row][col] / augmented[col][col]
   for cola in range(a_							,    size + 1      ):
    augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
 return [
     [round(augmented[row][size] / augmented[row][row]							,    10      )] for row in range(a_      )
 ]
def   lowerCAmelCase						(					__UpperCamelCase      ):
 '''simple docstring'''





 UpperCAmelCase__					:  int					   =					len(a_      )
 UpperCAmelCase__					:  Matrix					   =					[[0 for _ in range(a_      )] for _ in range(a_      )]
 UpperCAmelCase__					:  Matrix					   =					[[0] for _ in range(a_      )]
 UpperCAmelCase__					:  Matrix
 UpperCAmelCase__					:  int
 UpperCAmelCase__					:  int
 UpperCAmelCase__					:  int

 for x_val, y_val in enumerate(a_      ):
  for col in range(a_      ):
   UpperCAmelCase__					:  str					   =					(x_val + 1) ** (size - col - 1)
  UpperCAmelCase__					:  Dict					   =					y_val

 UpperCAmelCase__					:  Union[str, Any]					   =					solve(a_							,    a_      )

 def interpolated_func(__UpperCamelCase      ) -> int:
  return sum(
      round(coeffs[x_val][0]      ) * (var ** (size - x_val - 1))
      for x_val in range(a_      )      )

 return interpolated_func
def   lowerCAmelCase						(					__UpperCamelCase      ):
 '''simple docstring'''





 return (
     1
     - variable
     + variable**2
     - variable**3
     + variable**4
     - variable**5
     + variable**6
     - variable**7
     + variable**8
     - variable**9
     + variable**10
 )
def   lowerCAmelCase						(					__UpperCamelCase = question_function							,    __UpperCamelCase = 10      ):
 '''simple docstring'''





 UpperCAmelCase__					:  list[int]					   =					[func(a_      ) for x_val in range(1							,    order + 1      )]

 UpperCAmelCase__					:  list[Callable[[int], int]]					   =					[
     interpolate(data_points[:max_coeff]      ) for max_coeff in range(1							,    order + 1      )
 ]

 UpperCAmelCase__					:  int					   =					0
 UpperCAmelCase__					:  Callable[[int], int]
 UpperCAmelCase__					:  int

 for poly in polynomials:
  UpperCAmelCase__					:  Tuple					   =					1
  while func(a_      ) == poly(a_      ):
   x_val += 1

  ret += poly(a_      )

 return ret


if __name__ == "__main__":
      print(F"{solution() = }")








"""simple docstring"""




from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


__UpperCAmelCase =				{
    'configuration_table_transformer': [
        'TABLE_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'TableTransformerConfig',
        'TableTransformerOnnxConfig',
    ]
}

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      __UpperCAmelCase =				[
          'TABLE_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST',
          'TableTransformerForObjectDetection',
          'TableTransformerModel',
          'TableTransformerPreTrainedModel',
      ]


if TYPE_CHECKING:
      from .configuration_table_transformer import (
          TABLE_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
          TableTransformerConfig,
          TableTransformerOnnxConfig,
      )

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_table_transformer import (
                TABLE_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
                TableTransformerForObjectDetection,
                TableTransformerModel,
                TableTransformerPreTrainedModel,
            )

else:
      import sys

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





