

import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_torch


if is_torch_available():
 import torch

 from transformers.generation import DisjunctiveConstraint







@require_torch
class 	__UpperCamelCase    (    unittest.TestCase						):

  def __lowerCamelCase		(		self      ):
      '''simple docstring'''

      _lowerCAmelCase       :   Optional[int]  =    [[1, 2, 4], [1, 2, 3, 4]]
      _lowerCAmelCase       :   Tuple  =    DisjunctiveConstraint(UpperCamelCase_      )
      self.assertTrue(isinstance(dc.token_ids    ,UpperCamelCase_      )      )

      with self.assertRaises(UpperCamelCase_      ):
          DisjunctiveConstraint(torch.LongTensor([[1, 2, 4], [1, 2, 3]]      )      )

      with self.assertRaises(UpperCamelCase_      ):
          DisjunctiveConstraint([torch.LongTensor([1, 2, 4]      ), torch.LongTensor([1, 2, 3, 4, 5]      )]      )

  def __lowerCamelCase		(		self      ):
      '''simple docstring'''

      _lowerCAmelCase       :   Union[str, Any]  =    [[1, 2], [1, 2, 3, 4]]

      with self.assertRaises(UpperCamelCase_      ):
          DisjunctiveConstraint(UpperCamelCase_      )  # fails here

  def __lowerCamelCase		(		self      ):
      '''simple docstring'''

      _lowerCAmelCase       :   List[Any]  =    [[1, 2, 3], [1, 2, 4]]

      _lowerCAmelCase       :   Optional[int]  =    DisjunctiveConstraint(UpperCamelCase_      )

      _lowerCAmelCase       :   Any  =    dc.update(1      )
      _lowerCAmelCase       :   Dict  =    stepped is True and completed is False and reset is False
      self.assertTrue(UpperCamelCase_      )
      self.assertTrue(not dc.completed      )
      self.assertTrue(dc.current_seq == [1]      )

      _lowerCAmelCase       :   Dict  =    dc.update(2      )
      _lowerCAmelCase       :   int  =    stepped is True and completed is False and reset is False
      self.assertTrue(UpperCamelCase_      )
      self.assertTrue(not dc.completed      )
      self.assertTrue(dc.current_seq == [1, 2]      )

      _lowerCAmelCase       :   Optional[int]  =    dc.update(3      )
      _lowerCAmelCase       :   str  =    stepped is True and completed is True and reset is False
      self.assertTrue(UpperCamelCase_      )
      self.assertTrue(dc.completed      )  # Completed!
      self.assertTrue(dc.current_seq == [1, 2, 3]      )







  def __lowerCamelCase		(		self      ):
      '''simple docstring'''

      _lowerCAmelCase       :   str  =    [[1, 2, 3], [1, 2, 4, 5], [1, 2, 5]]

      _lowerCAmelCase       :   Union[str, Any]  =    DisjunctiveConstraint(UpperCamelCase_      )

      _lowerCAmelCase       :   Dict  =    dc.update(1      )
      self.assertTrue(not dc.completed      )
      self.assertTrue(dc.current_seq == [1]      )

      _lowerCAmelCase       :   List[str]  =    dc.update(2      )
      self.assertTrue(not dc.completed      )
      self.assertTrue(dc.current_seq == [1, 2]      )

      _lowerCAmelCase       :   int  =    dc.update(4      )
      self.assertTrue(not dc.completed      )
      self.assertTrue(dc.current_seq == [1, 2, 4]      )

      _lowerCAmelCase       :   List[Any]  =    dc.update(5      )
      self.assertTrue(dc.completed      )  # Completed!
      self.assertTrue(dc.current_seq == [1, 2, 4, 5]      )

      dc.reset()

      _lowerCAmelCase       :   Dict  =    dc.update(1      )
      self.assertTrue(not dc.completed      )
      self.assertTrue(dc.remaining() == 3      )
      self.assertTrue(dc.current_seq == [1]      )

      _lowerCAmelCase       :   Optional[Any]  =    dc.update(2      )
      self.assertTrue(not dc.completed      )
      self.assertTrue(dc.remaining() == 2      )
      self.assertTrue(dc.current_seq == [1, 2]      )

      _lowerCAmelCase       :   Any  =    dc.update(5      )
      self.assertTrue(dc.completed      )  # Completed!
      self.assertTrue(dc.remaining() == 0      )
      self.assertTrue(dc.current_seq == [1, 2, 5]      )








"""simple docstring"""






from __future__ import annotations

from collections.abc import Callable

_lowerCAmelCase						=		list[list[float | int]]

def 		lowerCamelCase__		(					_lowerCamelCase ,   _lowerCamelCase   ):

    '''simple docstring'''



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

    for row in range(_lowerCamelCase   ):
        for col in range(_lowerCamelCase   ):
            _lowerCAmelCase       :   Union[str, Any]  =    matrix[row][col]

        _lowerCAmelCase       :   Tuple  =    vector[row][0]

    _lowerCAmelCase       :   Dict  =    0
    _lowerCAmelCase       :   Any  =    0
    while row < size and col < size:
        # pivoting
        _lowerCAmelCase       :   Optional[int]  =    max((abs(augmented[rowa][col]   ), rowa) for rowa in range(_lowerCamelCase ,   _lowerCamelCase   )   )[
            1
        ]
        if augmented[pivot_row][col] == 0:
            col += 1
            continue
        else:
            _lowerCAmelCase,					_lowerCAmelCase       :   Tuple  =    augmented[pivot_row], augmented[row]

        for rowa in range(row + 1 ,   _lowerCamelCase   ):
            _lowerCAmelCase       :   Dict  =    augmented[rowa][col] / augmented[row][col]
            _lowerCAmelCase       :   Optional[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 ,   _lowerCamelCase   ):
        for row in range(_lowerCamelCase   ):
            _lowerCAmelCase       :   int  =    augmented[row][col] / augmented[col][col]
            for cola in range(_lowerCamelCase ,   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(_lowerCamelCase   )
    ]

def 		lowerCamelCase__		(					_lowerCamelCase   ):

    '''simple docstring'''



    _lowerCAmelCase       :   int  =    len(_lowerCamelCase   )
    _lowerCAmelCase       :   Matrix  =    [[0 for _ in range(_lowerCamelCase   )] for _ in range(_lowerCamelCase   )]
    _lowerCAmelCase       :   Matrix  =    [[0] for _ in range(_lowerCamelCase   )]
    _lowerCAmelCase       :   Matrix
    _lowerCAmelCase       :   int
    _lowerCAmelCase       :   int
    _lowerCAmelCase       :   int

    for x_val, y_val in enumerate(_lowerCamelCase   ):
        for col in range(_lowerCamelCase   ):
            _lowerCAmelCase       :   Union[str, Any]  =    (x_val + 1) ** (size - col - 1)
        _lowerCAmelCase       :   Optional[int]  =    y_val

    _lowerCAmelCase       :   List[Any]  =    solve(_lowerCamelCase ,   _lowerCamelCase   )

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

    return interpolated_func

def 		lowerCamelCase__		(					_lowerCamelCase   ):

    '''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__		(					_lowerCamelCase = question_function ,   _lowerCamelCase = 10   ):

    '''simple docstring'''



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

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

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

    for poly in polynomials:
        _lowerCAmelCase       :   Any  =    1
        while func(_lowerCamelCase   ) == poly(_lowerCamelCase   ):
            x_val += 1

        ret += poly(_lowerCamelCase   )

    return ret


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





