






"""simple docstring"""





from math import factorial, pi



def   a    (     __UpperCAmelCase      :    float      ,   __UpperCAmelCase      :    int = 3_0  )    ->							float:

						if not isinstance(__UpperCAmelCase      ,   (int, float)  ):
												raise ValueError("""maclaurin_sin() requires either an int or float for theta"""  )

						if not isinstance(__UpperCAmelCase      ,   __UpperCAmelCase  ) or accuracy <= 0:
												raise ValueError("""maclaurin_sin() requires a positive int for accuracy"""  )

						__magic_name__:	Any							=       float(__UpperCAmelCase  )
						__magic_name__:	Optional[Any]							=       theta // (2 * pi)
						theta -= 2 * div * pi
						return sum(
						    (-1) ** r * theta ** (2 * r + 1) / factorial(2 * r + 1  ) for r in range(__UpperCAmelCase  )  )



def   a    (     __UpperCAmelCase      :    float      ,   __UpperCAmelCase      :    int = 3_0  )    ->							float:

						if not isinstance(__UpperCAmelCase      ,   (int, float)  ):
												raise ValueError("""maclaurin_cos() requires either an int or float for theta"""  )

						if not isinstance(__UpperCAmelCase      ,   __UpperCAmelCase  ) or accuracy <= 0:
												raise ValueError("""maclaurin_cos() requires a positive int for accuracy"""  )

						__magic_name__:	List[str]							=       float(__UpperCAmelCase  )
						__magic_name__:	Tuple							=       theta // (2 * pi)
						theta -= 2 * div * pi
						return sum((-1) ** r * theta ** (2 * r) / factorial(2 * r  ) for r in range(__UpperCAmelCase  )  )


if __name__ == "__main__":
							import doctest

							doctest.testmod()

							print(maclaurin_sin(10))
							print(maclaurin_sin(-10))
							print(maclaurin_sin(10, 15))
							print(maclaurin_sin(-10, 15))

							print(maclaurin_cos(5))
							print(maclaurin_cos(-5))
							print(maclaurin_cos(10, 15))
							print(maclaurin_cos(-10, 15))






'''simple docstring'''




def    lowerCamelCase__		(    SCREAMING_SNAKE_CASE   : list[int]							, SCREAMING_SNAKE_CASE   : list[int]							, SCREAMING_SNAKE_CASE   : int    ):
  return not any(
      neighbour == 1 and colored_vertices[i] == color
      for i, neighbour in enumerate(SCREAMING_SNAKE_CASE    )    )


def    lowerCamelCase__		(    SCREAMING_SNAKE_CASE   : list[list[int]]							, SCREAMING_SNAKE_CASE   : int							, SCREAMING_SNAKE_CASE   : list[int]							, SCREAMING_SNAKE_CASE   : int    ):

  # Base Case
  if index == len(SCREAMING_SNAKE_CASE    ):
    return True

  # Recursive Step
  for i in range(SCREAMING_SNAKE_CASE    ):
    if valid_coloring(graph[index]							, SCREAMING_SNAKE_CASE							, SCREAMING_SNAKE_CASE    ):
      # Color current vertex
      UpperCAmelCase    				=						i
      # Validate coloring
      if util_color(SCREAMING_SNAKE_CASE							, SCREAMING_SNAKE_CASE							, SCREAMING_SNAKE_CASE							, index + 1    ):
        return True
      # Backtrack
      UpperCAmelCase    				=						-1
  return False



def    lowerCamelCase__		(    SCREAMING_SNAKE_CASE   : list[list[int]]							, SCREAMING_SNAKE_CASE   : int    ):
  UpperCAmelCase    				=						[-1] * len(SCREAMING_SNAKE_CASE    )

  if util_color(SCREAMING_SNAKE_CASE							, SCREAMING_SNAKE_CASE							, SCREAMING_SNAKE_CASE							, 0    ):
    return colored_vertices

  return []


