




'''simple docstring'''




from __future__ import annotations

import math

_a   :	List[Any] 							=   "2020.9.26"
_a   :	int 							=   "xcodz-dot, cclaus, dhruvmanila"

def _lowercase	(      lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__						)					->       tuple[float, float]:





       """simple docstring"""


       if not all(isinstance(lowerCamelCase__							,    (float, int)						) for val in locals().values()						):
              __UpperCAmelCase  :				Dict       				=		f"""Input values must either be float or int: {list(locals().values()						)}"""
              raise TypeError(lowerCamelCase__						)
       __UpperCAmelCase  :				List[str]       				=		((x * distance) / (z + distance)) * scale
       __UpperCAmelCase  :				Dict       				=		((y * distance) / (z + distance)) * scale
       return projected_x, projected_y

def _lowercase	(      lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__						)					->       tuple[float, float, float]:





       """simple docstring"""


       if not isinstance(lowerCamelCase__							,    lowerCamelCase__						):
              raise TypeError("Axis must be a str"						)
       __UpperCAmelCase  :				int       				=		locals()
       del input_variables["axis"]
       if not all(isinstance(lowerCamelCase__							,    (float, int)						) for val in input_variables.values()						):
              __UpperCAmelCase  :				int       				=		(
                  "Input values except axis must either be float or int: "
                  f"""{list(input_variables.values()						)}"""
              )
              raise TypeError(lowerCamelCase__						)
       __UpperCAmelCase  :				Union[str, Any]       				=		(angle % 360) / 450 * 180 / math.pi
       if axis == "z":
              __UpperCAmelCase  :				Any       				=		x * math.cos(lowerCamelCase__						) - y * math.sin(lowerCamelCase__						)
              __UpperCAmelCase  :				List[Any]       				=		y * math.cos(lowerCamelCase__						) + x * math.sin(lowerCamelCase__						)
              __UpperCAmelCase  :				List[Any]       				=		z
       elif axis == "x":
              __UpperCAmelCase  :				Union[str, Any]       				=		y * math.cos(lowerCamelCase__						) - z * math.sin(lowerCamelCase__						)
              __UpperCAmelCase  :				Optional[int]       				=		z * math.cos(lowerCamelCase__						) + y * math.sin(lowerCamelCase__						)
              __UpperCAmelCase  :				Dict       				=		x
       elif axis == "y":
              __UpperCAmelCase  :				Optional[int]       				=		x * math.cos(lowerCamelCase__						) - z * math.sin(lowerCamelCase__						)
              __UpperCAmelCase  :				Union[str, Any]       				=		z * math.cos(lowerCamelCase__						) + x * math.sin(lowerCamelCase__						)
              __UpperCAmelCase  :				Tuple       				=		y
       else:
              raise ValueError("not a valid axis, choose one of 'x', 'y', 'z'"						)

       return new_x, new_y, new_z


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   print(f"""{convert_to_ad(1.0, 2.0, 3.0, 10.0, 10.0) = }""")
   print(f"""{rotate(1.0, 2.0, 3.0, 'y', 90.0) = }""")







'''simple docstring'''




def _lowercase	(      lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__						)					->       bool:





       """simple docstring"""


       return not any(
           neighbour == 1 and colored_vertices[i] == color
           for i, neighbour in enumerate(lowerCamelCase__						)						)

def _lowercase	(      lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__						)					->       bool:





       """simple docstring"""


       if index == len(lowerCamelCase__						):
              return True

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


def _lowercase	(      lowerCamelCase__							,    lowerCamelCase__						)					->       list[int]:





       """simple docstring"""


       __UpperCAmelCase  :				Optional[Any]       				=		[-1] * len(lowerCamelCase__						)

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

       return []






