

'''simple docstring'''
from __future__ import annotations


def 			_lowerCAmelCase   (		_UpperCamelCase		:	Optional[Any]				,					_UpperCamelCase		:	int				,					_UpperCamelCase		:	List[Any]				,					_UpperCamelCase		:	Any				,					_UpperCamelCase		:	List[str]				,					) ->     None:
     """simple docstring"""




     _SCREAMING_SNAKE_CASE				       =len(_SCREAMING_SNAKE_CASE							)

     # If row is equal to the size of the board it means there are a queen in each row in
     # the current board (possible_board)
     if row == n:
          # We convert the variable possible_board that looks like this: [1, 3, 0, 2] to
          # this: ['. Q . . ', '. . . Q ', 'Q . . . ', '. . Q . ']
          boards.append(['. ' * i + 'Q ' + '. ' * (n - 1 - i) for i in possible_board]							)
          return

     # We iterate each column in the row to find all possible results in each row
     for col in range(_SCREAMING_SNAKE_CASE							):
          # We apply that we learned previously. First we check that in the current board
          # (possible_board) there are not other same value because if there is it means
          # that there are a collision in vertical. Then we apply the two formulas we
          # learned before:
          #
          # 45º: y - x = b or 45: row - col = b
          # 135º: y + x = b or row + col = b.
          #
          # And we verify if the results of this two formulas not exist in their variables
          # respectively.  (diagonal_right_collisions, diagonal_left_collisions)
          #
          # If any or these are True it means there is a collision so we continue to the
          # next value in the for loop.
          if (
              col in possible_board
              or row - col in diagonal_right_collisions
              or row + col in diagonal_left_collisions
          ):
               continue

          # If it is False we call dfs function again and we update the inputs
          depth_first_search(
              [*possible_board, col]				,					[*diagonal_right_collisions, row - col]				,					[*diagonal_left_collisions, row + col]				,					_SCREAMING_SNAKE_CASE				,					_SCREAMING_SNAKE_CASE				,					)


def 			_lowerCAmelCase   (		_UpperCamelCase		:	Any							) ->     None:
     """simple docstring"""




     _SCREAMING_SNAKE_CASE				       =[]
     depth_first_search([]				,					[]				,					[]				,					_SCREAMING_SNAKE_CASE				,					_SCREAMING_SNAKE_CASE							)

     # Print all the boards
     for board in boards:
          for column in board:
               print(_SCREAMING_SNAKE_CASE							)
          print(''							)

     print(len(_SCREAMING_SNAKE_CASE							)				,					'solutions were found.'							)


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     n_queens_solution(4)







from math import pi, sqrt, tan





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if side_length < 0:
        raise ValueError('surface_area_cube() only accepts non-negative values'				)
    return 6 * side_length**2





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if length < 0 or breadth < 0 or height < 0:
        raise ValueError('surface_area_cuboid() only accepts non-negative values'				)
    return 2 * ((length * breadth) + (breadth * height) + (length * height))





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if radius < 0:
        raise ValueError('surface_area_sphere() only accepts non-negative values'				)
    return 4 * pi * radius**2





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if radius < 0:
        raise ValueError('surface_area_hemisphere() only accepts non-negative values'				)
    return 3 * pi * radius**2





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if radius < 0 or height < 0:
        raise ValueError('surface_area_cone() only accepts non-negative values'				)
    return pi * radius * (radius + (height**2 + radius**2) ** 0.5)





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if radius_a < 0 or radius_a < 0 or height < 0:
        raise ValueError(
            'surface_area_conical_frustum() only accepts non-negative values'				)
    _A     =							(height**2 + (radius_a - radius_a) ** 2) ** 0.5
    return pi * ((slant_height * (radius_a + radius_a)) + radius_a**2 + radius_a**2)





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if radius < 0 or height < 0:
        raise ValueError('surface_area_cylinder() only accepts non-negative values'				)
    return 2 * pi * radius * (height + radius)





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if torus_radius < 0 or tube_radius < 0:
        raise ValueError('surface_area_torus() only accepts non-negative values'				)
    if torus_radius < tube_radius:
        raise ValueError(
            'surface_area_torus() does not support spindle or self intersecting tori'				)
    return 4 * pow(_SCREAMING_SNAKE_CASE							,     2				) * torus_radius * tube_radius





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if length < 0 or width < 0:
        raise ValueError('area_rectangle() only accepts non-negative values'				)
    return length * width





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if side_length < 0:
        raise ValueError('area_square() only accepts non-negative values'				)
    return side_length**2





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if base < 0 or height < 0:
        raise ValueError('area_triangle() only accepts non-negative values'				)
    return (base * height) / 2





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if sidea < 0 or sidea < 0 or sidea < 0:
        raise ValueError('area_triangle_three_sides() only accepts non-negative values'				)
    elif sidea + sidea < sidea or sidea + sidea < sidea or sidea + sidea < sidea:
        raise ValueError('Given three sides do not form a triangle'				)
    _A     =							(sidea + sidea + sidea) / 2
    _A     =							sqrt(
        semi_perimeter
        * (semi_perimeter - sidea)
        * (semi_perimeter - sidea)
        * (semi_perimeter - sidea)				)
    return area





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if base < 0 or height < 0:
        raise ValueError('area_parallelogram() only accepts non-negative values'				)
    return base * height





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if basea < 0 or basea < 0 or height < 0:
        raise ValueError('area_trapezium() only accepts non-negative values'				)
    return 1 / 2 * (basea + basea) * height





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if radius < 0:
        raise ValueError('area_circle() only accepts non-negative values'				)
    return pi * radius**2





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if radius_x < 0 or radius_y < 0:
        raise ValueError('area_ellipse() only accepts non-negative values'				)
    return pi * radius_x * radius_y





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if diagonal_a < 0 or diagonal_a < 0:
        raise ValueError('area_rhombus() only accepts non-negative values'				)
    return 1 / 2 * diagonal_a * diagonal_a





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if not isinstance(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				) or sides < 3:
        raise ValueError(
            'area_reg_polygon() only accepts integers greater than or \
equal to three as number of sides'				)
    elif length < 0:
        raise ValueError(
            'area_reg_polygon() only accepts non-negative values as \
length of a side'				)
    return (sides * length**2) / (4 * tan(pi / sides				))
    return (sides * length**2) / (4 * tan(pi / sides				))


if __name__ == "__main__":
 import doctest

 doctest.testmod(verbose=True)  # verbose so we can see methods missing tests

 print("[DEMO] Areas of various geometric shapes: \n")
 print(f"Rectangle: {area_rectangle(10, 20) = }")
 print(f"Square: {area_square(10) = }")
 print(f"Triangle: {area_triangle(10, 10) = }")
 print(f"Triangle: {area_triangle_three_sides(5, 12, 13) = }")
 print(f"Parallelogram: {area_parallelogram(10, 20) = }")
 print(f"Rhombus: {area_rhombus(10, 20) = }")
 print(f"Trapezium: {area_trapezium(10, 20, 30) = }")
 print(f"Circle: {area_circle(20) = }")
 print(f"Ellipse: {area_ellipse(10, 20) = }")
 print("\nSurface Areas of various geometric shapes: \n")
 print(f"Cube: {surface_area_cube(20) = }")
 print(f"Cuboid: {surface_area_cuboid(10, 20, 30) = }")
 print(f"Sphere: {surface_area_sphere(20) = }")
 print(f"Hemisphere: {surface_area_hemisphere(20) = }")
 print(f"Cone: {surface_area_cone(10, 20) = }")
 print(f"Conical Frustum: {surface_area_conical_frustum(10, 20, 30) = }")
 print(f"Cylinder: {surface_area_cylinder(10, 20) = }")
 print(f"Torus: {surface_area_torus(20, 10) = }")
 print(f"Equilateral Triangle: {area_reg_polygon(3, 10) = }")
 print(f"Square: {area_reg_polygon(4, 10) = }")
 print(f"Reqular Pentagon: {area_reg_polygon(5, 10) = }")





