'''simple docstring'''
from math import pi, sqrt, tan



def  __lowerCamelCase       (      _UpperCamelCase  :  float					):


      '''simple docstring'''


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



def  __lowerCamelCase       (      _UpperCamelCase  :  float							,    _UpperCamelCase  :  float							,    _UpperCamelCase  :  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       (      _UpperCamelCase  :  float					):


      '''simple docstring'''


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



def  __lowerCamelCase       (      _UpperCamelCase  :  float					):


      '''simple docstring'''


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



def  __lowerCamelCase       (      _UpperCamelCase  :  float							,    _UpperCamelCase  :  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       (      _UpperCamelCase  :  float							,    _UpperCamelCase  :  float							,    _UpperCamelCase  :  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'''					)
      UpperCAmelCase_            =  (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       (      _UpperCamelCase  :  float							,    _UpperCamelCase  :  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       (      _UpperCamelCase  :  float							,    _UpperCamelCase  :  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(_UpperCamelCase							,    2					) * torus_radius * tube_radius



def  __lowerCamelCase       (      _UpperCamelCase  :  float							,    _UpperCamelCase  :  float					):


      '''simple docstring'''


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



def  __lowerCamelCase       (      _UpperCamelCase  :  float					):


      '''simple docstring'''


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



def  __lowerCamelCase       (      _UpperCamelCase  :  float							,    _UpperCamelCase  :  float					):


      '''simple docstring'''


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



def  __lowerCamelCase       (      _UpperCamelCase  :  float							,    _UpperCamelCase  :  float							,    _UpperCamelCase  :  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'''					)
      UpperCAmelCase_            =  (sidea + sidea + sidea) / 2
      UpperCAmelCase_            =  sqrt(
          semi_perimeter
          * (semi_perimeter - sidea)
          * (semi_perimeter - sidea)
          * (semi_perimeter - sidea)					)
      return area



def  __lowerCamelCase       (      _UpperCamelCase  :  float							,    _UpperCamelCase  :  float					):


      '''simple docstring'''


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



def  __lowerCamelCase       (      _UpperCamelCase  :  float							,    _UpperCamelCase  :  float							,    _UpperCamelCase  :  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       (      _UpperCamelCase  :  float					):


      '''simple docstring'''


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



def  __lowerCamelCase       (      _UpperCamelCase  :  float							,    _UpperCamelCase  :  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       (      _UpperCamelCase  :  float							,    _UpperCamelCase  :  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       (      _UpperCamelCase  :  int							,    _UpperCamelCase  :  float					):


      '''simple docstring'''


      if not isinstance(_UpperCamelCase							,    _UpperCamelCase					) 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) = }''')




'''simple docstring'''
from heapq import heappop, heappush

import numpy as np



def  __lowerCamelCase       (      _UpperCamelCase  :  np.ndarray							,    _UpperCamelCase  :  tuple[int, int]							,    _UpperCamelCase  :  tuple[int, int]							,    _UpperCamelCase  :  bool							,    ):


      '''simple docstring'''


      UpperCAmelCase_      ,		UpperCAmelCase_            =  grid.shape
      UpperCAmelCase_            =  [-1, 1, 0, 0]
      UpperCAmelCase_            =  [0, 0, -1, 1]
      if allow_diagonal:
            dx += [-1, -1, 1, 1]
            dy += [-1, 1, -1, 1]

      UpperCAmelCase_      ,		UpperCAmelCase_            =  [(0, source)], set()
      UpperCAmelCase_            =  np.full((rows, cols)							,    np.inf					)
      UpperCAmelCase_            =  0
      UpperCAmelCase_            =  np.empty((rows, cols)							,    dtype=_UpperCamelCase					)
      UpperCAmelCase_            =  None

      while queue:
            ((UpperCAmelCase_)      ,		(UpperCAmelCase_))            =  heappop(_UpperCamelCase					)
            if (x, y) in visited:
                  continue
            visited.add((x, y)					)

            if (x, y) == destination:
                  UpperCAmelCase_            =  []
                  while (x, y) != source:
                        path.append((x, y)					)
                        UpperCAmelCase_      ,		UpperCAmelCase_            =  predecessors[x, y]
                  path.append(_UpperCamelCase					)  # add the source manually
                  path.reverse()
                  return matrix[destination], path

            for i in range(len(_UpperCamelCase					)					):
                  UpperCAmelCase_      ,		UpperCAmelCase_            =  x + dx[i], y + dy[i]
                  if 0 <= nx < rows and 0 <= ny < cols:
                        UpperCAmelCase_            =  grid[nx][ny]
                        if next_node == 1 and matrix[nx, ny] > dist + 1:
                              heappush(_UpperCamelCase							,    (dist + 1, (nx, ny))					)
                              UpperCAmelCase_            =  dist + 1
                              UpperCAmelCase_            =  (x, y)

      return np.inf, []


if __name__ == "__main__":
      import doctest

      doctest.testmod()





