






from math import pi, sqrt, tan







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							float     ):
	if side_length < 0:
		raise ValueError("surface_area_cube() only accepts non-negative values"     )
	return 6 * side_length**2







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							float  ,						snake_case_      :							float  ,						snake_case_      :							float     ):
	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   SCREAMING_SNAKE_CASE       (				snake_case_      :							float     ):
	if radius < 0:
		raise ValueError("surface_area_sphere() only accepts non-negative values"     )
	return 4 * pi * radius**2







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							float     ):
	if radius < 0:
		raise ValueError("surface_area_hemisphere() only accepts non-negative values"     )
	return 3 * pi * radius**2







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							float  ,						snake_case_      :							float     ):
	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   SCREAMING_SNAKE_CASE       (				snake_case_      :							float  ,						snake_case_      :							float  ,						snake_case_      :							float     ):
	if radius_a < 0 or radius_a < 0 or height < 0:
		raise ValueError(
		    "surface_area_conical_frustum() only accepts non-negative values"     )
	snake_case__				:   Dict     =						(height**2 + (radius_a - radius_a) ** 2) ** 0.5
	return pi * ((slant_height * (radius_a + radius_a)) + radius_a**2 + radius_a**2)







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							float  ,						snake_case_      :							float     ):
	if radius < 0 or height < 0:
		raise ValueError("surface_area_cylinder() only accepts non-negative values"     )
	return 2 * pi * radius * (height + radius)







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							float  ,						snake_case_      :							float     ):
	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(snake_case_  ,						2     ) * torus_radius * tube_radius







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							float  ,						snake_case_      :							float     ):
	if length < 0 or width < 0:
		raise ValueError("area_rectangle() only accepts non-negative values"     )
	return length * width







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							float     ):
	if side_length < 0:
		raise ValueError("area_square() only accepts non-negative values"     )
	return side_length**2







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							float  ,						snake_case_      :							float     ):
	if base < 0 or height < 0:
		raise ValueError("area_triangle() only accepts non-negative values"     )
	return (base * height) / 2







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							float  ,						snake_case_      :							float  ,						snake_case_      :							float     ):
	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"     )
	snake_case__				:   Optional[Any]     =						(sidea + sidea + sidea) / 2
	snake_case__				:   List[str]     =						sqrt(
	    semi_perimeter
	    * (semi_perimeter - sidea)
	    * (semi_perimeter - sidea)
	    * (semi_perimeter - sidea)     )
	return area







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							float  ,						snake_case_      :							float     ):
	if base < 0 or height < 0:
		raise ValueError("area_parallelogram() only accepts non-negative values"     )
	return base * height







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							float  ,						snake_case_      :							float  ,						snake_case_      :							float     ):
	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   SCREAMING_SNAKE_CASE       (				snake_case_      :							float     ):
	if radius < 0:
		raise ValueError("area_circle() only accepts non-negative values"     )
	return pi * radius**2







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							float  ,						snake_case_      :							float     ):
	if radius_x < 0 or radius_y < 0:
		raise ValueError("area_ellipse() only accepts non-negative values"     )
	return pi * radius_x * radius_y







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							float  ,						snake_case_      :							float     ):
	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   SCREAMING_SNAKE_CASE       (				snake_case_      :							int  ,						snake_case_      :							float     ):
	if not isinstance(snake_case_  ,						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) = }")











from __future__ import annotations

import time

__lowerCamelCase      :    str   		=   list[tuple[int, int]]

__lowerCamelCase      :    Optional[int]   		=   [
    [0, 0, 0, 0, 0, 0, 0],
    [0, 1, 0, 0, 0, 0, 0],  # 0 are free path whereas 1's are obstacles
    [0, 0, 0, 0, 0, 0, 0],
    [0, 0, 1, 0, 0, 0, 0],
    [1, 0, 1, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 1, 0, 0],
]

__lowerCamelCase      :    Tuple   		=   [[-1, 0], [0, -1], [1, 0], [0, 1]]  # up, left, down, right



class 							SCREAMING_SNAKE_CASE__		:





					"""simple docstring"""






					def __init__(      self  :						Union[str, Any]							,	__A  :						int							,	__A  :						int							,	__A  :						int							,	__A  :						int							,	__A  :						Node | None ):
						snake_case__				:   Optional[int]     =						pos_x
						snake_case__				:   Dict     =						pos_y
						snake_case__				:   int     =						(pos_y, pos_x)
						snake_case__				:   Optional[int]     =						goal_x
						snake_case__				:   Tuple     =						goal_y
						snake_case__				:   str     =						parent



class 							SCREAMING_SNAKE_CASE__		:





					"""simple docstring"""






					def __init__(      self  :						List[Any]							,	__A  :						tuple[int, int]							,	__A  :						tuple[int, int] ):
						snake_case__				:   Tuple     =						Node(start[1]							,	start[0]							,	goal[1]							,	goal[0]							,	__A )
						snake_case__				:   Tuple     =						Node(goal[1]							,	goal[0]							,	goal[1]							,	goal[0]							,	__A )

						snake_case__				:   int     =						[self.start]
						snake_case__				:   Union[str, Any]     =						False



					def  _lowercase  (      self  :						Dict ):
						while self.node_queue:
							snake_case__				:   Optional[Any]     =						self.node_queue.pop(0 )

							if current_node.pos == self.target.pos:
								snake_case__				:   Optional[Any]     =						True
								return self.retrace_path(__A )

							snake_case__				:   int     =						self.get_successors(__A )

							for node in successors:
								self.node_queue.append(__A )

						if not self.reached:
							return [self.start.pos]
						return None



					def  _lowercase  (      self  :						Union[str, Any]							,	__A  :						Node ):
						snake_case__				:   str     =						[]
						for action in delta:
							snake_case__				:   str     =						parent.pos_x + action[1]
							snake_case__				:   Union[str, Any]     =						parent.pos_y + action[0]
							if not (0 <= pos_x <= len(grid[0] ) - 1 and 0 <= pos_y <= len(__A ) - 1):
								continue

							if grid[pos_y][pos_x] != 0:
								continue

							successors.append(
							    Node(__A							,	__A							,	self.target.pos_y							,	self.target.pos_x							,	__A ) )
						return successors






					def  _lowercase  (      self  :						Optional[Any]							,	__A  :						Node | None ):
						snake_case__				:   Tuple     =						node
						snake_case__				:   Any     =						[]
						while current_node is not None:
							path.append((current_node.pos_y, current_node.pos_x) )
							snake_case__				:   Tuple     =						current_node.parent
						path.reverse()
						return path



class 							SCREAMING_SNAKE_CASE__		:





					"""simple docstring"""






					def __init__(      self  :						Dict							,	__A  :						str							,	__A  :						int ):
						snake_case__				:   str     =						BreadthFirstSearch(__A							,	__A )
						snake_case__				:   int     =						BreadthFirstSearch(__A							,	__A )
						snake_case__				:   Tuple     =						False



					def  _lowercase  (      self  :						Optional[Any] ):
						while self.fwd_bfs.node_queue or self.bwd_bfs.node_queue:
							snake_case__				:   Any     =						self.fwd_bfs.node_queue.pop(0 )
							snake_case__				:   List[str]     =						self.bwd_bfs.node_queue.pop(0 )

							if current_bwd_node.pos == current_fwd_node.pos:
								snake_case__				:   List[str]     =						True
								return self.retrace_bidirectional_path(
								    __A							,	__A )

							snake_case__				:   Union[str, Any]     =						current_bwd_node
							snake_case__				:   Dict     =						current_fwd_node

							snake_case__				:   List[Any]     =						{
							    self.fwd_bfs: self.fwd_bfs.get_successors(__A ),
							    self.bwd_bfs: self.bwd_bfs.get_successors(__A ),
							}

							for bfs in [self.fwd_bfs, self.bwd_bfs]:
								for node in successors[bfs]:
									bfs.node_queue.append(__A )

						if not self.reached:
							return [self.fwd_bfs.start.pos]
						return None






					def  _lowercase  (      self  :						Any							,	__A  :						Node							,	__A  :						Node ):
						snake_case__				:   List[str]     =						self.fwd_bfs.retrace_path(__A )
						snake_case__				:   Optional[Any]     =						self.bwd_bfs.retrace_path(__A )
						bwd_path.pop()
						bwd_path.reverse()
						snake_case__				:   List[Any]     =						fwd_path + bwd_path
						return path


if __name__ == "__main__":
	# all coordinates are given in format [y,x]
	import doctest

	doctest.testmod()
	__lowerCamelCase      :    str   		=   (0, 0)
	__lowerCamelCase      :    List[str]   		=   (len(grid) - 1, len(grid[0]) - 1)
	for elem in grid:
		print(elem)

	__lowerCamelCase      :    Any   		=   time.time()
	__lowerCamelCase      :    Optional[Any]   		=   BreadthFirstSearch(init, goal)
	__lowerCamelCase      :    str   		=   bfs.search()
	__lowerCamelCase      :    Optional[Any]   		=   time.time() - start_bfs_time

	print("""Unidirectional BFS computation time : """, bfs_time)

	__lowerCamelCase      :    Optional[Any]   		=   time.time()
	__lowerCamelCase      :    Optional[int]   		=   BidirectionalBreadthFirstSearch(init, goal)
	__lowerCamelCase      :    str   		=   bd_bfs.search()
	__lowerCamelCase      :    Optional[Any]   		=   time.time() - start_bd_bfs_time

	print("""Bidirectional BFS computation time : """, bd_bfs_time)



