


"""simple docstring"""



from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403







def 						__lowerCAmelCase		(		lowercase						:						str		,							lowercase						:						complex		,							lowercase						:						str = "x"		,							lowercase						:						float = 10**-10		,							lowercase						:						int = 1		,							)			->		complex:


    """simple docstring"""





    snake_case					:   str         =					symbols(lowercase				)
    snake_case					:   str         =					lambdify(lowercase		,							lowercase				)
    snake_case					:   Tuple         =					lambdify(lowercase		,							diff(lowercase		,							lowercase				)				)

    snake_case					:   Tuple         =					starting_point

    while True:
        if diff_function(lowercase				) != 0:
            snake_case					:   str         =					prev_guess - multiplicity * func(lowercase				) / diff_function(
                lowercase				)
        else:
            raise ZeroDivisionError("Could not find root"				) from None

        # Precision is checked by comparing the difference of consecutive guesses
        if abs(next_guess - prev_guess				) < precision:
            return next_guess

        snake_case					:   Dict         =					next_guess


# Let's Execute
if __name__ == "__main__":
  # Find root of trigonometric function
  # Find value of pi
  print(F'''The root of sin(x) = 0 is {newton_raphson("sin(x)", 2)}''')

  # Find root of polynomial
  # Find fourth Root of 5
  print(F'''The root of x**4 - 5 = 0 is {newton_raphson("x**4 -5", 0.4 +5j)}''')

  # Find value of e
  print(
      """The root of log(y) - 1 = 0 is """,
      F'''{newton_raphson("log(y) - 1", 2, variable="y")}''',
  )

  # Exponential Roots
  print(
      """The root of exp(x) - 1 = 0 is""",
      F'''{newton_raphson("exp(x) - 1", 10, precision=0.0_05)}''',
  )

  # Find root of cos(x)
  print(F'''The root of cos(x) = 0 is {newton_raphson("cos(x)", 0)}''')









"""simple docstring"""



from __future__ import annotations

__snake_case         =					list[tuple[int, int]]

__snake_case         =					[
    [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],
]

__snake_case         =					([-1, 0], [0, -1], [1, 0], [0, 1])  # up, left, down, right







class _lowerCAmelCase       :







   def __init__(			self		,			UpperCamelCase__		,			UpperCamelCase__		,			UpperCamelCase__		,			UpperCamelCase__		,			UpperCamelCase__		,			UpperCamelCase__		,			)			->	str:

       '''simple docstring'''




       snake_case					:   int         =					pos_x
       snake_case					:   List[str]         =					pos_y
       snake_case					:   List[Any]         =					(pos_y, pos_x)
       snake_case					:   Optional[int]         =					goal_x
       snake_case					:   Dict         =					goal_y
       snake_case					:   Any         =					g_cost
       snake_case					:   List[Any]         =					parent
       snake_case					:   Union[str, Any]         =					self.calculate_heuristic()







   def 				lowerCamelCase	(			self		)			->	float:

       '''simple docstring'''




       snake_case					:   Optional[Any]         =					abs(self.pos_x - self.goal_x		)
       snake_case					:   Dict         =					abs(self.pos_y - self.goal_y		)
       return dx + dy







   def __lt__(			self		,			UpperCamelCase__		)			->	bool:

       '''simple docstring'''




       return self.f_cost < other.f_cost







class _lowerCAmelCase       :







   def __init__(			self		,			UpperCamelCase__		,			UpperCamelCase__		)			->	List[Any]:

       '''simple docstring'''




       snake_case					:   int         =					Node(start[1]		,			start[0]		,			goal[1]		,			goal[0]		,			0		,			UpperCamelCase__		)
       snake_case					:   List[Any]         =					Node(goal[1]		,			goal[0]		,			goal[1]		,			goal[0]		,			9_9999		,			UpperCamelCase__		)

       snake_case					:   Tuple         =					[self.start]
       snake_case					:   list[Node]         =					[]

       snake_case					:   Dict         =					False







   def 				lowerCamelCase	(			self		)			->	Path | None:

       '''simple docstring'''




       while self.open_nodes:
           # Open Nodes are sorted using __lt__
           self.open_nodes.sort()
           snake_case					:   str         =					self.open_nodes.pop(0		)

           if current_node.pos == self.target.pos:
               snake_case					:   Tuple         =					True
               return self.retrace_path(UpperCamelCase__		)

           self.closed_nodes.append(UpperCamelCase__		)
           snake_case					:   Optional[Any]         =					self.get_successors(UpperCamelCase__		)

           for child_node in successors:
               if child_node in self.closed_nodes:
                   continue

               if child_node not in self.open_nodes:
                   self.open_nodes.append(UpperCamelCase__		)
               else:
                   # retrieve the best current path
                   snake_case					:   Dict         =					self.open_nodes.pop(self.open_nodes.index(UpperCamelCase__		)		)

                   if child_node.g_cost < better_node.g_cost:
                       self.open_nodes.append(UpperCamelCase__		)
                   else:
                       self.open_nodes.append(UpperCamelCase__		)

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







   def 				lowerCamelCase	(			self		,			UpperCamelCase__		)			->	list[Node]:

       '''simple docstring'''




       snake_case					:   Dict         =					[]
       for action in delta:
           snake_case					:   Union[str, Any]         =					parent.pos_x + action[1]
           snake_case					:   str         =					parent.pos_y + action[0]

           if not (0 <= pos_x <= len(grid[0]		) - 1 and 0 <= pos_y <= len(UpperCamelCase__		) - 1):
               continue

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

           successors.append(
               Node(
                   UpperCamelCase__		,			UpperCamelCase__		,			self.target.pos_y		,			self.target.pos_x		,			parent.g_cost + 1		,			UpperCamelCase__		,			)		)
       return successors







   def 				lowerCamelCase	(			self		,			UpperCamelCase__		)			->	Path:

       '''simple docstring'''




       snake_case					:   Optional[int]         =					node
       snake_case					:   int         =					[]
       while current_node is not None:
           path.append((current_node.pos_y, current_node.pos_x)		)
           snake_case					:   Any         =					current_node.parent
       path.reverse()
       return path


if __name__ == "__main__":
  __snake_case         =					(0, 0)
  __snake_case         =					(len(grid) - 1, len(grid[0]) - 1)
  for elem in grid:
    print(elem)

  print("""------""")

  __snake_case         =					GreedyBestFirst(init, goal)
  __snake_case         =					greedy_bf.search()
  if path:
    for pos_x, pos_y in path:
      __snake_case         =					2

    for elem in grid:
      print(elem)





