





'''simple docstring'''


import math as m




def    __a (     UpperCAmelCase       ,			UpperCAmelCase       ,			UpperCAmelCase=0.001    )      ->Optional[int]:



	"""simple docstring"""







	return (f(a + h    ) - f(a - h    )) / (2 * h)




def    __a (     UpperCAmelCase       ,			UpperCAmelCase=0       ,			UpperCAmelCase=100       ,			UpperCAmelCase=0.0_001       ,			UpperCAmelCase=1E-6       ,			UpperCAmelCase=False    )      ->Optional[Any]:



	"""simple docstring"""







	A							  =      xa  # set the initial guess
	A							  =      [a]
	A							  =      abs(f(UpperCAmelCase    )    )
	A							  =      lambda UpperCAmelCase    : calc_derivative(UpperCAmelCase       ,			UpperCAmelCase       ,			h=UpperCAmelCase    )  # noqa: E731  Derivative of f(x)
	for _ in range(UpperCAmelCase    ):
		if fa(UpperCAmelCase    ) == 0:
			raise ValueError("""No converging solution found"""    )
		A							  =      a - f(UpperCAmelCase    ) / fa(UpperCAmelCase    )  # Calculate the next estimate
		if logsteps:
			steps.append(UpperCAmelCase    )
		if error < maxerror:
			break
	else:
		raise ValueError("""Iteration limit reached, no converging solution found"""    )
	if logsteps:
		# If logstep is true, then log intermediate steps
		return a, error, steps
	return a, error


if __name__ == "__main__":
				from matplotlib import pyplot as plt

				_lowerCamelCase				:	Tuple				    =       lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
				_lowerCamelCase    ,  _lowerCamelCase    ,  _lowerCamelCase				:	int				    =       newton_raphson(
				    f, xa=10, maxiter=1000, step=1e-6, logsteps=True
				)
				plt.plot([abs(f(x)) for x in steps])
				plt.xlabel('step')
				plt.ylabel('error')
				plt.show()
				print(f"solution = {{{solution:f}}}, error = {{{error:f}}}")








'''simple docstring'''


from __future__ import annotations



class 							__UpperCAmelCase  :







		'''simple docstring'''







		def __init__(self						:      Any      ,      _lowerCAmelCase						:      int      ):
			A							  =      value
			A							  =      None
			A							  =      None






class 							__UpperCAmelCase  :







		'''simple docstring'''







		__lowerCAmelCase 				=    42







		def __init__(self						:      List[str]      ):
			A							  =      0







		def        A     (self						:      Dict      ,      _lowerCAmelCase						:      Node | None      ,      _lowerCAmelCase						:      int      ):
			if node is None:
				return

			if path_sum == self.target:
				self.paths += 1

			if node.left:
				self.depth_first_search(node.left      ,      path_sum + node.left.value      )
			if node.right:
				self.depth_first_search(node.right      ,      path_sum + node.right.value      )







		def        A     (self						:      Optional[Any]      ,      _lowerCAmelCase						:      Node | None      ,      _lowerCAmelCase						:      int | None = None      ):
			if node is None:
				return 0
			if target is not None:
				A							  =      target

			self.depth_first_search(_lowerCAmelCase      ,      node.value      )
			self.path_sum(node.left      )
			self.path_sum(node.right      )

			return self.paths


if __name__ == "__main__":
				import doctest

				doctest.testmod()

