

'''simple docstring'''

import math as m

def     __magic_name__       ( A					,   A					,   A=0.001							)			->		str:
	return (f(a + h							) - f(a - h							)) / (2 * h)

def     __magic_name__       ( A					,   A=0					,   A=1_0_0					,   A=0.0_001					,   A=1E-6					,   A=False							)			->		Optional[int]:
	snake_case							 =				xa  # set the initial guess
	snake_case							 =				[a]
	snake_case							 =				abs(f(A							)							)
	snake_case							 =				lambda A							: calc_derivative(A					,   A					,   h=A							)  # noqa: E731  Derivative of f(x)
	for _ in range(A							):
		if fa(A							) == 0:
			raise ValueError('No converging solution found'							)
		snake_case							 =				a - f(A							) / fa(A							)  # Calculate the next estimate
		if logsteps:
			steps.append(A							)
		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_						   =			lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
						lowerCAmelCase_   ,	lowerCAmelCase_   ,	lowerCAmelCase_						   =			newton_raphson(
						    f, xa=1_0, maxiter=1_0_0_0, 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'''

lowerCAmelCase_						   =			{0: [1, 2], 1: [0, 3], 2: [0], 3: [1], 4: [5, 6], 5: [4, 6], 6: [4, 5]}

lowerCAmelCase_						   =			{0: [1, 2, 3], 1: [0, 3], 2: [0], 3: [0, 1], 4: [], 5: []}

def     __magic_name__       ( A					,   A					,   A							)			->		list:
	snake_case							 =				True
	snake_case							 =				[]

	for neighbour in graph[vert]:
		if not visited[neighbour]:
			connected_verts += dfs(A					,   A					,   A							)

	return [vert, *connected_verts]

def     __magic_name__       ( A							)			->		list:
	snake_case							 =				len(A							)
	snake_case							 =				graph_size * [False]
	snake_case							 =				[]

	for i in range(A							):
		if not visited[i]:
			snake_case							 =				dfs(A					,   A					,   A							)
			components_list.append(A							)

	return components_list


if __name__ == "__main__":
						import doctest

						doctest.testmod()





