
'''simple docstring'''







class 		__UpperCAmelCase   :


							def __init__( self						):





								"""simple docstring"""






								_snake_case     		=	{}


							def 				lowerCamelCase       ( self						):





								"""simple docstring"""






								print(self.vertex						)
								for i in self.vertex:
									print(lowerCAmelCase_					,     ' -> '					,     ' -> '.join([str(lowerCAmelCase_						) for j in self.vertex[i]]						)						)


							def 				lowerCamelCase       ( self					,     lowerCAmelCase_					,     lowerCAmelCase_						):





								"""simple docstring"""






								if from_vertex in self.vertex:
									self.vertex[from_vertex].append(lowerCAmelCase_						)
								else:
									# else make a new vertex
									_snake_case     		=	[to_vertex]


							def 				lowerCamelCase       ( self						):





								"""simple docstring"""






								_snake_case     		=	[False] * len(self.vertex						)

								# call the recursive helper function
								for i in range(len(self.vertex						)						):
									if not visited[i]:
										self.dfs_recursive(lowerCAmelCase_					,     lowerCAmelCase_						)




							def 				lowerCamelCase       ( self					,     lowerCAmelCase_					,     lowerCAmelCase_						):





								"""simple docstring"""






								_snake_case     		=	True

								print(lowerCAmelCase_					,     end=' '						)

								# Recur for all the vertices that are adjacent to this node
								for i in self.vertex:
									if not visited[i]:
										self.dfs_recursive(lowerCAmelCase_					,     lowerCAmelCase_						)


if __name__ == "__main__":
					lowercase					:							Optional[Any]   =      Graph()
					g.add_edge(0, 1)
					g.add_edge(0, 2)
					g.add_edge(1, 2)
					g.add_edge(2, 0)
					g.add_edge(2, 3)
					g.add_edge(3, 3)

					g.print_graph()
					print("DFS:")
					g.dfs()

					# OUTPUT:
					# 0  ->  1 -> 2
					# 1  ->  2
					# 2  ->  0 -> 3
					# 3  ->  3
					# DFS:
					#  0 1 2 3






'''simple docstring'''







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







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A    ,       __A = "x"    ,       __A = 10**-10    ,       __A = 1    ,       ) ->			complex:
	_snake_case     		=	symbols(__A			)
	_snake_case     		=	lambdify(__A    ,       __A			)
	_snake_case     		=	lambdify(__A    ,       diff(__A    ,       __A			)			)

	_snake_case     		=	starting_point

	while True:
		if diff_function(__A			) != 0:
			_snake_case     		=	prev_guess - multiplicity * func(__A			) / diff_function(
			    __A			)
		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     		=	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=0.005)}''',
					)

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

