"""simple docstring"""







from __future__ import annotations

from decimal import Decimal
from math import *  # noqa: F403

from sympy import diff


def      __lowerCAmelCase(		__UpperCAmelCase     ,__UpperCAmelCase     ,__UpperCAmelCase = 10**-10			):






							"""simple docstring"""





							_lowercase :    Optional[int]							=							a
							while True:
														_lowercase :    str							=							Decimal(__UpperCAmelCase			) - (
														    Decimal(eval(__UpperCAmelCase			)			) / Decimal(eval(str(diff(__UpperCAmelCase			)			)			)			)  # noqa: S307
														)
														# This number dictates the accuracy of the answer
														if abs(eval(__UpperCAmelCase			)			) < precision:  # noqa: S307
																					return float(__UpperCAmelCase			)


# 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
						print(f"""The root of x**2 - 5*x + 2 = 0 is {newton_raphson('x**2 - 5*x + 2', 0.4)}""")
						# Find Square Root of 5
						print(f"""The root of log(x) - 1 = 0 is {newton_raphson('log(x) - 1', 2)}""")
						# Exponential Roots
						print(f"""The root of exp(x) - 1 = 0 is {newton_raphson('exp(x) - 1', 0)}""")




"""simple docstring"""







def      __lowerCAmelCase(		__UpperCAmelCase     ,__UpperCAmelCase     ,__UpperCAmelCase			):






	"""simple docstring"""





	return not any(
	    neighbour == 1 and colored_vertices[i] == color
	    for i, neighbour in enumerate(__UpperCAmelCase			)			)


def      __lowerCAmelCase(		__UpperCAmelCase     ,__UpperCAmelCase     ,__UpperCAmelCase     ,__UpperCAmelCase			):






	"""simple docstring"""





	if index == len(__UpperCAmelCase			):
		return True

	# Recursive Step
	for i in range(__UpperCAmelCase			):
		if valid_coloring(graph[index]     ,__UpperCAmelCase     ,__UpperCAmelCase			):
			# Color current vertex
			_lowercase :    str							=							i
			# Validate coloring
			if util_color(__UpperCAmelCase     ,__UpperCAmelCase     ,__UpperCAmelCase     ,index + 1			):
				return True
			# Backtrack
			_lowercase :    List[str]							=							-1
	return False







def      __lowerCAmelCase(		__UpperCAmelCase     ,__UpperCAmelCase			):






	"""simple docstring"""





	_lowercase :    Any							=							[-1] * len(__UpperCAmelCase			)

	if util_color(__UpperCAmelCase     ,__UpperCAmelCase     ,__UpperCAmelCase     ,0			):
		return colored_vertices

	return []



