

from __future__ import annotations

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

from sympy import diff



def       __lowerCAmelCase      (						A       ,     A       ,     A = 10**-10    ):
	UpperCAmelCase_       				=			a
	while True:
		UpperCAmelCase_       				=			Decimal(A    ) - (
		    Decimal(eval(A    )    ) / Decimal(eval(str(diff(A    )    )    )    )  # noqa: S307
		)
		# This number dictates the accuracy of the answer
		if abs(eval(A    )    ) < precision:  # noqa: S307
			return float(A    )


# 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)}')


from __future__ import annotations

from collections import Counter
from random import random

class 						__UpperCamelCase    :




	def __init__(		self	:						Any							):


		'''simple docstring'''







		UpperCAmelCase_       				=			{}




	def       __A					(		self	:						List[str]		,	lowerCAmelCase	:						str							):


		'''simple docstring'''







		UpperCAmelCase_       				=			{}




	def       __A					(		self	:						Union[str, Any]		,	lowerCAmelCase	:						str		,	lowerCAmelCase	:						str		,	lowerCAmelCase	:						float							):


		'''simple docstring'''







		if nodea not in self.connections:
			self.add_node(lowerCAmelCase							)
		if nodea not in self.connections:
			self.add_node(lowerCAmelCase							)
		UpperCAmelCase_       				=			probability




	def       __A					(		self	:						Tuple							):


		'''simple docstring'''







		return list(self.connections							)




	def       __A					(		self	:						str		,	lowerCAmelCase	:						str							):


		'''simple docstring'''







		UpperCAmelCase_       				=			0
		UpperCAmelCase_       				=			random()

		for dest in self.connections[node]:
			current_probability += self.connections[node][dest]
			if current_probability > random_value:
				return dest
		return ""



def       __lowerCAmelCase      (						A       ,     A       ,     A    ):
	UpperCAmelCase_       				=			MarkovChainGraphUndirectedUnweighted()

	for nodea, nodea, probability in transitions:
		graph.add_transition_probability(A       ,     A       ,     A    )

	UpperCAmelCase_       				=			Counter(graph.get_nodes()    )
	UpperCAmelCase_       				=			start

	for _ in range(A    ):
		UpperCAmelCase_       				=			graph.transition(A    )
		visited[node] += 1

	return visited


if __name__ == "__main__":
				import doctest

				doctest.testmod()