






from math import factorial, pi



def 					_lowerCamelCase(			lowerCAmelCase__				:		Optional[Any]    ,    lowerCAmelCase__				:		Dict = 30      ):





				'''simple docstring'''







				if not isinstance(lowerCAmelCase__    ,    (int, float)      ):
								raise ValueError('maclaurin_sin() requires either an int or float for theta'      )

				if not isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ) or accuracy <= 0:
								raise ValueError('maclaurin_sin() requires a positive int for accuracy'      )

				SCREAMING_SNAKE_CASE_   :	Optional[int]													=   float(lowerCAmelCase__      )
				SCREAMING_SNAKE_CASE_   :	Any													=   theta // (2 * pi)
				theta -= 2 * div * pi
				return sum(
				    (-1) ** r * theta ** (2 * r + 1) / factorial(2 * r + 1      ) for r in range(lowerCAmelCase__      )      )



def 					_lowerCamelCase(			lowerCAmelCase__				:		List[Any]    ,    lowerCAmelCase__				:		Tuple = 30      ):





				'''simple docstring'''







				if not isinstance(lowerCAmelCase__    ,    (int, float)      ):
								raise ValueError('maclaurin_cos() requires either an int or float for theta'      )

				if not isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ) or accuracy <= 0:
								raise ValueError('maclaurin_cos() requires a positive int for accuracy'      )

				SCREAMING_SNAKE_CASE_   :	Any													=   float(lowerCAmelCase__      )
				SCREAMING_SNAKE_CASE_   :	int													=   theta // (2 * pi)
				theta -= 2 * div * pi
				return sum((-1) ** r * theta ** (2 * r) / factorial(2 * r      ) for r in range(lowerCAmelCase__      )      )


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				print(maclaurin_sin(10))
				print(maclaurin_sin(-10))
				print(maclaurin_sin(10, 15))
				print(maclaurin_sin(-10, 15))

				print(maclaurin_cos(5))
				print(maclaurin_cos(-5))
				print(maclaurin_cos(10, 15))
				print(maclaurin_cos(-10, 15))







from __future__ import annotations

from collections import Counter
from random import random


class 							__a							:





		'''simple docstring'''



		def __init__(						self       ):
						SCREAMING_SNAKE_CASE_   :	List[str]													=   {}


		def   __snake_case			(						self ,    UpperCamelCase__       ):
						SCREAMING_SNAKE_CASE_   :	int													=   {}


		def   __snake_case			(						self ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__       ):
						if nodea not in self.connections:
										self.add_node(UpperCamelCase__       )
						if nodea not in self.connections:
										self.add_node(UpperCamelCase__       )
						SCREAMING_SNAKE_CASE_   :	Tuple													=   probability


		def   __snake_case			(						self       ):
						return list(self.connections       )






		def   __snake_case			(						self ,    UpperCamelCase__       ):
						SCREAMING_SNAKE_CASE_   :	Dict													=   0
						SCREAMING_SNAKE_CASE_   :	List[Any]													=   random()

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






def 					_lowerCamelCase(			lowerCAmelCase__				:		str    ,    lowerCAmelCase__				:		list[tuple[str, str, float]]    ,    lowerCAmelCase__				:		int      ):





				'''simple docstring'''







				SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   MarkovChainGraphUndirectedUnweighted()

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

				SCREAMING_SNAKE_CASE_   :	List[str]													=   Counter(graph.get_nodes()      )
				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   start

				for _ in range(lowerCAmelCase__      ):
								SCREAMING_SNAKE_CASE_   :	Dict													=   graph.transition(lowerCAmelCase__      )
								visited[node] += 1

				return visited


if __name__ == "__main__":
				import doctest

				doctest.testmod()