

import math as m

def 	a						(				_UpperCAmelCase							: Dict			,       _UpperCAmelCase							: Optional[Any]			,       _UpperCAmelCase							: List[str]=0.0_01						):







		'''simple docstring'''





		return (f(a + h						) - f(a - h						)) / (2 * h)

def 	a						(				_UpperCAmelCase							: Optional[Any]			,       _UpperCAmelCase							: Optional[Any]=0			,       _UpperCAmelCase							: Optional[Any]=1_00			,       _UpperCAmelCase							: Union[str, Any]=0.00_01			,       _UpperCAmelCase							: str=1e-6			,       _UpperCAmelCase							: str=False						):







		'''simple docstring'''





		__UpperCAmelCase   :					List[Any]													=     xa  # set the initial guess
		__UpperCAmelCase   :					List[str]													=     [a]
		__UpperCAmelCase   :					Tuple													=     abs(f(_UpperCAmelCase						)						)
		__UpperCAmelCase   :					List[Any]													=     lambda _UpperCAmelCase						: calc_derivative(_UpperCAmelCase			,       _UpperCAmelCase			,       h=_UpperCAmelCase						)  # noqa: E731  Derivative of f(x)
		for _ in range(_UpperCAmelCase						):
				if fa(_UpperCAmelCase						) == 0:
						raise ValueError('''No converging solution found'''						)
				__UpperCAmelCase   :					List[str]													=     a - f(_UpperCAmelCase						) / fa(_UpperCAmelCase						)  # Calculate the next estimate
				if logsteps:
						steps.append(_UpperCAmelCase						)
				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

				__A             =lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
				__A      ,      __A      ,      __A             =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}}}''')










from __future__ import annotations

import random
from collections.abc import Iterable
from typing import Any, Generic, TypeVar

__A             =TypeVar("T", bound=bool)

class 		UpperCAmelCase__      (      Generic[T]       ):




			'''simple docstring'''






			def __init__(       self							:			List[Any]	,	a_							:			T			):
					'''simple docstring'''





					__UpperCAmelCase   :					T													=     value
					__UpperCAmelCase   :					RandomizedHeapNode[T] | None													=     None
					__UpperCAmelCase   :					RandomizedHeapNode[T] | None													=     None




			@property
			def 			snake_case__					(       self							:			Any			):
					'''simple docstring'''





					return self._value




			@staticmethod
			def 			snake_case__					(       a_							:			RandomizedHeapNode[T] | None	,	a_							:			RandomizedHeapNode[T] | None			):
					'''simple docstring'''





					if not roota:
							return roota

					if not roota:
							return roota

					if roota.value > roota.value:
							__UpperCAmelCase							, __UpperCAmelCase   :					int													=     roota, roota

					if random.choice([True, False]			):
							__UpperCAmelCase							, __UpperCAmelCase   :					Union[str, Any]													=     roota.right, roota.left

					__UpperCAmelCase   :					Optional[Any]													=     RandomizedHeapNode.merge(roota.left	,	a_			)

					return roota

class 		UpperCAmelCase__      (      Generic[T]       ):




			'''simple docstring'''






			def __init__(       self							:			Tuple	,	a_							:			Iterable[T] | None = ()			):
					'''simple docstring'''





					__UpperCAmelCase   :					RandomizedHeapNode[T] | None													=     None

					if data:
							for item in data:
									self.insert(a_			)




			def 			snake_case__					(       self							:			List[str]	,	a_							:			T			):
					'''simple docstring'''





					__UpperCAmelCase   :					Optional[Any]													=     RandomizedHeapNode.merge(self._root	,	RandomizedHeapNode(a_			)			)




			def 			snake_case__					(       self							:			Optional[int]			):
					'''simple docstring'''





					__UpperCAmelCase   :					Optional[Any]													=     self.top()

					if self._root is None:
							return None

					__UpperCAmelCase   :					Tuple													=     RandomizedHeapNode.merge(self._root.left	,	self._root.right			)

					return result




			def 			snake_case__					(       self							:			Any			):
					'''simple docstring'''





					if not self._root:
							raise IndexError('''Can\'t get top element for the empty heap.'''			)
					return self._root.value




			def 			snake_case__					(       self							:			Optional[Any]			):
					'''simple docstring'''





					__UpperCAmelCase   :					str													=     None




			def 			snake_case__					(       self							:			Tuple			):
					'''simple docstring'''





					__UpperCAmelCase   :					List[Any]													=     []
					while self:
							result.append(self.pop()			)

					return result




			def __bool__(       self							:			List[Any]			):
					'''simple docstring'''





					return self._root is not None


if __name__ == "__main__":
				import doctest

				doctest.testmod()





