
import math
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import SchedulerMixin, SchedulerOutput







class        A_   (			__lowerCamelCase      ,	__lowerCamelCase   ):




	'''simple docstring'''


	_UpperCamelCase     :     Optional[Any]							 =       1





	@register_to_config
	def __init__(       self		,    snake_case = 1000		,    snake_case = None       ):
		# set `betas`, `alphas`, `timesteps`
		self.set_timesteps(snake_case       )

		# standard deviation of the initial noise distribution
		lowercase       =    1.0

		# For now we only support F-PNDM, i.e. the runge-kutta method
		# For more information on the algorithm please take a look at the paper: https://arxiv.org/pdf/2202.09778.pdf
		# mainly at formula (9), (12), (13) and the Algorithm 2.
		lowercase       =    4

		# running values
		lowercase       =    []





	def 	SCREAMING_SNAKE_CASE__						(       self		,    snake_case		,    snake_case = None       ):
		lowercase       =    num_inference_steps
		lowercase       =    torch.linspace(1		,    0		,    num_inference_steps + 1       )[:-1]
		lowercase       =    torch.cat([steps, torch.tensor([0.0]       )]       )

		if self.config.trained_betas is not None:
			lowercase       =    torch.tensor(self.config.trained_betas		,    dtype=torch.floataa       )
		else:
			lowercase       =    torch.sin(steps * math.pi / 2       ) ** 2

		lowercase       =    (1.0 - self.betas**2) ** 0.5

		lowercase       =    (torch.atana(self.betas		,    self.alphas       ) / math.pi * 2)[:-1]
		lowercase       =    timesteps.to(snake_case       )

		lowercase       =    []





	def 	SCREAMING_SNAKE_CASE__						(       self		,    snake_case		,    snake_case		,    snake_case		,    snake_case = True		,    ):
		if self.num_inference_steps is None:
			raise ValueError(
			    'Number of inference steps is \'None\', you need to run \'set_timesteps\' after creating the scheduler'       )

		lowercase       =    (self.timesteps == timestep).nonzero().item()
		lowercase       =    timestep_index + 1

		lowercase       =    sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
		self.ets.append(snake_case       )

		if len(self.ets       ) == 1:
			lowercase       =    self.ets[-1]
		elif len(self.ets       ) == 2:
			lowercase       =    (3 * self.ets[-1] - self.ets[-2]) / 2
		elif len(self.ets       ) == 3:
			lowercase       =    (23 * self.ets[-1] - 16 * self.ets[-2] + 5 * self.ets[-3]) / 12
		else:
			lowercase       =    (1 / 24) * (55 * self.ets[-1] - 59 * self.ets[-2] + 37 * self.ets[-3] - 9 * self.ets[-4])

		lowercase       =    self._get_prev_sample(snake_case		,    snake_case		,    snake_case		,    snake_case       )

		if not return_dict:
			return (prev_sample,)

		return SchedulerOutput(prev_sample=snake_case       )





	def 	SCREAMING_SNAKE_CASE__						(       self		,    snake_case		,    *snake_case		,    **snake_case       ):
		return sample





	def 	SCREAMING_SNAKE_CASE__						(       self		,    snake_case		,    snake_case		,    snake_case		,    snake_case       ):
		lowercase       =    self.alphas[timestep_index]
		lowercase       =    self.betas[timestep_index]

		lowercase       =    self.alphas[prev_timestep_index]
		lowercase       =    self.betas[prev_timestep_index]

		lowercase       =    (sample - sigma * ets) / max(snake_case		,    1E-8       )
		lowercase       =    next_alpha * pred + ets * next_sigma

		return prev_sample





	def __len__(       self       ):
		return self.config.num_train_timesteps



import sys
from collections import defaultdict







class        A_   :




	'''simple docstring'''


	def __init__(       self       ):
		lowercase       =    []





	def 	SCREAMING_SNAKE_CASE__						(       self		,    snake_case       ):
		return self.node_position[vertex]





	def 	SCREAMING_SNAKE_CASE__						(       self		,    snake_case		,    snake_case       ):
		lowercase       =    pos





	def 	SCREAMING_SNAKE_CASE__						(       self		,    snake_case		,    snake_case		,    snake_case		,    snake_case       ):
		if start > size // 2 - 1:
			return
		else:
			if 2 * start + 2 >= size:
				lowercase       =    2 * start + 1
			else:
				if heap[2 * start + 1] < heap[2 * start + 2]:
					lowercase       =    2 * start + 1
				else:
					lowercase       =    2 * start + 2
			if heap[smallest_child] < heap[start]:
				lowercase  ,					lowercase       =    heap[smallest_child], positions[smallest_child]
				lowercase  ,					lowercase       =    (
				    heap[start],
				    positions[start],
				)
				lowercase  ,					lowercase       =    temp, tempa

				lowercase       =    self.get_position(positions[smallest_child]       )
				self.set_position(
				    positions[smallest_child]		,    self.get_position(positions[start]       )       )
				self.set_position(positions[start]		,    snake_case       )

				self.top_to_bottom(snake_case		,    snake_case		,    snake_case		,    snake_case       )





	def 	SCREAMING_SNAKE_CASE__						(       self		,    snake_case		,    snake_case		,    snake_case		,    snake_case       ):
		lowercase       =    position[index]

		while index != 0:
			lowercase       =    int((index - 2) / 2       ) if index % 2 == 0 else int((index - 1) / 2       )

			if val < heap[parent]:
				lowercase       =    heap[parent]
				lowercase       =    position[parent]
				self.set_position(position[parent]		,    snake_case       )
			else:
				lowercase       =    val
				lowercase       =    temp
				self.set_position(snake_case		,    snake_case       )
				break
			lowercase       =    parent
		else:
			lowercase       =    val
			lowercase       =    temp
			self.set_position(snake_case		,    0       )





	def 	SCREAMING_SNAKE_CASE__						(       self		,    snake_case		,    snake_case       ):
		lowercase       =    len(snake_case       ) // 2 - 1
		for i in range(snake_case		,    -1		,    -1       ):
			self.top_to_bottom(snake_case		,    snake_case		,    len(snake_case       )		,    snake_case       )





	def 	SCREAMING_SNAKE_CASE__						(       self		,    snake_case		,    snake_case       ):
		lowercase       =    positions[0]
		lowercase       =    sys.maxsize
		self.top_to_bottom(snake_case		,    0		,    len(snake_case       )		,    snake_case       )
		return temp






def 							UpperCAmelCase_		(							__SCREAMING_SNAKE_CASE							):
	lowercase       =    Heap()

	lowercase       =    [0] * len(__SCREAMING_SNAKE_CASE							)
	lowercase       =    [-1] * len(__SCREAMING_SNAKE_CASE							)  # Neighboring Tree Vertex of selected vertex
	# Minimum Distance of explored vertex with neighboring vertex of partial tree
	# formed in graph
	lowercase       =    []  # Heap of Distance of vertices from their neighboring vertex
	lowercase       =    []

	for vertex in range(len(__SCREAMING_SNAKE_CASE							)							):
		distance_tv.append(sys.maxsize							)
		positions.append(__SCREAMING_SNAKE_CASE							)
		heap.node_position.append(__SCREAMING_SNAKE_CASE							)

	lowercase       =    []
	lowercase       =    1
	lowercase       =    sys.maxsize
	for neighbor, distance in adjacency_list[0]:
		lowercase       =    0
		lowercase       =    distance
	heap.heapify(__SCREAMING_SNAKE_CASE ,							__SCREAMING_SNAKE_CASE							)

	for _ in range(1 ,							len(__SCREAMING_SNAKE_CASE							)							):
		lowercase       =    heap.delete_minimum(__SCREAMING_SNAKE_CASE ,							__SCREAMING_SNAKE_CASE							)
		if visited[vertex] == 0:
			tree_edges.append((nbr_tv[vertex], vertex)							)
			lowercase       =    1
			for neighbor, distance in adjacency_list[vertex]:
				if (
				    visited[neighbor] == 0
				    and distance < distance_tv[heap.get_position(__SCREAMING_SNAKE_CASE							)]
				):
					lowercase       =    distance
					heap.bottom_to_top(
					    __SCREAMING_SNAKE_CASE ,							heap.get_position(__SCREAMING_SNAKE_CASE							) ,							__SCREAMING_SNAKE_CASE ,							__SCREAMING_SNAKE_CASE							)
					lowercase       =    vertex
	return tree_edges


if __name__ == "__main__":  # pragma: no cover
	# < --------- Prims Algorithm --------- >
	UpperCAmelCase	      = int(input('''Enter number of edges: ''').strip())
	UpperCAmelCase	      = defaultdict(list)
	for _ in range(edges_number):
		UpperCAmelCase	      = [int(x) for x in input().strip().split()]
		adjacency_list[edge[0]].append([edge[1], edge[2]])
		adjacency_list[edge[1]].append([edge[0], edge[2]])
	print(prisms_algorithm(adjacency_list))

