





"""simple docstring"""

from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

_lowerCamelCase  :			Union[str, Any]        =       TypeVar('T')

def 		lowercase_      (		_UpperCAmelCase	):




	"""simple docstring"""






	return (position - 1) // 2

def 		lowercase_      (		_UpperCAmelCase	):




	"""simple docstring"""






	return (2 * position) + 1

def 		lowercase_      (		_UpperCAmelCase	):




	"""simple docstring"""






	return (2 * position) + 2

class        lowercase      (    Generic[T]):







				def __init__(							self   :					str       ):



					"""simple docstring"""

					A_  :				list[tuple[T, int]]	   =		[]
					A_  :				dict[T, int]	   =		{}
					A_  :				int	   =		0







				def __len__(							self   :					List[str]       ):



					"""simple docstring"""

					return self.elements







				def __repr__(							self   :					str       ):



					"""simple docstring"""

					return str(self.heap       )







				def 					a_  (							self   :					Optional[int]       ):



					"""simple docstring"""

					return self.elements == 0







				def 					a_  (							self   :					Tuple      ,     _lowerCamelCase   :					List[Any]      ,     _lowerCamelCase   :					Union[str, Any]       ):



					"""simple docstring"""

					self.heap.append((elem, weight)       )
					A_  :				Optional[Any]	   =		self.elements
					self.elements += 1
					self._bubble_up(lowercase__       )







				def 					a_  (							self   :					Dict       ):



					"""simple docstring"""

					if self.elements > 1:
						self._swap_nodes(0      ,     self.elements - 1       )
					A_  :				int	   =		self.heap.pop()
					del self.position_map[elem]
					self.elements -= 1
					if self.elements > 0:
						A_  :				List[Any]	   =		self.heap[0]
						self._bubble_down(lowercase__       )
					return elem







				def 					a_  (							self   :					Tuple      ,     _lowerCamelCase   :					Tuple      ,     _lowerCamelCase   :					Optional[int]       ):



					"""simple docstring"""

					A_  :				Union[str, Any]	   =		self.position_map[elem]
					A_  :				Tuple	   =		(elem, weight)
					if position > 0:
						A_  :				Tuple	   =		get_parent_position(lowercase__       )
						A_  :				List[Any]	   =		self.heap[parent_position]
						if parent_weight > weight:
							self._bubble_up(lowercase__       )
						else:
							self._bubble_down(lowercase__       )
					else:
						self._bubble_down(lowercase__       )







				def 					a_  (							self   :					Any      ,     _lowerCamelCase   :					Union[str, Any]       ):



					"""simple docstring"""

					A_  :				int	   =		self.position_map[elem]
					if curr_pos == 0:
						return None
					A_  :				Optional[int]	   =		get_parent_position(lowercase__       )
					A_  :				List[Any]	   =		self.heap[curr_pos]
					A_  :				int	   =		self.heap[parent_position]
					if parent_weight > weight:
						self._swap_nodes(lowercase__      ,     lowercase__       )
						return self._bubble_up(lowercase__       )
					return None







				def 					a_  (							self   :					Union[str, Any]      ,     _lowerCamelCase   :					Optional[int]       ):



					"""simple docstring"""

					A_  :				int	   =		self.position_map[elem]
					A_  :				Optional[Any]	   =		self.heap[curr_pos]
					A_  :				int	   =		get_child_left_position(lowercase__       )
					A_  :				Union[str, Any]	   =		get_child_right_position(lowercase__       )
					if child_left_position < self.elements and child_right_position < self.elements:
						A_  :				str	   =		self.heap[child_left_position]
						A_  :				Optional[Any]	   =		self.heap[child_right_position]
						if child_right_weight < child_left_weight and child_right_weight < weight:
							self._swap_nodes(lowercase__      ,     lowercase__       )
							return self._bubble_down(lowercase__       )
					if child_left_position < self.elements:
						A_  :				Optional[int]	   =		self.heap[child_left_position]
						if child_left_weight < weight:
							self._swap_nodes(lowercase__      ,     lowercase__       )
							return self._bubble_down(lowercase__       )
					else:
						return None
					if child_right_position < self.elements:
						A_  :				List[Any]	   =		self.heap[child_right_position]
						if child_right_weight < weight:
							self._swap_nodes(lowercase__      ,     lowercase__       )
							return self._bubble_down(lowercase__       )
					return None







				def 					a_  (							self   :					List[str]      ,     _lowerCamelCase   :					int      ,     _lowerCamelCase   :					str       ):



					"""simple docstring"""

					A_  :				List[str]	   =		self.heap[nodea_pos][0]
					A_  :				List[Any]	   =		self.heap[nodea_pos][0]
					A_  :				Optional[Any]	   =		(
					    self.heap[nodea_pos],
					    self.heap[nodea_pos],
					)
					A_  :				Dict	   =		nodea_pos
					A_  :				List[str]	   =		nodea_pos

class        lowercase      (    Generic[T]):







				def __init__(							self   :					List[str]       ):



					"""simple docstring"""

					A_  :				dict[T, dict[T, int]]	   =		{}
					A_  :				int	   =		0







				def __repr__(							self   :					Tuple       ):



					"""simple docstring"""

					return str(self.connections       )







				def __len__(							self   :					Any       ):



					"""simple docstring"""

					return self.nodes







				def 					a_  (							self   :					Any      ,     _lowerCamelCase   :					Optional[int]       ):



					"""simple docstring"""

					if node not in self.connections:
						A_  :				List[str]	   =		{}
						self.nodes += 1







				def 					a_  (							self   :					List[Any]      ,     _lowerCamelCase   :					str      ,     _lowerCamelCase   :					Dict      ,     _lowerCamelCase   :					Tuple       ):



					"""simple docstring"""

					self.add_node(lowercase__       )
					self.add_node(lowercase__       )
					A_  :				int	   =		weight
					A_  :				Any	   =		weight

def 		lowercase_      (		_UpperCAmelCase  ,      ):




	"""simple docstring"""






	A_  :				dict[T, int]	   =		{node: maxsize for node in graph.connections}
	A_  :				dict[T, T | None]	   =		{node: None for node in graph.connections}

	A_  :				MinPriorityQueue[T]	   =		MinPriorityQueue()
	for node, weight in dist.items():
		priority_queue.push(SCREAMING_SNAKE_CASE_  ,      SCREAMING_SNAKE_CASE_	)

	if priority_queue.is_empty():
		return dist, parent

	# initialization
	A_  :				Union[str, Any]	   =		priority_queue.extract_min()
	A_  :				int	   =		0
	for neighbour in graph.connections[node]:
		if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
			A_  :				Tuple	   =		dist[node] + graph.connections[node][neighbour]
			priority_queue.update_key(SCREAMING_SNAKE_CASE_  ,      dist[neighbour]	)
			A_  :				Dict	   =		node

    # running prim's algorithm
	while not priority_queue.is_empty():
		A_  :				List[str]	   =		priority_queue.extract_min()
		for neighbour in graph.connections[node]:
			if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
				A_  :				Dict	   =		dist[node] + graph.connections[node][neighbour]
				priority_queue.update_key(SCREAMING_SNAKE_CASE_  ,      dist[neighbour]	)
				A_  :				List[Any]	   =		node
	return dist, parent











"""simple docstring"""

from __future__ import annotations

from collections import namedtuple

def 		lowercase_      (		_UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase	):




	"""simple docstring"""






	A_  :				int	   =		namedtuple('''result'''  ,      '''name value'''	)
	if (voltage, current, power).count(0	) != 1:
		raise ValueError('''Only one argument must be 0'''	)
	elif power < 0:
		raise ValueError(
		    '''Power cannot be negative in any electrical/electronics system'''	)
	elif voltage == 0:
		return result('''voltage'''  ,      power / current	)
	elif current == 0:
		return result('''current'''  ,      power / voltage	)
	elif power == 0:
		return result('''power'''  ,      float(round(abs(voltage * current	)  ,      2	)	)	)
	else:
		raise ValueError('''Exactly one argument must be 0'''	)


if __name__ == "__main__":
		import doctest

		doctest.testmod()





