

from __future__ import annotations

def 						UpperCamelCase (lowercase_:			list[int]   ,				lowercase_:			list[int]   ,				lowercase_:			int )					->				tuple[float, list[float]]:
	A__							:   Tuple					       =		list(range(len(lowercase_ ) ) )
	A__							:   Union[str, Any]					       =		[v / w for v, w in zip(lowercase_   ,				lowercase_ )]
	index.sort(key=lambda lowercase_ : ratio[i]   ,				reverse=lowercase_ )

	A__							:   float					       =		0
	A__							:   list[float]					       =		[0] * len(lowercase_ )
	for i in index:
		if weight[i] <= capacity:
			A__							:   Optional[int]					       =		1
			max_value += value[i]
			capacity -= weight[i]
		else:
			A__							:   Union[str, Any]					       =		capacity / weight[i]
			max_value += value[i] * capacity / weight[i]
			break

	return max_value, fractions


if __name__ == "__main__":
	import doctest

	doctest.testmod()






from queue import PriorityQueue
from typing import Any

import numpy as np

def 						UpperCamelCase (lowercase_:			dict   ,				lowercase_:			str   ,				lowercase_:			set   ,				lowercase_:			set   ,				lowercase_:			dict   ,				lowercase_:			dict   ,				lowercase_:			PriorityQueue   ,				lowercase_:			dict   ,				lowercase_:			float | int   ,				)					->				float | int:
	for nxt, d in graph[v]:
		if nxt in visited_forward:
			continue
		A__							:   Any					       =		cst_fwd.get(lowercase_   ,				np.inf )
		A__							:   List[Any]					       =		cst_fwd[v] + d
		if new_cost_f < old_cost_f:
			queue.put((new_cost_f, nxt) )
			A__							:   Tuple					       =		new_cost_f
			A__							:   Any					       =		v
		if nxt in visited_backward:
			if cst_fwd[v] + d + cst_bwd[nxt] < shortest_distance:
				A__							:   Optional[int]					       =		cst_fwd[v] + d + cst_bwd[nxt]
	return shortest_distance

def 						UpperCamelCase (lowercase_:			str   ,				lowercase_:			str   ,				lowercase_:			dict   ,				lowercase_:			dict )					->				int:
	A__							:   Dict					       =		-1

	A__							:   List[Any]					       =		set()
	A__							:   Union[str, Any]					       =		set()
	A__							:   Optional[Any]					       =		{source: 0}
	A__							:   int					       =		{destination: 0}
	A__							:   Optional[Any]					       =		{source: None}
	A__							:   Union[str, Any]					       =		{destination: None}
	A__							:   PriorityQueue[Any]					       =		PriorityQueue()
	A__							:   PriorityQueue[Any]					       =		PriorityQueue()

	A__							:   List[Any]					       =		np.inf

	queue_forward.put((0, source) )
	queue_backward.put((0, destination) )

	if source == destination:
		return 0

	while not queue_forward.empty() and not queue_backward.empty():
		A__       ,       A__							:   Tuple					       =		queue_forward.get()
		visited_forward.add(lowercase_ )

		A__       ,       A__							:   Optional[Any]					       =		queue_backward.get()
		visited_backward.add(lowercase_ )

		A__							:   List[Any]					       =		pass_and_relaxation(
		    lowercase_   ,				lowercase_   ,				lowercase_   ,				lowercase_   ,				lowercase_   ,				lowercase_   ,				lowercase_   ,				lowercase_   ,				lowercase_   ,				)

		A__							:   List[Any]					       =		pass_and_relaxation(
		    lowercase_   ,				lowercase_   ,				lowercase_   ,				lowercase_   ,				lowercase_   ,				lowercase_   ,				lowercase_   ,				lowercase_   ,				lowercase_   ,				)

		if cst_fwd[v_fwd] + cst_bwd[v_bwd] >= shortest_distance:
			break

	if shortest_distance != np.inf:
		A__							:   int					       =		shortest_distance
	return shortest_path_distance


A_	:			List[Any]  	=      {
    'B': [['C', 1]],
    'C': [['D', 1]],
    'D': [['F', 1]],
    'E': [['B', 1], ['G', 2]],
    'F': [],
    'G': [['F', 1]],
}
A_	:			Optional[int]  	=      {
    'B': [['E', 1]],
    'C': [['B', 1]],
    'D': [['C', 1]],
    'F': [['D', 1], ['G', 1]],
    'E': [[None, np.inf]],
    'G': [['E', 2]],
}

if __name__ == "__main__":
	import doctest

	doctest.testmod()



