




'''simple docstring'''
import heapq






def A__					(  UpperCAmelCase_						,						UpperCAmelCase_						,						UpperCAmelCase_							):
						_UpperCamelCase      :	int				       =     [(0, start)]  # cost from start node,end node
						_UpperCamelCase      :	int				       =     set()
						while heap:
												(_UpperCamelCase)      :	str				       =     heapq.heappop(__lowerCamelCase							)
												if u in visited:
																		continue
												visited.add(__lowerCamelCase							)
												if u == end:
																		return cost
												for v, c in graph[u]:
																		if v in visited:
																								continue
																		_UpperCamelCase      :	Optional[int]				       =     cost + c
																		heapq.heappush(__lowerCamelCase						,						(next_item, v)							)
						return -1


snake_case_				:			List[str]						 =						{
    """A""": [["""B""", 2], ["""C""", 5]],
    """B""": [["""A""", 2], ["""D""", 3], ["""E""", 1], ["""F""", 1]],
    """C""": [["""A""", 5], ["""F""", 3]],
    """D""": [["""B""", 3]],
    """E""": [["""B""", 4], ["""F""", 3]],
    """F""": [["""C""", 3], ["""E""", 3]],
}
snake_case_				:			str						 =						{
    """B""": [["""C""", 1]],
    """C""": [["""D""", 1]],
    """D""": [["""F""", 1]],
    """E""": [["""B""", 1], ["""F""", 3]],
    """F""": [],
}
snake_case_				:			Dict						 =						{
    """B""": [["""C""", 1]],
    """C""": [["""D""", 1]],
    """D""": [["""F""", 1]],
    """E""": [["""B""", 1], ["""G""", 2]],
    """F""": [],
    """G""": [["""F""", 1]],
}

snake_case_				:			List[Any]						 =						dijkstra(G, 'E', 'C')
print(short_distance)  # E -- 3 --> F -- 3 --> C == 6

snake_case_				:			Tuple						 =						dijkstra(Ga, 'E', 'F')
print(short_distance)  # E -- 3 --> F == 3

snake_case_				:			List[Any]						 =						dijkstra(Ga, 'E', 'F')
print(short_distance)  # E -- 2 --> G -- 1 --> F == 3

if __name__ == "__main__":
					import doctest

					doctest.testmod()







'''simple docstring'''
from __future__ import annotations

from queue import Queue






class 							lowercase__			:





	def __init__(				self      :       int				):







							'''simple docstring'''
							_UpperCamelCase      :	dict[int, list[int]]				       =     {}





	def 			UpperCamelCase_						(				self      :       int				):







							'''simple docstring'''
							for i in self.vertices:
													print(lowerCamelCase__				,' : '				,' -> '.join([str(lowerCamelCase__				) for j in self.vertices[i]]				)				)





	def 			UpperCamelCase_						(				self      :       Optional[Any]				,lowerCamelCase__      :       int				,lowerCamelCase__      :       int				):







							'''simple docstring'''
							if from_vertex in self.vertices:
													self.vertices[from_vertex].append(lowerCamelCase__				)
							else:
													_UpperCamelCase      :	Any				       =     [to_vertex]





	def 			UpperCamelCase_						(				self      :       int				,lowerCamelCase__      :       int				):







							'''simple docstring'''
							_UpperCamelCase      :	Dict				       =     set()

							# create a first in first out queue to store all the vertices for BFS
							_UpperCamelCase      :	Queue				       =     Queue()

							# mark the source node as visited and enqueue it
							visited.add(lowerCamelCase__				)
							queue.put(lowerCamelCase__				)

							while not queue.empty():
													_UpperCamelCase      :	Optional[Any]				       =     queue.get()

													# loop through all adjacent vertex and enqueue it if not yet visited
													for adjacent_vertex in self.vertices[vertex]:
																			if adjacent_vertex not in visited:
																									queue.put(lowerCamelCase__				)
																									visited.add(lowerCamelCase__				)
							return visited


if __name__ == "__main__":
					from doctest import testmod

					testmod(verbose=True)

					snake_case_				:			int						 =						Graph()
					g.add_edge(0, 1)
					g.add_edge(0, 2)
					g.add_edge(1, 2)
					g.add_edge(2, 0)
					g.add_edge(2, 3)
					g.add_edge(3, 3)

					g.print_graph()
					# 0  :  1 -> 2
					# 1  :  2
					# 2  :  0 -> 3
					# 3  :  3

					assert sorted(g.bfs(2)) == [0, 1, 2, 3]


