

from __future__ import annotations

__lowerCamelCase						    =      {
    '''A''': ['''B''', '''C''', '''E'''],
    '''B''': ['''A''', '''D''', '''E'''],
    '''C''': ['''A''', '''F''', '''G'''],
    '''D''': ['''B'''],
    '''E''': ['''A''', '''B''', '''D'''],
    '''F''': ['''C'''],
    '''G''': ['''C'''],
}


class    A__ :



    def __init__(   self						,			UpperCamelCase__						,			UpperCamelCase__    )  -> None:





           '''simple docstring'''
           A_		   = graph
           # mapping node to its parent in resulting breadth first tree
           A_		   = {}
           A_		   = source_vertex



    def    snake_case_     (   self    )  -> None:





           '''simple docstring'''
           A_		   = {self.source_vertex}
           A_		   = None
           A_		   = [self.source_vertex]  # first in first out queue

           while queue:
                  A_		   = queue.pop(0    )
                  for adjacent_vertex in self.graph[vertex]:
                         if adjacent_vertex not in visited:
                                visited.add(__A    )
                                A_		   = vertex
                                queue.append(__A    )







    def    snake_case_     (   self						,			UpperCamelCase__    )  -> str:





           '''simple docstring'''
           if target_vertex == self.source_vertex:
                  return self.source_vertex

           A_		   = self.parent.get(__A    )
           if target_vertex_parent is None:
                  A_		   = (
                      f'''No path from vertex: {self.source_vertex} to vertex: {target_vertex}'''
                  )
                  raise ValueError(__A    )

           return self.shortest_path(__A    ) + f'''->{target_vertex}'''


if __name__ == "__main__":
      __lowerCamelCase						    =      Graph(graph, '''G''')
      g.breath_first_search()
      print(g.shortest_path('''D'''))
      print(g.shortest_path('''G'''))
      print(g.shortest_path('''Foo'''))



'''simple docstring'''







import heapq as hq
import math
from collections.abc import Iterator


class    A__ :



    def __init__(   self						,			UpperCamelCase__    )  -> Dict:





           '''simple docstring'''
           A_		   = str(id_    )
           A_		   = None
           A_		   = None
           A_		   = []
           A_		   = {}  # {vertex:distance}



    def __lt__(   self						,			UpperCamelCase__    )  -> Optional[int]:





           '''simple docstring'''
           return self.key < other.key



    def __repr__(   self    )  -> Dict:





           '''simple docstring'''
           return self.id



    def    snake_case_     (   self						,			UpperCamelCase__    )  -> Dict:





           '''simple docstring'''
           self.neighbors.append(UpperCamelCase__    )







    def    snake_case_     (   self						,			UpperCamelCase__						,			UpperCamelCase__    )  -> Optional[Any]:





           '''simple docstring'''
           A_		   = weight

def  UpperCAmelCase__      ( UpperCAmelCase__,    UpperCAmelCase__,    UpperCAmelCase__,    UpperCAmelCase__			)     ->     Optional[int]:
       # add the neighbors:
       graph[a - 1].add_neighbor(graph[b - 1]			)
       graph[b - 1].add_neighbor(graph[a - 1]			)
       # add the edges:
       graph[a - 1].add_edge(graph[b - 1],    UpperCAmelCase__			)
       graph[b - 1].add_edge(graph[a - 1],    UpperCAmelCase__			)
def  UpperCAmelCase__      ( UpperCAmelCase__,    UpperCAmelCase__			)     ->     list:
       A_		   = []
       for u in graph:
              A_		   = math.inf
              A_		   = None
       A_		   = 0
       A_		   = graph[:]
       while q:
              A_		   = min(UpperCAmelCase__			)
              q.remove(UpperCAmelCase__			)
              for v in u.neighbors:
                     if (v in q) and (u.edges[v.id] < v.key):
                            A_		   = u
                            A_		   = u.edges[v.id]
       for i in range(1,    len(UpperCAmelCase__			)			):
              a.append((int(graph[i].id			) + 1, int(graph[i].pi.id			) + 1)			)
       return a
def  UpperCAmelCase__      ( UpperCAmelCase__,    UpperCAmelCase__			)     ->     Iterator[tuple]:
       for u in graph:
              A_		   = math.inf
              A_		   = None
       A_		   = 0

       A_		   = list(UpperCAmelCase__			)
       hq.heapify(UpperCAmelCase__			)

       while h:
              A_		   = hq.heappop(UpperCAmelCase__			)
              for v in u.neighbors:
                     if (v in h) and (u.edges[v.id] < v.key):
                            A_		   = u
                            A_		   = u.edges[v.id]
                            hq.heapify(UpperCAmelCase__			)

       for i in range(1,    len(UpperCAmelCase__			)			):
              yield (int(graph[i].id			) + 1, int(graph[i].pi.id			) + 1)
def  UpperCAmelCase__      ( )     ->     None:
       pass


if __name__ == "__main__":
      import doctest

      doctest.testmod()
