

from __future__ import annotations

__lowerCamelCase						    =      '''#'''


class    A__ :



    def __init__(   self    )  -> None:





           '''simple docstring'''
           A_		   = {}



    def    snake_case_     (   self						,			UpperCamelCase__    )  -> None:





           '''simple docstring'''
           A_		   = self._trie
           for char in text:
                  if char not in trie:
                         A_		   = {}
                  A_		   = trie[char]
           A_		   = True



    def    snake_case_     (   self						,			UpperCamelCase__    )  -> tuple | list:





           '''simple docstring'''
           A_		   = self._trie
           for char in prefix:
                  if char in trie:
                         A_		   = trie[char]
                  else:
                         return []
           return self._elements(UpperCamelCase__    )







    def    snake_case_     (   self						,			UpperCamelCase__    )  -> tuple:





           '''simple docstring'''
           A_		   = []
           for c, v in d.items():
                  A_		   = [""" """] if c == END else [(c + s) for s in self._elements(UpperCamelCase__    )]
                  result.extend(UpperCamelCase__    )
           return tuple(UpperCamelCase__    )

__lowerCamelCase						    =      Trie()
__lowerCamelCase						    =      ('''depart''', '''detergent''', '''daring''', '''dog''', '''deer''', '''deal''')
for word in words:
      trie.insert_word(word)
def  UpperCAmelCase__      ( UpperCAmelCase__			)     ->     tuple:
       A_		   = trie.find_word(UpperCAmelCase__			)
       return tuple(string + word for word in suffixes			)
def  UpperCAmelCase__      ( )     ->     None:
       print(autocomplete_using_trie("""de"""			)			)


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      main()



'''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()
