





from __future__ import annotations




def 						A_			(  lowercase_  )			->						Any:



       if len(__A  ) == 0:
              raise ValueError('''find_max() arg is an empty sequence'''  )
       _snake_case      :							Dict     				=						nums[0]
       for x in nums:
              if x > max_num:
                     _snake_case      :							Optional[Any]     				=						x
       return max_num


if __name__ == "__main__":
   import doctest

   doctest.testmod(verbose=True)













from __future__ import annotations

class 				A    :



      def __init__(					self     ,  lowercase_					)      ->   None:



             '''simple docstring'''

             _snake_case      :							Optional[Any]     				=						vertices
             _snake_case      :							int     				=						[[0] * vertices for _ in range(lowercase_					)]



      def    __a (					self     ,  lowercase_					)      ->   None:



             '''simple docstring'''

             print('''Vertex \t Distance from Source'''					)
             for vertex in range(self.vertices					):
                    print(lowercase_     ,  '''\t\t'''     ,  distances_from_source[vertex]					)



      def    __a (					self     ,  lowercase_     ,  lowercase_					)      ->   int:



             '''simple docstring'''

             _snake_case      :							List[Any]     				=						1E7
             _snake_case      :							Tuple     				=						0

             # Search not nearest vertex not in the shortest path tree
             for vertex in range(self.vertices					):
                    if distances_from_source[vertex] < minimum and visited[vertex] is False:
                           _snake_case      :							Dict     				=						distances_from_source[vertex]
                           _snake_case      :							int     				=						vertex
             return min_index



      def    __a (					self     ,  lowercase_					)      ->   None:



             '''simple docstring'''

             _snake_case      :							List[Any]     				=						[int(1E7					)] * self.vertices  # distances from the source
             _snake_case      :							List[Any]     				=						0
             _snake_case      :							List[str]     				=						[False] * self.vertices

             for _ in range(self.vertices					):
                    _snake_case      :							List[Any]     				=						self.minimum_distance(lowercase_     ,  lowercase_					)
                    _snake_case      :							List[str]     				=						True

                    # Update dist value of the adjacent vertices
                    # of the picked vertex only if the current
                    # distance is greater than new distance and
                    # the vertex in not in the shortest path tree
                    for v in range(self.vertices					):
                           if (
                               self.graph[u][v] > 0
                               and visited[v] is False
                               and distances[v] > distances[u] + self.graph[u][v]
                           ):
                                  _snake_case      :							Any     				=						distances[u] + self.graph[u][v]

             self.print_solution(lowercase_					)


if __name__ == "__main__":
   lowerCAmelCase_   =   Graph(9)
   lowerCAmelCase_   =   [
       [0, 4, 0, 0, 0, 0, 0, 8, 0],
       [4, 0, 8, 0, 0, 0, 0, 1_1, 0],
       [0, 8, 0, 7, 0, 4, 0, 0, 2],
       [0, 0, 7, 0, 9, 1_4, 0, 0, 0],
       [0, 0, 0, 9, 0, 1_0, 0, 0, 0],
       [0, 0, 4, 1_4, 1_0, 0, 2, 0, 0],
       [0, 0, 0, 0, 0, 2, 0, 1, 6],
       [8, 1_1, 0, 0, 0, 0, 1, 0, 7],
       [0, 0, 2, 0, 0, 0, 6, 7, 0],
   ]
   graph.dijkstra(0)






