


def  lowerCAmelCase_ (							UpperCamelCase_  )     ->		int:
       UpperCamelCase_          =  set()
       # edges = list of graph's edges
       UpperCamelCase_          =  get_edges(_lowercase  )

       # While there are still elements in edges list, take an arbitrary edge
       # (from_node, to_node) and add his extremity to chosen_vertices and then
       # remove all arcs adjacent to the from_node and to_node
       while edges:
              UpperCamelCase_       , UpperCamelCase_          =  edges.pop()
              chosen_vertices.add(_lowercase  )
              chosen_vertices.add(_lowercase  )
              for edge in edges.copy():
                     if from_node in edge or to_node in edge:
                            edges.discard(_lowercase  )
       return chosen_vertices




def  lowerCAmelCase_ (							UpperCamelCase_  )     ->		Dict:
       UpperCamelCase_          =  set()
       for from_node, to_nodes in graph.items():
              for to_node in to_nodes:
                     edges.add((from_node, to_node)  )
       return edges


if __name__ == "__main__":
     import doctest

     doctest.testmod()

     # graph = {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
     # print(f"Matching vertex cover:\n{matching_min_vertex_cover(graph)}")








import sys




def  lowerCAmelCase_ (							UpperCamelCase_  )     ->		Union[str, Any]:
       UpperCamelCase_          =  len(UpperCamelCase_  )
       UpperCamelCase_          =  [[0 for x in range(UpperCamelCase_  )] for x in range(UpperCamelCase_  )]
       UpperCamelCase_          =  [[0 for x in range(UpperCamelCase_  )] for x in range(UpperCamelCase_  )]

       for chain_length in range(2					,		UpperCamelCase_  ):
              for a in range(1					,		n - chain_length + 1  ):
                     UpperCamelCase_          =  a + chain_length - 1

                     UpperCamelCase_          =  sys.maxsize
                     for c in range(UpperCamelCase_					,		UpperCamelCase_  ):
                            UpperCamelCase_          =  (
                                matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
                            )
                            if cost < matrix[a][b]:
                                   UpperCamelCase_          =  cost
                                   UpperCamelCase_          =  c
       return matrix, sol




def  lowerCAmelCase_ (							UpperCamelCase_					,		UpperCamelCase_					,		UpperCamelCase_  )     ->		List[str]:
       if i == j:
              print("A" + str(UpperCamelCase_  )					,		end=" "  )
       else:
              print("("					,		end=" "  )
              print_optiomal_solution(UpperCamelCase_					,		UpperCamelCase_					,		optimal_solution[i][j]  )
              print_optiomal_solution(UpperCamelCase_					,		optimal_solution[i][j] + 1					,		UpperCamelCase_  )
              print(")"					,		end=" "  )




def  lowerCAmelCase_ (							)     ->		Any:
       UpperCamelCase_          =  [30, 35, 15, 5, 10, 20, 25]
       UpperCamelCase_          =  len(UpperCamelCase_  )
       # Size of matrix created from above array will be
       # 30*35 35*15 15*5 5*10 10*20 20*25
       UpperCamelCase_       , UpperCamelCase_          =  matrix_chain_order(UpperCamelCase_  )

       print("No. of Operation required: " + str(matrix[1][n - 1]  )  )
       print_optiomal_solution(UpperCamelCase_					,		1					,		n - 1  )


if __name__ == "__main__":
     main()

