João Augusto

Which of the following concepts is central to the study of evolving networks? A) Clustering coefficient B) Preferential attachment C) Network robustness D) Shortest path length E) None of the above Original Idea by João Augusto Ferreira de Moura

 Find the derivative of the function  f ( x ) = 2 x 3 − 4 x + 1 x 2 + 1 f(x) = \frac{2x^3 - 4x + 1}{x^2 + 1} Options: A) 6 x 2 ( x 2 + 1 ) − ( 2 x 3 − 4 x + 1 ) ( 2 x ) ( x 2 + 1 ) 2 \frac{6x^2(x^2 + 1) - (2x^3 - 4x + 1)(2x)}{(x^2 + 1)^2} ​ B) ( 6 x 2 − 4 ) ( x 2 + 1 ) − ( 2 x 3 − 4 x + 1 ) ( 2 x ) ( x 2 + 1 ) 2 \frac{(6x^2 - 4)(x^2 + 1) - (2x^3 - 4x + 1)(2x)}{(x^2 + 1)^2} ​ C) ( 6 x 2 − 4 ) ( x 2 + 1 ) − ( 2 x 3 − 4 x + 1 ) ( 2 ) ( x 2 + 1 ) 2 \frac{(6x^2 - 4)(x^2 + 1) - (2x^3 - 4x + 1)(2)}{(x^2 + 1)^2} D) ( 6 x 2 − 4 ) ( x 2 + 1 ) − ( 2 x 3 − 4 x + 1 ) ( x ) ( x 2 + 1 ) 2 \frac{(6x^2 - 4)(x^2 + 1) - (2x^3 - 4x + 1)(x)}{(x^2 + 1)^2} ​ E) None of the above​ Original idea by: João Augusto Ferreira de Moura

  Given the undirected graph bellow: What is the distance from A to all nodes in this graph if we use a BFS algorithm starting from A? a) A - 0, B - 1, C - 2, D - 1, E - 2, F - 3, H - 4, G - 0 b) A - 0, B - 1, C - 2, D - 1, E - 2, F - 2, H - 3, G - 4 c) A - 0, B - 1, C - 2, D - 1, E - 2, F - 2, H - 3, G - Null d) A - 0, B - 1, C - 2, D - 1, E - 2, F - 2, H - 3, G - Null e) None of the above

Select one correct alternative about the BFS algorithm:  a) BFS uses a stack to store the vertices to be explored. b) A BFS can be used to find a path from one vertex to another in an unweighted graph, but it does not guarantee that this path is the shortest possible. c) A BFS can be used in undirected unweighted graphs to determine the distance between an initial vertex and all other vertices that make up the same connected component. d) A BFS is used in weighted graphs to determine the shortest path between a vertex and all others. e) None of the above. Original idea by: João Augusto Ferreira de Moura

  Observing the directed graph bellow From which vertices should the DFS start so that all vertices are visited at least once. a) 5 and 3 b) 4 and 2 c) 6 and 3 d) 6 and 2 e) none of the above