$1.$ Find a topological ordering for the graph in Figure $9\mathrm{.}81.$

$2.$a$.$ Find the shortest path from A to all other vertices for the graph in Figure $9\mathrm{.}82.$ b$.$ Find the shortest unweighted path from B to all other vertices for the graph in Figure $9\mathrm{.}82.$

$3.$A$.$ Give an example where Dijkstra$$s algorithm gives the wrong answer in the presence of a negative edge but no negative$-$cost cycle. B$.$ Show that the weighted shortest$-$path algorithm suggested in Section $9\mathrm{.}3\mathrm{.}3$ works if there are negative$-$weight edges, but no negative$-$cost cycles, and that the running time of this algorithm is O$(|$E$||$V$|).$