Problem$3.$ Show the ordering of vertices produced by topological sorting when it is run on the DAG of figure $22\mathrm{.}8$ in the $3^{rd}$ edition textbook$($page $615).$

a$.$ Give the ordering by the DFS$-$based topological sorting algorithm. Show the result after each step, and the final ordering.

b$.$ Give the ordering by the easy$-$topological sorting algorithm. Show the result after each step, and the final ordering.