$$Consider the DirectedDFS algorithm $13\mathrm{.}11$ from the book or as given in class. It does not distinguish between forward and cross edges.$$

a$.$ Modify this algorithm to differentiate between these edges; that is$,$ give its pseudocode. Thus, edges can be one of four types: tree, back, cross or forward.$$

b$.$ Give an example of running your algorithm.$$

c$.$ Prove its correctness for labeling these four edges and its running time.$$

$$Consider the DirectedDFS algorithm $13\mathrm{.}11$ from the book or as given in class. It does not distinguish between forward and cross edges.$$

a$.$ Modify this algorithm to differentiate between these edges; that is$,$ give its pseudocode. Thus, edges can be one of four types: tree, back, cross or forward.$$

b$.$ Give an example of running your algorithm.$$

c$.$ Prove its correctness for labeling these four edges and its running time.$$

$$Consider the DirectedDFS algorithm $13\mathrm{.}11$ from the book or as given in class. It does not distinguish between forward and cross edges.$$

a$.$ Modify this algorithm to differentiate between these edges; that is$,$ give its pseudocode. Thus, edges can be one of four types: tree, back, cross or forward.$$

b$.$ Give an example of running your algorithm.$$

c$.$ Prove its correctness for labeling these four edges and its running time.$$

$$Consider the DirectedDFS algorithm $13\mathrm{.}11$ from the book or as given in class. It does not distinguish between forward and cross edges.$$

a$.$ Modify this algorithm to differentiate between these edges; that is$,$ give its pseudocode. Thus, edges can be one of four types: tree, back, cross or forward.$$

b$.$ Give an example of running your algorithm.$$

c$.$ Prove its correctness for labeling these four edges and its running time.$$