. A path cover of a directed graph G = (V, E) is a set P of vertex-disjoint paths such that every vertex in V is included in exactly one path in P. Paths may start and endanywhere, and they may be of any length, including 0. A minimum path cover of G is a path cover containing the fewest possible paths. a) Give an efficient algorithm to find a minimum path cover of a directed acyclicgraph G = (V, E).

b) Does your algorithm work for directed graphs that contain cycles? Explain.