Question

Which of the following is TRUE about Topological Sorting?

1. Topological Sort can be used as a subroutine to find shortest paths in a weighted DAG in time O(V+E); in particular, the time does not depend on the magnitudes of the weights on the edges, and the weights on the edges may be negative.
2. A Topological Sort algorithm sorts the nodes of an arbitrary directed graph G in an order that is consistent with all the paths in G, that is if there is a path from u to v in G then u precedes v in the resulting sorted list.
3. Topological Sort sorts an array of numbers of length n in time O(n).
4. When Topological Sort is used to find shortest paths in a weighted DAG, no relaxation steps are necessary.
5. Topological Sort of a DAG can be implemented easily using DFS in time O(V+E), based on the times when the nodes in the DAG are first encountered in the DFS.

Answer 1

Topological Sort of a DAG can be implemented easily using DFS in time O(V+E), based on the times when the nodes in the DAG are first encountered in the DFS.