Write an algorithm with the fastest possible time complexity, please do not write a program and list the time complexity.

We are given a DFS tree. Direct the edges away from the root. Show that each vertex has a directed path to the root that uses at most one backward edge, if and only if all the leaves have an edge to the root. Remark: The direction given to edges imply that you can go in the DFS tree from a parent to a child but not from a child to a parent. Note that backward edges are not directed and thus you can be used in on both directions.