Suppose that G is a directed graph. It was discussed that an algorithm will determine whether a given vertex can reach every other vertex in the graph (this is the 1-to-many reachability problem). Consider the following similar problem: given graph G, is there any node in G that can reach every other node in G? Such a node is called a source node. We want to know whether any node of G is a source node. A trivial algorithm for this is to execute DFS n times, using each node in G as the start node of the DFS. But the total time for this algorithm is O( n* (n+m)).

Describe a linear time algorithm for this does di-graph G have a source node problem.