### Algorithm for computing a topological ordering of a dag

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##### Reference no: EM1327920

An algorithm for computing a topological ordering of a DAG (Directed Acyclic Graph) repeatedly finds a node with no incoming edges and deletes it. This will eventually produce a topological ordering, provided that the input graph really is a DAG.

But suppose that we're given an arbitrary graph that may or may not be a DAG. Extend the topological ordering algorithm so that given an input directed graph G it outputs one of two things: (a) a topological ordering, thus establishing that G is a DAG; or (b) a cycle in G, and thus establishing that G is not a DAG. The running time of your algorithm should be O(m+n) for a directed graph with n nodes and medges.

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