Let G = (V,E) be a directed graph (not necessarily acyclic). Design an efficient algorithmto label the vertices of the graph with distinct labels from1 to |V | such that the label of each vertex v is greater than the label of at least one of v’s predecessors (if v has any), or to determine that no such labeling is possible (w is a predecessor of v iff (w, v) ∈ E). Your algorithm should run in time O(n + e).

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