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You are given a directed graph G with n vertices and m edges. A number of the vertices is an assignment of a color to

You are given a directed graph G with n vertices and m edges. A number of the vertices is an assignment of a color to each vertex: with the following restriction: if (u,v)is an edge in the graph then number(u) <= number(v)

Design algorithm that returns maximum number of different number that can be used to number the graph. Give run time analysis.

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