Question: Topological Sort: Let G = (V,E) be a complete directed acyclic graph that has an edge between every pair of vertices and whose vertices are

Topological Sort:

Let G = (V,E) be a complete directed acyclic graph that has an edge between every pair of vertices and whose vertices are labelled 1, 2, . . . , n, where n = |V |. To determine the direction of an edge between two vertices in V you are only allowed to ask a query. A query consists of two specified vertices u and v and is answered as follows:

from u to v if (u,v)E ,or

from v to u if (v,u)E

Give a worst-case lower bound (as a function of n) for the number of queries required to find a topological sort of G. (Hint: this problem can be solved by popular algorithms)

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