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Suppose a polynomial time algorithm is discovered that correctly computes the largest clique in a given graph. In this scenario, which one of the following represents the correct Venn diagram of the complexity classes P, NP and NP Complete (NPC)?

1. (A)
2. (B)
3. (C)
4. (D)

Correct answer: (A)

Solution

If a polynomial time algorithm exists for the largest clique problem, which is NP-complete, it implies that all problems in NP can also be solved in polynomial time, thus making P equal to NP. This situation is accurately represented in option (A), where NP-complete problems are a subset of P.

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