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)?

The problem of finding the maximum (largest) clique in a graph is an NP-hard optimization problem, and its corresponding decision version (CLIQUE) is NP-complete.

If a polynomial-time algorithm is discovered that solves the largest clique problem, it can solve the decision version in polynomial time as well. Since CLIQUE is NP-complete, solving it in polynomial time implies:

When $\text{P} = \text{NP}$, every non-trivial language in $\text{P}$ is also NP-complete under polynomial-time many-one reductions. This causes the classes to collapse into one:

Thus, all three complexity classes are identical and represented by a single region $\text{P} = \text{NP} = \text{NPC}$, which corresponds to diagram (D).