Question: Consider this algorithm for solving the CLIQUE problem. First, generate all subsets of the vertices containing exactly (k) vertices. There are (Oleft(n^{k}ight)) such subsets altogether.

Consider this algorithm for solving the CLIQUE problem. First, generate all subsets of the vertices containing exactly \(k\) vertices. There are \(O\left(n^{k}ight)\) such subsets altogether. Then, check whether any subgraphcs induced by these subsets is complete. If this algorithm ran in polynomial time, what would be its significance? Why is this not a polynomial-time algorithm for the CLIQUE problem?

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