How can you classify a problem as NP-complete?

To classify a problem as NP-complete, it is essential to determine two specific criteria. First, the problem must be in the class NP, which means that any proposed solution can be verified in polynomial time. Second, the problem must satisfy the condition that every problem in NP can be reduced to it in polynomial time. This reduction effectively shows that if we can find a polynomial-time solution for the NP-complete problem, then we can use that solution to solve all problems in NP within polynomial time as well.

This classification is crucial because it helps in understanding the complexity of various computational problems. If a new problem is shown to be NP-complete, it can be interpreted as being as hard as the hardest problems in NP, indicating that no polynomial-time solution is known for it, and finding one would be a significant breakthrough in computer science.

The other options do not accurately represent the criteria for NP-completeness. For instance, a problem having no solution does not help classify it as NP-complete; in fact, many NP-complete problems have solutions that can be verified. Likewise, a problem that can be solved in polynomial time is classified as being in P, not NP-complete. Finally, any problem solvable by brute force does not