NP-Complete

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In complexity theory, the NP-complete problems are the most difficult problems in NP ("non-deterministic polynomial time") in the sense that they are the smallest subclass of NP that could conceivably remain outside of P, the class of deterministic polynomial-time problems. The reason is that a deterministic, polynomial-time solution to any NP-complete problem would also be a solution to every other problem in NP. The complexity class consisting of all NP-complete problems is sometimes referred to as NP-C. A more formal definition is given below.

One example of an NP-complete problem is the subset sum problem which is: given a finite set of integers, determine whether any non-empty subset of them sums to zero. A supposed answer is very easy to verify for correctness, but no one knows a significantly faster way to solve the problem than to try every single possible subset, which is very slow.