Theory of NP-Completeness

The theory of NP-Completeness deals with classifying problems based on how difficult they are to solve. NP problems are those where, given a solution, we can verify its correctness quickly, but finding that solution might take a very long time. NP-Complete problems are the hardest in this group; if we find an efficient way to solve one NP-Complete problem, it would mean all problems in NP could be solved efficiently. This concept helps computer scientists understand the limits of problem-solving and where efforts for optimization or new algorithms should focus.