I get NP completeness, but I don't understand why it's said that by solving one NP complete problem, all of them are solved. Is it saying that solving one NP complete problem proves that all of them are solvable?
2026-03-26 22:17:42.1774563462
Why is it that if one NP complete problem is solved, all NP problems are solved?
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All NP-complete problems are already solvable, they're just intractable. That said, if one NP-complete problem is proven to be on P, then all of them are on P and thus, tractable. This happens because all NP-complete problems can be reduced one to each other in polynomial time; they are essentially the same problem under polynomial-time reductions.