If you're signaling that you've talked to 1000 capitalist libertarians and 999 of them believe the quoted words, I question your sample.
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...there it is proved that there is no polynomial time complexity algorithm that finds the optimal solution.
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Are you familiar with asymptotic time complexity aka Big-O? That (and maybe the concept of a reduction) are the only challenging concepts required.
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"class of complexity problems with optimal algorithmic solution in polynomial time" = any problem you can solve in O(n^k) for any k = P NP = problems you can _check if you solved correctly_ in O(n^k) but we dunno if there's a way to _solve_ them in O(n^k)
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