A millennium prize problem that hasn't yet been resolved. Assuming it takes NP polynomial time to verify a solution by an algorithm is the polynomial time P taken to actually find a solution by the algorithm equal to NP? Does such a solution exist?
Np hard problems cannot be solved fast by known machines, especially for large instances. If you find a polynomial solution for one of them, then u found the solution for all problems belong to np class.There is no solution yet, and probably there is not. I believe, in future maybe quantum computers or another technology will solve this kind of problems in a moment.We ll see or maybe not.