Question at position 17 If you find a polynomial-time solution to even one NP-Complete problem, then every problem in NP can also be solved in polynomial time.TrueFalse题目解析

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The question presents a statement about NP-Complete problems and asks you to judge True or False.
Option 1: True. This option aligns with a fundamental concept in computational complexity: every NP-Complete problem is NP-hard and belongs to NP. If you can solve one NP-Complete problem in polynomial time, you can transform any other problem in NP into that NP-Complete problem in polynomial time and then solve it in polynomial time as well. This effectively shows P = NP, meaning all problems in NP admit polynomial-time solutions. Therefore, this statement correctly captures the consequence of a polynomial-time solution for a single NP-Complete problem.
Option 2: False. This would be incorrect because it ignores the standard reduction framework: an efficient (polynomial-time) algorithm for one NP-Complete problem would imply efficient solutions for all problems in NP via reductions. The false claim would deny the ripple effect of such a breakthrough, which contradicts established theory.
In summary, the true statement hinges on the impact of solving an NP-Complete problem efficiently, which, due to NP-completeness and polynomial-time reductions, would extend to all problems in NP.

Question at position 17 If you find a polynomial-time solution to even one NP-Complete problem, then every problem in NP can also be solved in polynomial time.TrueFalse题目解析

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