Question at position 8 What does it mean if a problem belongs to the class NP? Its solution can be verified but not found in polynomial timeIts solution can neither be verified nor found in polynomial timeIt can be solved in polynomial timeIt cannot be solved by any algorithmClear my selection题目解析

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Question at position 8 What does it mean if a problem belongs to the class NP? Its solution can be verified but not found in polynomial timeIts solution can neither be verified nor found in polynomial timeIt can be solved in polynomial timeIt cannot be solved by any algorithmClear my selection题目解析

BlackTom AI · Accepted Answer

Consider the concept being tested: the definition of NP.
Option 1: 'Its solution can be verified but not found in polynomial time' This captures the essence of NP: given a candidate solution (a certificate), we can verify its correctness in polynomial time, even if finding that solution may take super-polynomial time in general. This option aligns with the standard definition and thus is correct.
Option 2: 'Its solution can neither be verified nor found in polynomial time' This statement contradicts the core idea of NP, which guarantees verifiability in polynomial time given a certificate. Since verifiability is the defining feature, this option is incorrect.
Option 3: 'It can be solved in polynomial time' This would place the problem in P, not NP (though NP includes P as a subset). The claim that all NP problems can be solved in polynomial time is not generally true unless P = NP, so as a blanket statement it is false.
Option 4: 'It cannot be solved by any algorithm' This is false for NP problems, as many NP problems can be solved by algorithms given sufficient time or special cases; moreover, NP is about verification of certificates, not about absolute unsolvability. This option is incorrect.

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