Question at position 18 Which of the following best describes NP-Complete problems? Problems to which all other NP problems can be reduced in polynomial timeProblems whose solutions cannot be verified efficientlyProblems that are solved faster than P problemsProblems that are easier than all NP problemsClear my selection题目解析

Question

BlackTom AI · Accepted Answer

We start by restating the core idea being tested: the definition of NP-Complete problems in computational complexity.
Option 1: 'Problems to which all other NP problems can be reduced in polynomial time' This is the canonical characterization of NP-Complete problems: they are in NP and every problem in NP can be reduced to them in polynomial time, making them the hardest problems in NP under polynomial-time reductions.
Option 2: 'Problems whose solutions cannot be verified efficiently' This contradicts the very nature of NP, which stands for nondeterministic polynomial time, i.e., problems whose solutions can be verified in polynomial time given a certificate. If solutions cannot be verified efficiently, the problem would not be in NP, so this statement is false.
Option 3: 'Problems that are solved faster than P problems' By definition, P is the class of problems solvable in polynomial time. A problem solved faster than P would imply a time bound that is sub-polynomial, which is not the standard criterion for NP-Complete, and many problems cannot even be solved in polynomial time at all. This mischaracterizes computational complexity classes and is therefore incorrect.
Option 4: 'Problems that are easier than all NP problems' If a problem were easier than all NP problems, it would be in P (assuming P is not larger than NP), but NP-Complete problems are the hardest within NP, not the easiest. This statement misrepresents the hierarchy and is inaccurate regarding NP-Complete status.
In summary, each wrong option either contradicts the fundamental definition of NP-Complete or misstates the relationships between complexity classes. The only option that aligns with the standard definition is the first one.

View Explanation

Log in for full answers

Similar Questions

When considering P, NP, NP complete, and NP hard

Find the BEST Match for computational complexity with respect to PER LAYER complexity (ie. what is the complexity of a single layer of each wrt the variables below). n denotes sequence length d denotes representation dimension 1: Self-Attention (vanilla) 2: Recurrent (vanilla)

zyBooks_15_2 (Context: ZyBooks Ch. 15.6.2 discusses comparing algorithm performance.) According to the ZyBooks activity you completed, computational complexity analysis allows the efficiency of algorithms to be compared.

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

More Practical Tools for International Students

Homework AI Solver

Stylized Writing Assistant

Plagiarism Checker Assistant

Citation Assistant

In-Class Translation Assistant

Class Notes Assistant

Quiz Search Assistant

Past Exam Questions by School

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler