If any one NP-Complete problem is solved in polynomial time, what will be the consequence?

Options

  • A. Only that problem will belong to P
  • B. P will be equal to NP
  • C. NP will become empty
  • D. More than one of the above
  • E. None of the above

Correct Answer (Detailed Explanation is Below)

B. P will be equal to NP

Detailed Explanation

  • Important Concept: If even one NP-Complete problem has a polynomial-time algorithm, every problem in NP can also be solved in polynomial time.
  • Conclusion: P = NP.
  • This is one of the most important unsolved questions in theoretical computer science.