# Is it possible for a problem to be in both P and NP?

## Is it possible for a problem to be in both P and NP?

Is it possible for a problem to be in both P and NP? Yes. Since P is a subset of NP, every problem in P is in both P and NP.

**What are the differences between the NP-hard and NP-complete problems?**

A problem X is NP-Complete if there is an NP problem Y, such that Y is reducible to X in polynomial time….Difference between NP-Hard and NP-Complete:

NP-hard | NP-Complete |
---|---|

To solve this problem, it do not have to be in NP . | To solve this problem, it must be both NP and NP-hard problems. |

Do not have to be a Decision problem. | It is exclusively a Decision problem. |

**What is the relationship among the NP NP-hard NP-complete and P problems?**

All other problems in class NP can be reduced to problem p in polynomial time. NP-hard problems are partly similar but more difficult problems than NP complete problems. They don’t themselves belong to class NP (or if they do, nobody has invented it, yet), but all problems in class NP can be reduced to them.

### How P class problem is different from NP class problem?

In this theory, the class P consists of all those decision problems (defined below) that can be solved on a deterministic sequential machine in an amount of time that is polynomial in the size of the input; the class NP consists of all those decision problems whose positive solutions can be verified in polynomial time …

**Which problems are NP-complete?**

NP-complete problem, any of a class of computational problems for which no efficient solution algorithm has been found. Many significant computer-science problems belong to this class—e.g., the traveling salesman problem, satisfiability problems, and graph-covering problems.

**Which of the given problem are NP-complete?**

Explanation: Hamiltonian circuit, bin packing, partition problems are NP complete problems.

## Under which situation a problem belongs to the class NP?

**What are NP class problems?**

A problem is called NP (nondeterministic polynomial) if its solution can be guessed and verified in polynomial time; nondeterministic means that no particular rule is followed to make the guess. If a problem is NP and all other NP problems are polynomial-time reducible to it, the problem is NP-complete.

**Which of the following problem is not NP-complete but Undecidable?**

Detailed Solution The halting problem is NP-Hard, not NP-Complete, but is undecidable. Hence option 2 is correct.