# How do you know if a problem is P or NP?

## How do you know if a problem is P or NP?

One such class, consisting of counting problems, is called #P: whereas an NP problem asks “Are there any solutions?”, the corresponding #P problem asks “How many solutions are there?” Clearly, a #P problem must be at least as hard as the corresponding NP problem, since a count of solutions immediately tells if at least …

**What is the relationship between P and NP?**

P versus NP It is not known whether P = NP. However, many problems are known in NP with the property that if they belong to P, then it can be proved that P = NP. If P ≠ NP, there are problems in NP that are neither in P nor in NP-Complete. The problem belongs to class P if it’s easy to find a solution for the problem.

### What happens if P vs NP is solved?

If P equals NP, every NP problem would contain a hidden shortcut, allowing computers to quickly find perfect solutions to them. But if P does not equal NP, then no such shortcuts exist, and computers’ problem-solving powers will remain fundamentally and permanently limited.

**What is P and NP problems?**

P is set of problems that can be solved by a deterministic Turing machine in Polynomial time. • NP is set of problems that can be solved by a Non-deterministic Turing Machine in Polynomial time.

## What is the relationship between P NP and NP-complete problems?

Difference between NP-Hard and NP-Complete:

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

NP-Hard problems(say X) can be solved if and only if there is a NP-Complete problem(say Y) that can be reducible into X in polynomial time. | NP-Complete problems can be solved by a non-deterministic Algorithm/Turing Machine in polynomial time. |

**Who Solved P versus NP problem?**

In 2000 American mathematician Stephen Smale devised an influential list of 18 important mathematical problems for solving in the 21st century. The third problem on his list was the P versus NP problem.

### What is NP problem example?

Difference between NP-Hard and NP-Complete:

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

Example: Halting problem, Vertex cover problem, etc. | Example: Determine whether a graph has a Hamiltonian cycle, Determine whether a Boolean formula is satisfiable or not, Circuit-satisfiability problem, etc. |

**What is the relation between P and NP class problems?**

NP is set of problems that can be solved by a Non-deterministic Turing Machine in Polynomial time. P is subset of NP (any problem that can be solved by deterministic machine in polynomial time can also be solved by non-deterministic machine in polynomial time) but P≠NP.

## What is the difference between Class P and Class NP?

Step 1 − If a problem is in class P, it is nothing but we can find a solution to that type of problem in polynomial time. Step 2 − If a problem is in class NP, it is nothing but that we can verify a possible solution in polynomial time.