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

P = the set of problems that are solvable in polynomial time by a Deterministic Turing Machine. NP = the set of decision problems (answer is either yes or no) that are solvable in nondeterministic polynomial time i.e can be solved in polynomial time by a Nondeterministic Turing Machine[4].

**What is P vs NP millennium problem?**

NP is one of the Clay Mathematics Institute Millennium Prize Problems, seven problems judged to be among the most important open questions in mathematics. P vs. NP is about finding algorithms, or computer programs, to solve particular math problems, and whether or not “good” algorithms exist to solve these problems.

### What is the difference between P and NP-complete?

P is the class of decision problems which can be solved in polynomial time by a deterministic Turing machine. NP is the class of decision problems which can be solved in polynomial time by a non-deterministic Turing machine.

**What is P and NP problem with example?**

Thus if any one NP-Complete problem can be solved in polynomial time, then every NP-Complete problem can be solved in polynomial time, and every problem in NP can be solved in polynomial time (i.e. P=NP). The most famous example would be the Traveling Salesmen problem.

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

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.

**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.

### Is P equal to NP?

If any NP-complete problem is in P, then it would follow that P = NP. However, many important problems have been shown to be NP-complete, and no fast algorithm for any of them is known.

**What is P and NP in TOC?**

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

## Why P NP is important?

Now, if P=NP, we could find solutions to search problems as easily as checking whether those solutions are good. This would essentially solve all the algorithmic challenges that we face today and computers could solve almost any task.

**What happens if we solve P vs NP?**