## What is NP-hard problems explain with examples?

Another example of an NP-hard problem is the optimization problem of finding the least-cost cyclic route through all nodes of a weighted graph. This is commonly known as the travelling salesman problem. There are decision problems that are NP-hard but not NP-complete such as the halting problem.

## What is the relationship among P NP NP-complete and NP-hard 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 are NP-complete problems give examples?**

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.

### What is P NPC and NPH problems?

If any NPC Problem is polynomial time reducible to a problem X, that problem X belongs to NP-Hard class. Hence, all NP-Complete problems are also NPH. In other words if a NPH problem is non-deterministic polynomial time solvable, it is a NPC problem.

### Which type of problem may be NP-hard?

A problem is NP-hard if all problems in NP are polynomial time reducible to it, even though it may not be in NP itself. If a polynomial time algorithm exists for any of these problems, all problems in NP would be polynomial time solvable.

**How do I know if I have NP-hard problems?**

A problem is NP-Complete if it is a part of both NP and NP-Hard Problem. A non-deterministic Turing machine can solve NP-Complete problem in polynomial time. 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.

#### Can you solve NP-hard problems?

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.

#### Why do we need to prove NP completeness?

Proving a problem NP-Complete is a research success because it frees you from having to search for an efficient and exact solution for the general problem you are studying.