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

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

A Problem X is NP-Hard if there is an NP-Complete 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. |

**Is there anything harder than NP-hard?**

There are complexity classes more “difficult” than NP, for example PSPACE, EXPTIME or EXPSPACE, and all these contain NP-hard but not NP-complete problems. Show activity on this post. Turing halting problem is undecidable and it belongs to NP-Hard set.

### Is NP-complete NP-hard?

NP-complete problems are those problems that are both NP-Hard and in the complexity class NP. Therefore, to show that any given problem is NP-complete, you need to show that the problem is both in NP and that it is NP-hard.

**Is every NP-hard problem NP-complete?**

@PeterRaeves All NP-complete problems are NP-hard, by definition: NP-complete = (NP and NP-hard). The inverse is not true: there are problems (such as the Halting Problem) in NP-hard that are not in NP-complete. “NP (not solvable in polynomial time) ” — that’s not what NP means. NP is “Non-deterministic-polynomial”.

## Is NP-complete harder than NP-hard?

The complexity class of problems of this form is called NP, an abbreviation for “nondeterministic polynomial time”. A problem is said to be NP-hard if everything in NP can be transformed in polynomial time into it even though it may not be in NP. Conversely, a problem is NP-complete if it is both in NP and NP-hard.

**Why is travel salesman NP-complete?**

Why is TSP not NP-complete? The simple answer is that it’s NP-hard, but it’s not in NP. Since it’s not in NP, it can’t be NP-complete. In TSP you’re looking for the shortest loop that goes through every city in a given set of cities.