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# Difference between NP hard and NP complete problem

Prerequisite: NP-Completeness

NP Problem:
The NP problems set of problems whose solutions are hard to find but easy to verify and are solved by Non-Deterministic Machine in polynomial time.

NP-Hard Problem:
A Problem X is NP-Hard if there is an NP-Complete problem Y, such that Y is reducible to X in polynomial time. NP-Hard problems are as hard as NP-Complete problems. NP-Hard Problem need not be in NP class.

If every problem of NP can be polynomial time reduced to it called as NP Hard.

A lot of times takes the particular problem solve and reducing different problems.

example :

1.  Hamiltonian cycle .
2. optimization problem .
3. Shortest path

A problem X is NP-Complete if there is an NP problem Y, such that Y is reducible to X in polynomial time. NP-Complete problems are as hard as NP 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.

A problem is np-complete when it is both np and np hard combines together.

this means np complete problems can be verified in polynomial time.

Example

1. Decision problems.
2. Regular graphs.

Difference between NP-Hard and NP-Complete

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