# NP-Hard **A class of decision problems to which any problem solvable in [[nondeterministic polynomial time]] can be [[Polynomial Time Reduction|polynomially reduced]].** >[!Example] NP-Hard > A decision problem $H$ is **NP-hard** if for any problem $N$ which can be solved in nondeterministic polynomial time, there is a *polynomial time reduction* from $N$ to $H$. ![[NPEulerDiagram.svg]] An NP-hard problem is *at least as difficult* as any problem in NP, though the contrapositive is not necessarily true. There exists problems to which NP problems are reducible to yet are also *undecidable*, that is, it is not possible to create an algorithm which always correctly answers the problem. Problems to which NP problems are reducible but are also decidable are [[NP-complete]] problems.