3 Answers.

No.

A problem is Np-Hard if all NP problems are reducible to an instance of that problem in polynomial time.

Some NP-Hard problems cannot be solved in nondeterministic polynomial time, and are not in NP.24 Oct 2018

## Can NP complete problems be solved?

The main thing to take away from an NP-complete problem is that it cannot be solved in polynomial time in any known way. NP-Hard/NP-Complete is a way of showing that certain classes of problems are not solvable in realistic time.24 Nov 2008

## Can NP hard problems be solved in polynomial time?

Consequences. If P ≠ NP, then NP-hard problems cannot be solved in polynomial time. Some NP-hard optimization problems can be polynomial-time approximated up to some constant approximation ratio (in particular, those in APX) or even up to any approximation ratio (those in PTAS or FPTAS).

## What makes NP hard difficult?

NP-Hard Problem. A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP-problem (nondeterministic polynomial time) problem. NP-hard therefore means “at least as hard as any NP-problem,” although it might, in fact, be harder.

## Are NP hard problems in NP?

NP is the set of all problems whose solutions can be verified in polynomial time. NP-hard problems are informally defined as those that can’t be solved in polynomial time. In other words, the problems that are harder than P.9 Jun 2017