# What is NP-hard problem with example?

## What is NP-hard problem with example?

An example of an NP-hard problem is the decision subset sum problem: given a set of integers, does any non-empty subset of them add up to zero? That is a decision problem and happens to be NP-complete.

## What is the hardest problem in NP?

NP-complete problems are the hardest problems in the NP set. A decision problem L is NP-complete if: 1) L is in NP (Any given solution for NP-complete problems can be verified quickly, but there is no efficient known solution). 2) Every problem in NP is reducible to L in polynomial time (Reduction is defined below).

How can the NP-hard problems be solved?

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. To solve this problem, it do not have to be in NP .

### What is NP-hard class problem?

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. These problems are called NP-complete.

### What are P and NP problems?

Roughly speaking, P is a set of relatively easy problems, and NP is a set that includes what seem to be very, very hard problems, so P = NP would imply that the apparently hard problems actually have relatively easy solutions.

Are NP-hard problems in NP?

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. The NP-complete problems represent the hardest problems in NP.

#### How do you show something is NP-hard?

To prove that problem A is NP-hard, reduce a known NP-hard problem to A. In other words, to prove that your problem is hard, you need to describe an ecient algorithm to solve a dierent problem, which you already know is hard, using an hypothetical ecient algorithm for your problem as a black-box subroutine.

#### How do you show a problem is NP-hard?

How do you know if a problem is NP-hard?

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.

## What are NP problems?

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. Attention reader! Don’t stop learning now.

## What are Karp’s 21 NP-complete problems?

In computational complexity theory, Karp’s 21 NP-complete problems are a set of computational problems which are NP-complete.

How do you know if a problem is NP-complete?

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.

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