## What is P NP and NP-hard problems?

NP is set of problems that can be solved by a Non-deterministic Turing Machine in Polynomial time. P is subset of NP (any problem that can be solved by deterministic machine in polynomial time can also be solved by non-deterministic machine in polynomial time) but P≠NP.

### Which is an example of NP-hard problem?

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.

#### Are there harder problems than NP?

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.

**What is P problem example?**

An example of a decision problem in P is: Given a list of n integers and an integer k, is there an integer in the list greater than k? Plainly the question can be answered in time linear to n by stepping through the list and checking whether an integer is greater than k.

**Why P NP is hard?**

The P vs NP problem has an unusual status in that people have thought of rigorous reasons that it’s hard. Second, when people prove a “barrier result” (meaning, a negative result about how not to prove a conjecture), obviously the community will take it as a challenge to find new ideas that circumvent the barrier.

## What does P and NP stand for?

P stands for polynomial time. NP stands for non-deterministic polynomial time. Definitions: Polynomial time means that the complexity of the algorithm is O(n^k), where n is the size of your data (e. g. number of elements in a list to be sorted), and k is a constant.

### What are tractable and Nontractable problems?

Tractable Problem: a problem that is solvable by a polynomial-time algorithm. The upper bound is polynomial. Intractable Problem: a problem that cannot be solved by a polynomial-time al- gorithm. The lower bound is exponential.

#### How do you solve NP-hard problems?

Option One: Approximation Algorithms In some cases, you may be able to combat NP-hardness by using an approximation algorithm. For example, a canonical example of an NP-hard problem is the traveling salesman problem. In this problem, you’re given as input a complete graph representing a transportation network.

**What is P NP NP-complete NP-hard?**

NP-Complete problems are problems that live in both the NP and NP-Hard classes. This means that NP-Complete problems can be verified in polynomial time and that any NP problem can be reduced to this problem in polynomial time. Below is a venn diagram of the different class spaces.

**Is chess P complete?**

For this reason games like chess cannot themselves be NP-complete, as they only have a finite (albeit unthinkably large) number of possible positions.

## What is tractable decision problem?

Tractable problem, in computational complexity theory, a problem that can be solved in polynomial time. Tractable, ease of obtaining a mathematical solution such as a closed-form expression.

### What is NP hardness explain?

A decision problem is NP-hard when there exists a polynomial-time many-one reduction of any NP problem to the current NP hard problem. Basically, to prove a problem NP hard we need to reduce it to a problem which is already labelled NP hard. This reduction has to take polynomial time,though.