# Which problems are np complete?

Last Update: April 20, 2022

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NP-complete problem, any of a class of computational problems

computational problems
In theoretical computer science, a computational problem is a problem that a computer might be able to solve or a question that a computer may be able to answer. For example, the problem of factoring. "Given a positive integer n, find a nontrivial prime factor of n."
https://en.wikipedia.org › wiki › Computational_problem
for which no efficient solution algorithm has been found. Many significant computer-science problems belong to this class—e.g., the traveling salesman problem, satisfiability problems, and graph-covering problems.

## How many NP complete problems are there?

This list is in no way comprehensive (there are more than 3000 known NP-complete problems). Most of the problems in this list are taken from Garey and Johnson's seminal book Computers and Intractability: A Guide to the Theory of NP-Completeness, and are here presented in the same order and organization.

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

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).

## What is NP completeness give an example for NP-complete problem?

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 . ... It is exclusively a Decision problem. Example: Halting problem, Vertex cover problem, Circuit-satisfiability problem, etc.

## Is the sorting problem NP-complete?

Sorting Numbers

Given a list of numbers, you can verify that whether the list is sorted or not in polynomial time, so the problem is clearly NP. There are known algorithms to sort a list of numbers in polynomial time. (Bubble sort O(n^2) etc. ).

## 8. NP-Hard and NP-Complete Problems

18 related questions found

### Which type of problem may be NP-hard?

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.

### Is N Queens NP-complete?

The n-queens completion puzzle is a form of mathematical problem common in computer science and described as “NP-complete”. These are interesting problems because if an efficient solution can be found for one NP-complete problem, it can be used to solve all NP-complete problems.

### What is NP problem 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.

### Are NP problems solvable?

The short answer is that if a problem is in NP, it is indeed solvable.

### Are NP-hard problems solvable?

This is known as Cook's theorem. What makes NP-complete problems important is that if a deterministic polynomial time algorithm can be found to solve one of them, every NP problem is solvable in polynomial time (one problem to rule them all).

### What does it mean if Q is NP-hard?

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.

### Can NP-hard reduce to NP-complete?

(If P and NP are the same class, then NP-intermediate problems do not exist because in this case every NP-complete problem would fall in P, and by definition, every problem in NP can be reduced to an NP-complete problem.)

### Can P be reduced to NP?

Quick reply: No, it does not. Recall the definition of NP-hard problems. A problem X is NP-Hard if every problem in NP can be polynomially reduced to X. If on the other hand a problem X can be polynomially reduced to some NP-complete problem Y, it means that Y is at least as hard as X, not the other way around.

### How do I prove my NP?

We can solve Y in polynomial time: reduce it to X. Therefore, every problem in NP has a polytime algorithm and P = NP. then X is NP-complete. In other words, we can prove a new problem is NP-complete by reducing some other NP-complete problem to it.

### Is NP equal to NP-complete?

What is the point of classifying the two if they are the same? In other words, if we have an NP problem then through (2) this problem can transform into an NP-complete problem. Therefore, the NP problem is now NP-complete, and NP = NP-complete. Both classes are equivalent.

### Is it possible for a problem to be in both P and NP?

Is it possible for a problem to be in both P and NP? Yes. Since P is a subset of NP, every problem in P is in both P and NP.

### What happens if P vs NP is solved?

If P equals NP, every NP problem would contain a hidden shortcut, allowing computers to quickly find perfect solutions to them. But if P does not equal NP, then no such shortcuts exist, and computers' problem-solving powers will remain fundamentally and permanently limited.

### Is P vs NP solvable?

P is the set of all decision problems that are efficiently solvable and is a subset of NP. Basic Arithmetic is solvable in Polynomial-time, thus belongs to P.

### Is NP equal to P?

6 Answers. P stands for polynomial time. NP stands for non-deterministic polynomial time.

### Is Euler cycle NP-complete?

A graph is called Eulerian if it has an Eulerian Cycle and called Semi-Eulerian if it has an Eulerian Path. The problem seems similar to Hamiltonian Path which is NP complete problem for a general graph. Fortunately, we can find whether a given graph has a Eulerian Path or not in polynomial time.

### Why is knapsack problem NP-hard?

the time needed increases in exponential term, so it's a NPC problem. This is because the knapsack problem has a pseudo-polynomial solution and is thus called weakly NP-Complete (and not strongly NP-Complete).

### Is 8 queen a problem with NP?

N Queens Completion Is NP Complete. The problem of putting eight queens on the chess board so as no queen attacks another is a solved problem, as is placing n queens on an nxn board. However if you place some queens on the board and ask for a completion then the problem is NP complete.

### Are n queens solvable?

The n-queens problem is solvable for n=1 and n≥4. So the decision problem is solvable in constant time.

### What is 8 queen problem in DAA?

The eight queens problem is the problem of placing eight queens on an 8×8 chessboard such that none of them attack one another (no two are in the same row, column, or diagonal). More generally, the n queens problem places n queens on an n×n chessboard. There are different solutions for the problem.

### How P and NP problems are related?

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.