## What is NP-hard and NP-complete 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 NP-complete problems?**

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

### Does NP-complete mean NP-hard?

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. Conversely, a problem is NP-complete if it is both in NP and NP-hard. The NP-complete problems represent the hardest problems in NP.

**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 meant by NP-complete?

(definition) Definition: The complexity class of decision problems for which answers can be checked for correctness, given a certificate, by an algorithm whose run time is polynomial in the size of the input (that is, it is NP) and no other NP problem is more than a polynomial factor harder.

**Are all NP problems NP-complete?**

Not necessarily. It can happen that NP is a known upper-bound (ie. we know how to solve it in non-deterministic polynomial time) but not a known lower-bound (a more efficient algorithm may or may not exist). An example of such a problem is graph isomorphism.

### What is P and NP problems?

P is set of problems that can be solved by a deterministic Turing machine in Polynomial time. • NP is set of problems that can be solved by a Non-deterministic Turing Machine in Polynomial time.

**Are puzzles NP-complete?**

Often this difficulty can be shown mathematically, in the form of computational intractibility results: every NP-complete problem is in some sense a puzzle, and conversely many puzzles are NP-complete. Two-player games often have higher complexities such as being PSPACE-complete.

## What is difference between NP and P?

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.

**What is recursion and backtracking?**

Difference between Recursion and Backtracking: In recursion, the function calls itself until it reaches a base case. In backtracking, we use recursion to explore all the possibilities until we get the best result for the problem.

### Is Sudoku A NP?

Sudoku is NP-complete when generalized to a n × n grid however a standard 9 × 9 Sudoku is not NP- complete.