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What (who) is P versus NP problem - definition
P versus NP problem
![quadratic fit]] suggests that the algorithmic complexity of the problem is O((log(''n''))<sup>2</sup>).<ref name=Pisinger2003>Pisinger, D. 2003. "Where are the hard knapsack problems?" Technical Report 2003/08, Department of Computer Science, University of Copenhagen, Copenhagen, Denmark</ref>](https://commons.wikimedia.org/wiki/Special:FilePath/KnapsackEmpComplexity.GIF?width=200 "quadratic fit]] suggests that the algorithmic complexity of the problem is O((log(''n''))<sup>2</sup>).<ref name=Pisinger2003>Pisinger, D. 2003. \"Where are the hard knapsack problems?\" Technical Report 2003/08, Department of Computer Science, University of Copenhagen, Copenhagen, Denmark</ref>")
![NP]], NP-complete, and NP-hard set of problems (excluding the empty language and its complement, which belong to P but are not NP-complete)](https://commons.wikimedia.org/wiki/Special:FilePath/P np np-complete np-hard.svg?width=200 "NP]], NP-complete, and NP-hard set of problems (excluding the empty language and its complement, which belong to P but are not NP-complete)")
UNSOLVED PROBLEM IN COMPUTER SCIENCE ABOUT TIME COMPLEXITY
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The P versus NP problem is a major unsolved problem in theoretical computer science. In informal terms, it asks whether every problem whose solution can be quickly verified can also be quickly solved.
NP-hard
COMPLEXITY CLASS
NP hard; Np hard; Np-hard; NP-Hard Problem; NP-HARD; NP-hard problems; NP-Hard; NP-hard
<complexity> A set or property of computational {search
problems}. A problem is NP-hard if solving it in {polynomial
time} would make it possible to solve all problems in class
NP in polynomial time.
Some NP-hard problems are also in NP (these are called
"NP-complete"), some are not. If you could reduce an NP
problem to an NP-hard problem and then solve it in polynomial
time, you could solve all NP problems.
See also computational complexity.
[Examples? ]
(1995-04-10)
NP-hardness
COMPLEXITY CLASS
NP hard; Np hard; Np-hard; NP-Hard Problem; NP-HARD; NP-hard problems; NP-Hard; NP-hard
In computational complexity theory, NP-hardness (non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally "at least as hard as the hardest problems in NP". A simple example of an NP-hard problem is the subset sum problem.
