NP and NPC

Roughly speaking, the class NP consists of problems
for which it can be verified in polynomial time that a solution to the problem is indeed
what it claims to be. The NP–complete problems are a close-knit party from a complexity
point of view, in the sense that if any NP–complete problem admits a polynomial–time
solution, then so do all NP–complete problems. The subset of problems in NP for which a polynomial algorithm exists
is known as P. The abbreviations NP and P stand for nondeterministic polynomial and
polynomial respectively. Historically, the class NP was first introduced in terms of nondeterministic
Turing machines. The study of this type of problems is generally listed
under the denominator of combinatorial optimization.