




But the computer must still verify that the guessed solution is correct
Therefore, the class NP contains:



From Wikipedia:

See: click here

And because years of CS research could not settle this question, it implies that:






Mathematical formulation:
max: v_{1}×x_{1} + v_{2}×x_{2} + ... + v_{N}×x_{N} s.t.: w_{1}×x_{1} + w_{2}×x_{2} + ... + w_{N}×x_{N} ≤ W 

$64,000 question:





Size of the input = 2N + 1 (numbers) !!!!!

You can look at the situation this way:


there are 2 possible divisions of the problems in the class NP:
If P = NP  If P ≠ NP 


However, a solution for an NPcomplete problem can be verified by an algorithm in polynomial time
We call these problems: NPhard problems
Wikipedia page: click here



