Generating of Nonnegative Solution for a Linear Diophantion Eqution

In general case, computing the nonnegative solution for a linear Diophantine Equation is NP complete. In this paper, we show that if components of the coefficient vector have not the same sign, then we can get a (and even infinit) nonnegative solution in a polynomial time. Therefore, in this case, the problems belong to the P class, polynomial time solvable problems. For generating the nonnegative solutions we suggest an algorithm that is simple and fast. For this purpose, first of all we obtain a special type of nonnegative integer solutions for corresponding homogeneous Diophanti Equation and then add a suitable linear nonnegative integer combination of them to a special solution of the Diophantine Eqation such that a nonnegative integer vector, that is a nonnegative solution for the Diophantine Equation, is obtained.