There is a pseudo-polynomial time algorithm using dynamic programming.

A similar dynamic programming solution for the 0/1 knapsack problem also runs in pseudo-polynomial time.

Weakly polynomial-time should not be confused with pseudo-polynomial time.

Although the notion of pseudo-polynomial time is used almost exclusively for numeric problems, the concept can be generalized:

It is, however, pseudo-polynomial time.

There is a fully polynomial-time approximation scheme, which uses the pseudo-polynomial time algorithm as a subroutine, described below.

If all weights () are nonnegative integers, the knapsack problem can be solved in pseudo-polynomial time using dynamic programming.

An NP-complete problem with known pseudo-polynomial time algorithms is called weakly NP-complete.

The partition problem can be viewed as a special case of the subset sum problem and the pseudo-polynomial time dynamic programming solution given above generalizes to a solution for the subset sum problem.

In computational complexity theory, a numeric algorithm runs in pseudo-polynomial time if its running time is polynomial in the numeric value of the input (which is exponential in the length of the input - its number of digits).