# Pseudo-polynomial time algorithm for NP-Complete Problems

For problems like Knapsack there is a pseudo-polynomial time algorithm and it is NP-complete. So we reduce every other problem in NP in polytime to Knapsack.

But why don't we have then a pseudo-polynomial time algorithm for all problems in NP?

An algorithm runs in pseudo-polynomial time if its running time is polynomial in the numeric values in the input. It doesn't make sense to talk about pseudo-polynomial time algorithms for all problems in $$NP$$ since many of them do not have numeric values in their input at all.
However, if you are looking at two problems for which the definition does apply (for instance 2-Partition (weakly $$NP$$-complete, has a pseudopolynomial time algorithm) and 3-Partition (strongly $$NP$$-complete, not believed to have a pseudopolynomial time algorithm) then how is it possible a polynomial reduction from 3-Partition to 2-Partition does not result in a pseudopolynomial algorithm for 3-Partition?