I've just read this article about solving the below minimum subset sum using dynamic programming technique.
Given a list of $N$ coins, their values $(V_1, V_2, ... , V_N)$, and the total sum S. Find the minimum number of coins the sum of which is $S$ (we can use as many coins of one type as we want), or report that it's not possible to select coins in such a way that they sum up to $S$.
How can I use the same technique to find the maximum subset of coins that sums up to $S$? And what is the recurrence relation for this 2nd problem?