Finding all solutions to subset sum for integers with bounded weights
The dynamic programming algorithm can be adapted to give all solutions. You create a table $A$. The cell $A_{k,w}$ contains enough information to enumerate all subsets of $\{w_1,\ldots,w_k\}$ summing to $w$. When $k = 0$, this is trivial. Given $A_{k-1,\cdot}$, $A_{k,w}$ points at the two cells $A_{k-1,w},A_{k-1,w-w_k}$ (if they exist). The second pointer is also annotated with $w_k$. If you look at $A_{50,W}$, you can reconstruct all subsets by considering all paths going all the way to $A_{0,0}$. This can be done using a simple recursive procedure.