It is always a good idea to find a recursive algorithm first and then turn it into a table. 1. $f(C,n)$ 2. $~~$if(C = $\emptyset$) return 0; 3. $~~$else 4. $~~~~$opt = 0; 5. $~~~~$for each $c\in C$ do 6. $~~~~~~D=\{d\in C:d<c\}$ 7. $~~~~~~E=\{e-c:e\in D,e>c\}$ 8. $~~~~~~opt = min\{opt,f(D,c)+f(E,n-c)\}$ 9. $~~~~$return $opt+n$; So you may ask: isn't there too many subsets of C to be put in a table? Observe that only 'consecutive' subsets are needed. And there are only $n \choose 2$ of them.(why?) Another problem is: some entries will change value in $E$. We can walk around this by indicating start and end in each $f$ rather than just specifying the length.