Set Min[i] equal to Infinity for all of i
Min[0]=0

// Solution 1
For i = 1 to S
   For j = 0 to N - 1
      If (Vj<=i AND Min[i-Vj]+1<Min[i])
         Then Min[i]=Min[i-Vj]+1

// Solution 2
For i = 1 to S
   For j = 0 to N - 1
      If(Min[i+j] > Min[i] + 1)
         Then Min[i+j] = Min[i] + 1

Output Min[S]