Looking for good algorithm to calculate a list of figures

Question

Hello,
Given a list of figures:
1899.09
345.55
300.00
130.05
90023.00
45.90
120.50
8831781.56
505.00
45.55
Then the program need to find all the possible addition of figures that will able to produce a answer, for example, 550.55
Then the possible additions are:
300.00 + 120.50 + 130.05 = 550.55
505.00 + 45.55 = 550.55
any good algorithm or sample code?
Thanks for any help.

Answer 1

A general knapsack problem solver is overkill here if one just wants to find a combination that fits 'perfectly'. If the list of numbers is small (< 100), a simple exhaustive search will do fine (read: it's fast). Have a look at the following sample class that solves this particular problem. Note that the set of numbers is a set of integer numbers, because floating point numbers don't add up well; in particular large and small numbers added will result in very inaccurate sums.
kind regards,
public class Comb {
     private int   u; // index of used numbers sofar
     private int   s; // the sum to be found
     private int[] c; // the candidate numbers
        // given a set of numbers and a sum, instantiate a solver
     public Comb(int[] c, int s) {
          this.c= c;
          this.s= s;
          this.u= c.length;
        // yes, swap two elements in array c
     private void swap(int i, int j) {
          int t= c;
          c[i] = c[j];
          c[j] = t;
// use the number at index i as a try
     private void use(int i) {
          swap(i, --u);
// unuse the number at index i
     private void unuse(int i) {
          swap(i, u++);
// proccess (e.g. print) a current solution
// note that this method could throw an exception if
// just one solution is needed.
     private void solution() {
          for (int i= u; i < c.length; ++i) {
               System.out.print(c[i]);
               if (i < c.length-1)
                    System.out.print("+");
          System.out.println("="+s);
// find all solutions to this problem
     public void find(int t) {
          if (t == 0) // ready?
               solution();
          else if (t > 0) // still more to do?
               for (int i= 0; i < u; ++i) {
                    use(i);
                    find(t-c);
                    unuse(i);
// solve the example problem ... == 11
     public static void main(String[] args) {
          int c[]= { 5, 3, 6, 8 };
          int s = 11;
          new Comb(c, s).find(s);