Loop 2 dimentional array to determine best case

Question

Can you figure this out???
I've got a 2 dimitional array with trips and units and I need to find the best trip to unit matches that will result in the least amount. The number of elements of each is not constant but for this example I will show 4 each.
Here's my table..
     U1     U2     U3     U4
T1     50     75     100     0
T2     100     125     0     75
T3     30     45     55     100
T4     40     55     0     90
Here are all posible combinations that need to be checked with there resulting values.
T1     U1     U1     U1     U1     U1     U1
T2     U2     U2     U3     U3     U4     U4
T3     U3     U4     U2     U4     U2     U3
T4     U4     U3     U4     U2     U3     U2
Amt     325     275     185     205     170     235
T1     U2     U2     U2     U2     U2     U2
T2     U1     U1     U3     U3     U4     U4
T3     U3     U4     U1     U4     U1     U3
T4     U4     U3     U4     U1     U3     U1
Amt     320     275     195     215     180     245
T1     U3     U3     U3     U3     U3     U3
T2     U1     U1     U2     U2     U4     U4
T3     U2     U4     U1     U4     U1     U2
T4     U4     U2     U4     U1     U2     U1
Amt     335     355     345     365     260     260
T1     U4     U4     U4     U4     U4     U4
T2     U1     U1     U2     U2     U3     U3
T3     U2     U3     U1     U3     U1     U2
T4     U3     U2     U3     U1     U2     U1
Amt     145     210     155     220     85     85
The lowest amount is 85 which can be reached two differnt ways.
My question is how can I create a loop using a set amount of indexes (even though the # of elements might change) to search through all posible combinations?

Answer 1

I think this might be what you're after, provided your matrixes are 4x4 5x5 6x6 etc
I've included a commented out 5x5, for testing
as written, this will only work up to 9x9, any more and additional code is required to separate the Integer.parseInt's to 10,11 etc
class CombinationsMatrix
  private static int lowestCombo;
  private static boolean firstCombo = true;
  private static int matrix[][] = {{50,75,100,0},{100,125,0,75},
                                   {30,45,55,100},{40,55,0,90}};
  /*private static int matrix[][] = {{50,75,100,0,1000},{100,125,0,75,1000},
                                   {30,45,55,100,1000},{40,55,0,90,1000},
                                   {10,20,30,40,1000}};*/
  public static void main(String args[])
    String numbers = "";
    for(int i=0; i<matrix.length;i++) numbers += i;
    getCombos("",numbers);
    System.out.println("lowest combo = "+lowestCombo);
    System.exit(0);
  private static void getCombos(String str1, String str2)
    int i = str2.length()-1;
    if(i < 1)
      String str3 = str1+str2;
      int thisCombo=0;
      for(int x = 0; x < str3.length(); x++)
        thisCombo += matrix[x][Integer.parseInt(str3.substring(x,x+1))];
      System.out.println(thisCombo);
      if(firstCombo)
        lowestCombo = thisCombo;
        firstCombo = false;
      else if(thisCombo < lowestCombo) lowestCombo = thisCombo;
    else
      for(int ii = 0; ii <= i; ii++)
        getCombos(str1 + str2.substring(ii,ii+1), str2.substring(0, ii) +
                                  str2.substring(str2.length() - (i-ii)));
}