Combination of a matrix of arrays of variable length

Question

I have to obtain all possibile combination of this kind of matrix:

String[][] matrix = {
   {"AA-123", "AA-124", "AA-125", "AA-126"},
   {"BB-12", "BB-13"},
   {"CC-1"},
};

After all, that is the final implementation. It's in Java, but the language may be irrilevant:

long nComb = 1;
for (int iMatr = 0; iMatr < matrix.length; iMatr++)
   nComb *= matrix[iMatr].length;

for (int iComb = 0; iComb < nComb; iComb++) {
   System.out.print("|");

   long nSec = 1;
   for (int iSec = 0; iSec < matrix.length; iSec++) {
       String[] sec = matrix[iSec];

       for (int iAtom = 0; iAtom < sec.length; iAtom++) {

           if (iAtom == ((iComb / nSec) % sec.length))
               System.out.print(1);
           else
               System.out.print(0);
       }

       nSec *= sec.length;
       System.out.print("|");
   }

   System.out.println();
}

I have to apply my logic on the if that it prints 1 or 0. I need to know what is the current element (index) of the combination of the array. The expected result:

|1000|10|1|
|0100|10|1|
|0010|10|1|
|0001|10|1|
|1000|01|1|
|0100|01|1|
|0010|01|1|
|0001|01|1|

Regards.

Edit:

I find a possible answer using another variable in the array iteration: nSec . It product increse by the lenght of the array over iterations, reaching at the last iteration the value of nComb .

Answer 1

I believe what you're after here is called the cartesianProduct of the multiple collections and this is already supported by a number of collection libraries in Java.

Personally I'd recommend using Guava ( https://code.google.com/p/guava-libraries/ ) which will allow you to define your problem as follows (conversion between Array and Set I will leave out as an exercise :):

import com.google.common.collect.Sets;
import java.util.List;
import java.util.Set;

public class CartesianProduct {

    public static void main(String[] args) {
        Set<List<String>> merged = Sets.cartesianProduct(
                Sets.newHashSet("AA-123", "AA-124", "AA-125", "AA-126"),
                Sets.newHashSet("BB-12", "BB-13"),
                Sets.newHashSet("CC-1")
        );
        System.out.println("Size: " + merged.size());
        System.out.println("Content: " + merged);
    }

}

By executing this code you will get the following result:

Size: 8
Content: [
   [AA-125, BB-13, CC-1], 
   [AA-125, BB-12, CC-1], 
   [AA-124, BB-13, CC-1], 
   [AA-124, BB-12, CC-1], 
   [AA-123, BB-13, CC-1], 
   [AA-123, BB-12, CC-1], 
   [AA-126, BB-13, CC-1], 
   [AA-126, BB-12, CC-1]
]

Then further you can process, sort and format output the way you require (and when printing it another guava class Joiner might come handy).