Question

I have the following challenge that I need to create unique object tuples out of object lists. The speical challenge is here how I can do it for dynamic list sizes (n-dimension)? It is easy in case you have a fixed dimension. I hope somebody knows a third party API or has some hints for me how I can reach this.

The exampel below shows it for a 3 lists, so it is easier to explain.
I have the objects sorted by its class in a list e.g.

lista = {a1,a2}
listb = {b1,b2,b3}
listc = {c1,c2}

I like to have the following tuples, so that each object is paired once with each other:

tuple1  = {a1,b1,c1}
tuple2  = {a1,b1,c2}
tuple3  = {a1,b2,c1}
tuple4  = {a1,b2,c2}
tuple5  = {a1,b3,c1}
tuple6  = {a1,b3,c2}
tuple7  = {a2,b1,c1}
tuple8  = {a2,b1,c2}
tuple9  = {a2,b2,c1}
tuple10 = {a2,b2,c2}
tuple11 = {a2,b3,c1}
tuple12 = {a2,b3,c2}

How can I achieve that in case

– the number of lists is dynamically
– the size of lists is dynamically

any hints or ideas? Thank you in advance

Answer 1

We can build up to the solution as follows. First notice that the case in which the sizes of the lists vary is never a problem in modern languages, because virtually all languages today support the variable-sized list. The trickier part is when the number of lists vary.

Here is the Python case for the fixed number of lists:

lista = ["a1","a2"]
listb = ["b1","b2","b3"]
listc = ["c1","c2"]
[(a,b,c) for a in lista for b in listb for c in listc]

For Java do the same thing. You will need three nested for-loops:

List<String> lista = Arrays.asList("a1","a2");
List<String> listb = Arrays.asList("b1","b2","b3");
List<String> listc = Arrays.asList("c1","c2");

List<List<String>> result = new ArrayList<List<String>>();
for (String a: lista) {
    for (String b: listb) {
        for (String c: listc) {
            result.add(Arrays.asList(a, b, c));
        }
    }
}
System.out.println(result);

This yields

[[a1, b1, c1], [a1, b1, c2], [a1, b2, c1], [a1, b2, c2], [a1, b3, c1], [a1, b3, c2], [a2, b1, c1], [a2, b1, c2], [a2, b2, c1], [a2, b2, c2], [a2, b3, c1], [a2, b3, c2]]

Now the trick is how do you do an indeterminate number of for loops? One way is to use recursion.

Start with the base case of 0 lists (or even 1) and then ask yourself: how does the result change when I add a new list? Then you can put together a nice little recursive formulation. Do you need help with this?

(Aside: In Python we have itertools for these kinds of things. I am not aware of any Java analog, but some googling might turn something up.)

Okay let’s develop the recursive formulation for an unbounded number of lists. If you have only only one list, say

a = ["a1", "a2"]

then the result is [["a1"],["a2"]]. But now let’s add another list:

a = ["b1", "b2"]

What is the answer now?

[[a1, b1], [a1, b2], [a2, b1], [a2, b2]]

How did we get that? The answer is we took each element of the new list and appended it to each element in the result. And every time we add a new list we will do the same. Suppose now we add ["c1","c2","c3"]. Do you see what we will get? If so, you should now be able to define the recursive step!

COMPLETE CODE

Okay I could not resist! Here you go.

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

/**
 * An application requested by a SO user.
 */
public class ProductExample {

    /**
     * Returns a list containing all possible products of a list of lists of strings.
     */
    public static List<List<String>> product(List<List<String>> lists) {
        List<List<String>> result = new ArrayList<List<String>>();

        if (lists.isEmpty()) {
            result.add(new ArrayList<String>());
            return result;
        }

        List<List<String>> partial = product(lists.subList(0, lists.size() - 1));
        for (List<String> list: partial) {
            for (String s: lists.get(lists.size() - 1)) {
                List<String> listCopy = new ArrayList<String>(list);
                listCopy.add(s);
                result.add(listCopy);
            }
        }
        return result;
    }


    public static void main(String[] args) {
        System.out.println(product(
                Arrays.asList(
                        Arrays.asList("a1", "a2"),
                        Arrays.asList("b1", "b2", "b3"),
                        Arrays.asList("c1", "c2"),
                        Arrays.asList("d1", "d2"))));
    }
}

Rant: This is sooooooo much easier in Python. Or Ruby. 🙂