Cartesian products of two sets in Java

Question

I'm trying to solve a problem from a textbook I'm using that has to do with cartesian products and sets without using built-in java APIs or any fancy function.

For example Set A contains = {1,3,4}

Set B contains = {2,5}

their products would yield to this result {(1,2),(1,5),(3,2),(3,5),(4,2),(4,5)}

I have written some methods to perform various functions on each set but here is what I came up with. How could I implement this to the sets?

public String cartesian(Set other)
{
    String result = "";
    int res;

    for ( int i = 0; i < this.size; ++i )
    {
        for ( int j = 0; j < other.size; ++j )
        {
            //System.out.println("@@@@@"+ other.size);
            //result = data[i] + ""+ other[i] + "";
            //res = data[i] *= other.data[j];

        }
    }

    return result;

}

The method returns the result as a string. My logic is to got through each set's element at the same time but I get stuck at thinking up a way to cross them together.

Here is the rest of my code.

 public class Sets {
        public static void main(String[] args)
    {

        Set set1;
        set1 = new Set();


        Set set2 = new Set();

        set1.add(1);
        set1.add(2);
        set1.add(3);

        set2.add(3);
        set2.add(4);
        /*set2.add(4);
        set2.add(5);*/

        //System.out.println(set1.difference(set2));

        System.out.println(set1.cartesianReformed(set2));



    }
}

User-defined Set class

class Set
{
    private int[] data;
    private int size;

    public Set()
    {
        data = new int[20];
        size = 0;

    }

    public void add(int value)
    {
        int[] copy;

        //avoiding duplicates
        if ( !in(value) )
        {
            if ( size > data.length )
            {
                copy = new int[data.length * 2];

                System.arraycopy(data, 0, copy,0,data.length);

                data = copy;
            }
            data[size] = value;

            size++;
        }
        else
        {
            System.out.println("You are trying to insert a number that's already here ---> " + value);
        }

    }

    public String toString()
    {
        String result = "{";
        for(int i = 0; i < size; i++)
        {
            result += "" + data[i];
            //Add a comma after all but the last item
            if ( i < size - 1 )
            {
                result += ",";
            }

        }
        result += "}";
        return result;
    }

    public boolean in(int value)
    {
        boolean result = false;

        for(int i = 0; i < size; i++)
        {
            if ( data[i] == value )
            {
                result = true;
            }
        }

        return result;
    }

    public Set intersection(Set other)
    {
        Set result = new Set();

        for ( int i = 0; i < size; ++i )
        {
            if ( other.in(data[i]) )
            {
                result.add(data[i]);
            }
        }
        return result;
    }

    public boolean equals(Set other)
    {
        boolean result = false;

        int count = 0;

        for ( int i = 0; i < size; ++i ) //iterating over this
        {
            if ( other.in(data[i]) )
            {
                count++;
            }

            if ( count == size )
            {
                result = true;
            }
        }
        return result;
    }

    public Set difference(Set other)
    {
        Set result = new Set();

        for(int i = 0; i < size; ++i)
        {
            if ( !other.in(data[i]) )
            {
                result.add(data[i]);
            }
        }

        return result;
    }



    public String cartesian(Set other)
    {
        String result = "";
        int res;

        for ( int i = 0; i < this.size; ++i )
        {
            for ( int j = 0; j < other.size; ++j )
            {
                //System.out.println("@@@@@"+ other.size);
                //result = data[i] + ""+ other[i] + "";
                //res = data[i] *= other.data[j];

            }
        }

        return result;

    }

    public Set union(Set other) {
        Set result = (Set)other.clone();
        for (int i = 0; i < size; i++) {
            result.add(data[i]);
        }
        return result;
    }

    public Object clone() {
        Set result = new Set();
        for (int i = 0; i < size; i++) {
            result.add(data[i]);
        }
        return result;
    }
}

Answer 1

Something like this will work:

public String cartesian (Set other)
{
    String [] cart = new String [this.size * other.size];

    int k = 0;
    for (int i : this.data)
    {
        for (int j : other.data)
        {
            cart[k++] = "(" + i + "," + j + ")";
        }
    }

    return Arrays.toString(cart);   
}

Returns:

[(1,2), (1,5), (3,2), (3,5), (4,2), (4,5)]

Note:

• Naming your class Set is a bad idea since it conflicts with java.util.Set.

Answer 2

Let's get to the crux of the matter. You essentially need all the combinations of elements in 2 lists. The following is a very simple way of looking at it, by using nested for-loops to go over the elements in the sets A and B.

Set<Integer> A = new HashSet<Integer>();
Set<Integer> B = new HashSet<Integer>();

for(int i = 1 ; i < 5 ; i++)
    A.add(i);

for(int i = 10 ; i < 13 ; i++)
    B.add(i);

System.out.println("A: " + A);
System.out.println("B: " + B);

List<Set<Integer>> list = new ArrayList<Set<Integer>>();

for(Integer i: A) {
    for(Integer j: B) {
        Set<Integer> combination = new HashSet<Integer>();
        combination.add(i);
        combination.add(j);
        list.add(combination);
    }
}
System.out.println(list);