algorithm to sum up a list of numbers for all combinations

Question

I have a list of numbers and I want to add up all the different combinations. For example:

• number as 1,4,7 and 13
• the output would be:

Answer 1

Here's how a simple recursive solution would look like, in Java:

public static void main(String[] args)
{
    f(new int[] {1,4,7,13}, 0, 0, "{");
}

static void f(int[] numbers, int index, int sum, String output)
{
    if (index == numbers.length)
    {
        System.out.println(output + " } = " + sum);
        return;
    }

    // include numbers[index]
    f(numbers, index + 1, sum + numbers[index], output + " " + numbers[index]);

    // exclude numbers[index]
    f(numbers, index + 1, sum, output);
}

Output:

{ 1 4 7 13 } = 25
{ 1 4 7 } = 12
{ 1 4 13 } = 18
{ 1 4 } = 5
{ 1 7 13 } = 21
{ 1 7 } = 8
{ 1 13 } = 14
{ 1 } = 1
{ 4 7 13 } = 24
{ 4 7 } = 11
{ 4 13 } = 17
{ 4 } = 4
{ 7 13 } = 20
{ 7 } = 7
{ 13 } = 13
{ } = 0