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 is a simple recursive Ruby implementation:

a = [1, 4, 7, 13]

def add(current, ary, idx, sum)
    (idx...ary.length).each do |i|
        add(current + [ary[i]], ary, i+1, sum + ary[i])
    end
    puts "#{current.join('+')} = #{sum}" if current.size > 1
end    
add([], a, 0, 0)

Which prints

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
4+7+13 = 24
4+7 = 11
4+13 = 17
7+13 = 20

If you do not need to print the array at each step, the code can be made even simpler and much faster because no additional arrays are created:

def add(ary, idx, sum)
    (idx...ary.length).each do |i|
        add(ary, i+1, sum + ary[i])
    end
    puts sum
end
add(a, 0, 0)

I dont think you can have it much simpler than that.

Answer 2

You might be interested in checking out the GNU Scientific Library if you want to avoid maintenance costs. The actual process of summing longer sequences will become very expensive (more-so than generating a single permutation on a step basis), most architectures have SIMD/vector instructions that can provide rather impressive speed-up (I would provide examples of such implementations but I cannot post URLs yet).

Answer 3

Thanks Zach,

I am creating a Bank Reconciliation solution. I dropped your code into jsbin.com to do some quick testing and produced this in Javascript:

function f(numbers,ids, index,  sum, output, outputid, find )
{
    if (index == numbers.length){
          var x ="";
          if (find == sum) {
              y= output + " } = " + sum + "  " + outputid + " }<br/>" ;
          }
        return;
    }
    f(numbers,ids, index + 1, sum + numbers[index], output + " " + numbers[index], outputid + " " + ids[index], find);
    f(numbers,ids, index + 1, sum, output, outputid,find);
}

var y;

f( [1.2,4,7,13,45,325,23,245,78,432,1,2,6],[1,2,3,4,5,6,7,8,9,10,11,12,13], 0, 0, '{','{', 24.2);
if (document.getElementById('hello')) {
  document.getElementById('hello').innerHTML = y;
}

I need it to produce a list of ID's to exclude from the next matching number.

I will post back my final solution using vb.net