Sorting 10 numbers

[Sam Benry]

I'm basically looking for a good algorithm or method to do the following:
I have 10 numbers, you can use List<Integer> or int[] or what ever you want.

I want to sort the 10 numbers so the sum of the first 5 is approximately (or exactly if possible) equal to the sum of the last 5. The sum of the first 5 must be as close as possible to the sum of the last 5.

How can I do that?
Thank you.

[saumil baxi]

one solution can be. If I have understood your problem correctly

Sort the numbers in such a way that .

You place the latest number at the last index.
Then Second latest at the first location.
Third Latest at Second last location and so on.

The sum of the first five elements would be close to sum of last five element in your List.

[fred rosenberger]

saumil baxi, I don't think that will work. What if your set of numbers were

1,2,3,4,5,6,7,8,9,100

If i'm reading your algorithm correctly, you would sort them like:

group 1: 100, 8, 6, 4, 2: Sum is 120
group 2: 9, 7, 5, 3, 1: Sum is 25
diff = 95

But this would be a better way to do it:

group 1: 100, 1, 2, 3, 4: Sum = 110
group 2: 5,6,7,8,9: Sum = 35
diff = 75

I think your best bet is to go through the numbers from largest to smallest. Add each number to whichever group has the lowest sum. If the sums are the same, it doesn't matter.

I haven't proved to myself this is the correct way to go, but it feels right to me...

[Sam Benry]

Interesting, I wrote this quickly, what do you think ?

    
public static void main(String[] args) 
{
List<Integer> ranks = new ArrayList<Integer>();
ranks.add(100);
ranks.add(2);
ranks.add(3);
ranks.add(4);
ranks.add(5);
ranks.add(6);
ranks.add(7);
ranks.add(8);
ranks.add(9);
ranks.add(1);

Collections.sort(ranks);
Collections.reverse(ranks);
 
int group1 = 0, group2 = 0;
int group1Counter = 0, group2Counter = 0;
for(int rank : ranks)
{
if (Math.min(group1, group2) == group1 && group1Counter < 5) 
{
group1 += rank;
group1Counter++;
}
else if(group2Counter < 5)
{
group2 += rank;
group2Counter++;
}
else if(group1Counter < 5)
{
group1 += rank;
group1Counter++;
}
}
System.out.println("Group1: " + group1);
System.out.println("Group2: " + group2);

System.out.println("Group1 Counter: " + group1Counter);
System.out.println("Group2 Counter: " + group2Counter);
}

[saumil baxi]

Fred you are right [ ]..