Selecting points such that sum of x coordinates = sum of y coordinates

Question

I have an array of Points. I need to select a subset of points from it, such that the sum of x coordinates of the points = sum of y coordinates of the points. If there are many such subsets, the one with largest sum of x coordinates is required. The sum of x coordinates needs to be reported.

I have written a brute force recursive method, which tests all possibilities.

Point[] a = new Point[n];
// ...
private int rec(int i, int x, int y) {
    if (i == n - 1) {
        if (x + a[i].x == y + a[i].y) return x + a[i].x;
        return (x == y) ? x : -1;
    }
    return Math.max(rec(i + 1, x, y), rec(i + 1, x + a[i].x, y + a[i].y));
}

The answer is rec(0, 0, 0).

My questions are:

1) Is there a dynamic programming solution for this?
2) If yes, could anyone please explain

Answer 1

I have a bit better (than brute force) algorithm.

1. Divided all coordinates into three sets:

    1: {(x,y): x>y}, 2: {(x,y):x==y}, 3:{(x,y): x lower-than y}

2. Set 2 have to be always included in the solution.
3. for each (x,y) from 1 define net=x-y and for each (x,y) form 3 define net=y-x
4. check all possible values you can obtained from nets in 1 and nets in 3.
5. then basing on the greatest match it is easy to construct the solution.

Does it make sense?