Best Meeting Point

A group of two or more people wants to meet and minimize the total travel distance. You are given a 2D grid of values 0 or 1, where each 1 marks the home of someone in the group. The distance is calculated using Manhattan Distance, where distance(p1, p2) = |p2.x - p1.x| + |p2.y - p1.y|.

For example, given three people living at (0,0), (0,4), and (2,2):

1 - 0 - 0 - 0 - 1
|   |   |   |   |
0 - 0 - 0 - 0 - 0
|   |   |   |   |
0 - 0 - 1 - 0 - 0
The point (0,2) is an ideal meeting point, as the total travel distance of 2+2+2=6 is minimal. So return 6.

    public int minTotalDistance(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;

        List<Integer> I = new ArrayList<>(m);
        List<Integer> J = new ArrayList<>(n);

        for(int i = 0; i < m; i++){
            for(int j = 0; j < n; j++){
                if(grid[i][j] == 1){
                    I.add(i);
                    J.add(j);
                }
            }
        }

        return getMin(I) + getMin(J);
    }

    private int getMin(List<Integer> list){
        int ret = 0;

        Collections.sort(list);

        int i = 0;
        int j = list.size() - 1;
        while(i < j){
            ret += list.get(j--) - list.get(i++);
        }

        return ret;
    }