Best Meeting Point

Q:

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.

A:

就是单独的计算横纵坐标的中间位置啊？注意，这里是median, 不是middle

public int minTotalDistance(int[][] grid) {
        if(grid==null || grid.length==0|| grid[0].length==0)
            return 0;
        int m = grid.length, n = grid[0].length;
        List<Integer> X = new LinkedList<Integer>();
        List<Integer> Y = new LinkedList<Integer>();
        double sumX=0, sumY =0;
        for(int i =0;i< m;i++) {
            for (int j = 0; j < n; j++) {
                if(grid[i][j] == 1){
                    X.add(i);
                    Y.add(j);
                    sumX += i;
                    sumY += j;
                }
            }
        }
        int medianX = X.get(X.size()/2);
        Collections.sort(Y);
        int medianY = Y.get(Y.size()/2);
        int res = 0;
        for(Integer x : X)
            res += Math.abs( x - medianX );
        for(Integer y : Y)
            res += Math.abs( y - medianY);
        return res;
    }

Mistakes: