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.

Hint:

1. Try to solve it in one dimension first. How can this solution apply to the two dimension case?

public class Solution {
    public int minTotalDistance(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        ArrayList<Integer> xs = new ArrayList<>();
        ArrayList<Integer> ys = new ArrayList<>();
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (grid[i][j] == 1) {
                    xs.add(i);
                    ys.add(j);
                }
            }
        }
        return getMin(xs) + getMin(ys);
    }
   
    private int getMin(ArrayList<Integer> list) {
        Collections.sort(list);
        int res = 0;
        int s = 0;
        int e = list.size() - 1;
        while (s <= e) {
            res += list.get(e--) - list.get(s++);
        }
        return res;
    }
}