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

• Time: O(n)
• Space: O(1)

public int minTotalDistance(int[][] grid) {
    if (grid == null || grid.length == 0) return 0;
    int ret = 0;
    List<Integer> listX = new ArrayList<>();
    List<Integer> listY = new ArrayList<>();
    for (int i = 0; i < grid.length; i++) {
        for (int j = 0; j < grid[0].length; j++) {
            listX.add(i);
            listY.add(j);
        }
    }
    Collections.sort(listX);
    Collections.sort(listY);
    int pivotX = listX.get(listX.size() / 2);
    int pivotY = listY.get(listY.size() / 2);
    for (Integer i : listX) ret += Math.abs(pivotX - i);
    for (Integer i : listY) ret += Math.abs(pivotY - i);
    return ret;
}