Leetcode: 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:

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

 1 public class Solution {
 2     public int minTotalDistance(int[][] grid) {
 3         List<Integer> xPos = new ArrayList<Integer>();
 4         List<Integer> yPos = new ArrayList<Integer>();
 5         for (int x=0; x<grid.length; x++) {
 6             for (int y=0; y<grid[0].length; y++) {
 7                 if (grid[x][y] == 1) {
 8                     xPos.add(x);
 9                     yPos.add(y);
10                 }
11             }
12         }
13         int minDis = 0;
14         for (int x : xPos) {
15             minDis += Math.abs(x - xPos.get(xPos.size()/2));
16         }
17         Collections.sort(yPos);
18         for (int y : yPos) {
19             minDis += Math.abs(y - yPos.get(yPos.size()/2));
20         }
21         return minDis;
22     }
23 }