LeetCode 296: 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 usingManhattan 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.

For one dimension axises, the middle point is the shortest distance. Thus, we just need to calculate x axis and y axis seperately.

http://blog.csdn.net/xudli/article/details/49420623 Code is from here.

    public class Solution {  
        //(0,0), (0,4), and (2,2)  
        public int minTotalDistance(int[][] grid) {  
            List<Integer> x = new ArrayList<>();  
            List<Integer> y = new ArrayList<>();  
              
            for(int i=0; i<grid.length; i++) {  
                for(int j=0; j<grid[0].length; j++) {  
                    if(grid[i][j]==1) {  
                        x.add(i);  
                        y.add(j);  
                    }  
                }  
            }  
              
            return getMP(x) + getMP(y);  
        }  
          
        private int getMP(List<Integer> l) {  
            Collections.sort(l);  
            int i=0, j=l.size()-1;  
            int res = 0;  
            /*
              or set up a mid point. int mid = (0 + x.size()) / 2;
            */
            while(i<j) {  
                res += l.get(j--) - l.get(i++);  
            }  
            return res;  
        }  
    }