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?

 

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public class Solution {
    public int minTotalDistance(int[][] grid) {
        List<Integer> row = new ArrayList<Integer>();
        List<Integer> col = new ArrayList<Integer>();
        
        for (int i = 0; i < grid.length; i++) {
            for (int j = 0; j < grid[i].length; j++) {
                if (grid[i][j] == 1) {
                    row.add(i);
                    col.add(j);
                }
            }
        }
        
        return getDistance(row) + getDistance(col);
    }
    
    private int getDistance(List<Integer> list) {
        Collections.sort(list);
        int result = 0;
        for (int i = 0, j = list.size() - 1; i < j; i++, j--)
            result += list.get(j) - list.get(i);
        return result;
    }
}