[LintCode/LeetCode] Best Meeting Point

Problem

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|.

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.

Solution

public class Solution {
    /**
     * @param grid: a 2D grid
     * @return: the minimize travel distance
     */
    public int minTotalDistance(int[][] grid) {
        // Write your code here
        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 getMD(x) + getMD(y);
    }
    public int getMD(List<Integer> nums) {
        // zhong dian is here
        Collections.sort(nums);
        int i = 0, j = nums.size()-1;
        int distance = 0;
        while (i < j) {
            distance += nums.get(j--) - nums.get(i++);
        }
        return distance;
    }
}