Best Meeting Point

标签：

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.

分析：http://massivealgorithms.blogspot.com/2015/10/leetcode-best-meeting-point-segmentfault.html

Suppose we have a set S of real numbers that ∑s∈S|s−x|is minimal if x is equal to themedian.

6是median,那么 (6-2)+(6-4) + (6-5) + (7-6) + (8-6) + (9-6) = 4 + 2+ 1+ 1+ 2+ 3 = 13 = (9-2) + (8-4) + (7-5)

public class Solution {
    public int minTotalDistance(int[][] grid) {
        List<Integer> xPoints = new ArrayList<>();
        List<Integer> yPoints = new ArrayList<>();

        for (int i = 0; i < grid.length; i++) {
            for (int j = 0; j < grid[0].length; j++) {
                if (grid[i][j] == 1) {
                    xPoints.add(i);
                    yPoints.add(j);
                }
            }
        }

        return getMP(xPoints) + getMP(yPoints);
    }

    private int getMP(List<Integer> points) {
        Collections.sort(points);
        int i = 0, j = points.size() - 1;
        int res = 0;
        while (i < j) {
            res += points.get(j--) - points.get(i++);
        }
        return res;
    }
}

Best Meeting Point

标签：

原文地址：http://www.cnblogs.com/beiyeqingteng/p/5739020.html