296. Best Meeting Point - jiejackyzhang/leetcode-note GitHub Wiki
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?
很有意思的一道题目，假设二维数组中一个点到其他给定点的Manhattan Distance最小，求distance和。 因为在一维数组中这个distance最小的点就是给定所有点的median，题目又给定使用曼哈顿距离，我们就可以把二维计算分解成为两个一维的计算。
public class Solution {
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;
while(i<j) {
res += l.get(j--) - l.get(i++);
}
return res;
}
}