# 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 using Manhattan Distance, where distance(p1, p2) = `|p2.x - p1.x| + |p2.y - p1.y|`.

Example:

``````Input:

1 - 0 - 0 - 0 - 1
|   |   |   |   |
0 - 0 - 0 - 0 - 0
|   |   |   |   |
0 - 0 - 1 - 0 - 0

Output: 6

Explanation: Given three people living at (0,0), (0,4), and (2,2):
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?

A_____P_______B_

C_____A_____P_______B______D

``````class Solution {
public:
int minTotalDistance(vector<vector<int>>& grid) {
vector<int> rows, cols;
for (int i = 0; i < grid.size(); ++i) {
for (int j = 0; j < grid[i].size(); ++j) {
if (grid[i][j] == 1) {
rows.push_back(i);
cols.push_back(j);
}
}
}
return minTotalDistance(rows) + minTotalDistance(cols);
}
int minTotalDistance(vector<int> v) {
int res = 0;
sort(v.begin(), v.end());
int i = 0, j = v.size() - 1;
while (i < j) res += v[j--] - v[i++];
return res;
}
};
``````

``````class Solution {
public:
int minTotalDistance(vector<vector<int>>& grid) {
vector<int> rows, cols;
for (int i = 0; i < grid.size(); ++i) {
for (int j = 0; j < grid[i].size(); ++j) {
if (grid[i][j] == 1) {
rows.push_back(i);
cols.push_back(j);
}
}
}
sort(cols.begin(), cols.end());
int res = 0, i = 0, j = rows.size() - 1;
while (i < j) res += rows[j] - rows[i] + cols[j--] - cols[i++];
return res;
}
};
``````

Github 同步地址：

https://github.com/grandyang/leetcode/issues/296

Minimum Moves to Equal Array Elements II

Shortest Distance from All Buildings

https://leetcode.com/problems/best-meeting-point/

https://leetcode.com/problems/best-meeting-point/discuss/74186/14ms-java-solution

https://leetcode.com/problems/best-meeting-point/discuss/74244/Simple-Java-code-without-sorting.

https://leetcode.com/problems/best-meeting-point/discuss/74193/Java-2msPython-40ms-two-pointers-solution-no-median-no-sort-with-explanation

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