[LeetCode296]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:

Try to solve it in one dimension first. How can this solution apply to the two dimension case?
Hide Tags Math Sort

根據提示，我們知道在一維的時候meet point如果爲median 距離最小， 所以該題就是在找median。

class Solution {
public:
    int minTotalDistance(vector<vector<int>>& grid) {
        vector<int> row;
        vector<int> col;
        for(int i = 0; i<grid.size(); ++i){
            for(int j = 0; j < grid[i].size(); ++j){
                if(grid[i][j] == 1){
                    row.push_back(i);
                    col.push_back(j);
                }
            }
        }
        sort(col.begin(), col.end());
        int m = row.size(), n = col.size();
        int midRow = (m%2) ? row[m/2] : (row[(m/2)-1] + row[(m/2)])/2;
        int midCol = (n%2) ? col[n/2] : (col[(n/2) - 1] + col[n/2])/2;
        int dist = 0;
        for(int i = 0; i<m; ++i) dist += abs(row[i] - midRow);
        for(int j = 0; j<n; ++j) dist += abs(col[j] - midCol);
        return dist;
    }
};