LeetCode #296. Best Meeting Point

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本文介绍了一种算法，用于找到二维网格中使所有参与者旅行距离之和最小的会议点。通过将问题转化为求解中位数位置，该算法有效地解决了最小化总曼哈顿距离的问题。

题目描述：

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.

class Solution {
public:
    int minTotalDistance(vector<vector<int>>& grid) {
        if(grid.size()==0||grid[0].size()==0) return 0;
        int m=grid.size();
        int n=grid[0].size();
        vector<int> row;
        vector<int> col;
        for(int i=0;i<m;i++)
        {
            for(int j=0;j<n;j++)
            {
                if(grid[i][j]==1)
                {
                    row.push_back(i);
                    col.push_back(j);
                }
            }
        }
        sort(row.begin(),row.end());
        sort(col.begin(),col.end());
        
        int row_mid=row[row.size()/2];
        int col_mid=col[col.size()/2];
        int result=0;
        for(auto x:row) result+=abs(row_mid-x);
        for(auto y:col) result+=abs(col_mid-y);
        return result;
    }
};