LeetCode – Best Meeting Point (Java)

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.

Java Solution

This problem is converted to find the median value on x-axis and y-axis.

```public int minTotalDistance(int[][] grid) { int m=grid.length; int n=grid[0].length;   ArrayList<Integer> cols = new ArrayList<Integer>(); ArrayList<Integer> rows = new ArrayList<Integer>(); for(int i=0; i<m; i++){ for(int j=0; j<n; j++){ if(grid[i][j]==1){ cols.add(j); rows.add(i); } } }   int sum=0;   for(Integer i: rows){ sum += Math.abs(i - rows.get(rows.size()/2)); }   Collections.sort(cols);   for(Integer i: cols){ sum+= Math.abs(i-cols.get(cols.size()/2)); }   return sum; }```
Category >> Algorithms
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