296 Best Meeting Point

Search…

296. Best Meeting Point​
1. Question
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
1 - 0 - 0 - 0 - 1
2
|   |   |   |   |
3
0 - 0 - 0 - 0 - 0
4
|   |   |   |   |
5
0 - 0 - 1 - 0 - 0
Copied!
The point(0,2)is an ideal meeting point, as the total travel distance of 2+2+2=6 is minimal. So return 6
2. Implementation
(1) Sort + Two Pointers
思路: 和#462的思路一样, 相遇的点在哪不影响最后的距离
1
class Solution {
2
    public int minTotalDistance(int[][] grid) {
3
        List<Integer> rows = new ArrayList<>();
4
        List<Integer> cols = new ArrayList<>();
5
​
6
        int m = grid.length, n = grid[0].length;
7
​
8
        for (int i = 0; i < m; i++) {
9
            for (int j = 0; j < n; j++) {
10
                if (grid[i][j] == 1) {
11
                    rows.add(i);
12
                    cols.add(j);
13
                }
14
            }
15
        }
16
        return getDistance(rows, false) + getDistance(cols, true);
17
    }
18
​
19
    public int getDistance(List<Integer> list, boolean isCol) {
20
        // rows这个list本身已经sorted，所以只对cols排序
21
        if (isCol) {
22
           Collections.sort(list); 
23
        }
24
​
25
        int start = 0, end = list.size() - 1;
26
        int dist = 0;
27
        while (start < end) {
28
            dist += list.get(end) - list.get(start);
29
            ++start;
30
            --end;
31
        }
32
        return dist;
33
    }
34
}
Copied!
3. Time & Space Complexity
Sort + Two Pointers: 时间复杂度O(mn + mlogm + nlogn), 空间复杂度O(Max(m,n))

280 Wiggle Sort

315 Count of Smaller Numbers After Self

Last modified 2yr ago

Copy link

Contents

296. Best Meeting Point

1. Question

2. Implementation

3. Time & Space Complexity

296. Best Meeting Point​

1. Question

2. Implementation

3. Time & Space Complexity

296. Best Meeting Point