[LeetCode] Best Meeting Point 最佳开会地点
Posted Grandyang
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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:
- Try to solve it in one dimension first. How can this solution apply to the two dimension case?
这道题让我们求最佳的开会地点,该地点需要到每个为1的点的曼哈顿距离之和最小,题目中给了提示,让从一维的情况来分析,先看一维时有两个点A和B的情况,
______A_____P_______B_______
可以发现,只要开会为位置P在 [A, B] 区间内,不管在哪,距离之和都是A和B之间的距离,如果P不在 [A, B] 之间,那么距离之和就会大于A和B之间的距离,现在再加两个点C和D:
______C_____A_____P_______B______D______
通过分析可以得出,P点的最佳位置就是在 [A, B] 区间内,这样和四个点的距离之和为AB距离加上 CD 距离,在其他任意一点的距离都会大于这个距离,那么分析出来了上述规律,这题就变得很容易了,只要给位置排好序,然后用最后一个坐标减去第一个坐标,即 CD 距离,倒数第二个坐标减去第二个坐标,即 AB 距离,以此类推,直到最中间停止,那么一维的情况分析出来了,二维的情况就是两个一维相加即可,参见代码如下:
解法一:
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; } };
我们也可以不用多写一个函数,直接对 rows 和 cols 同时处理,稍稍能简化些代码:
解法二:
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
类似题目:
Minimum Moves to Equal Array Elements II
Shortest Distance from All Buildings
参考资料:
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.
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