[LeetCode] Max Points on a Line

Given n points on a 2D plane, find the maximum number of points that lie on the same straight line.

经过同一个点且斜率相等的直线一定是同一条直线，所以我们只要分别计算每一个点与其它点的直线的斜率，统计斜率的个数，找出最大值。可以使用double来表示斜率，使用map<double, int>来统计个数。但是有两点要注意，那就是：

(1) 如果直线与x轴垂直，此时斜率是无穷大，要单独处理

(2) 所给的点中有些是相同的点，此时也要特殊处理一下。

 1 /**

 2  * Definition for a point.

 3  * struct Point {

 4  *     int x;

 5  *     int y;

 6  *     Point() : x(0), y(0) {}

 7  *     Point(int a, int b) : x(a), y(b) {}

 8  * };

 9  */

10 class Solution {

11 public:

12     int maxPoints(vector<Point>& points) {

13         int res = 0, same_cnt, ver_cnt, cnt;

14         unordered_map<double, int> mp;

15         double k;

16         for (int i = 0; i < points.size(); ++i) {

17             same_cnt = ver_cnt = cnt = 0;

18             mp.clear();

19             for (int j = 0; j < points.size(); ++j) {

20                 if (points[i].x == points[j].x) {

21                     if (points[i].y == points[j].y) {

22                         ++same_cnt; 

23                         continue;

24                     }else {

25                         ++ver_cnt;

26                         cnt = max(cnt, ver_cnt);

27                     }

28                 } else {

29                     k = (double) (points[i].y - points[j].y) / (points[i].x - points[j].x);

30                     ++mp[k];

31                     cnt = max(cnt, mp[k]);

32                 }

33             }

34             res = max(res, cnt + same_cnt);

35         }

36         return res;

37     }

38 };