[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。

/**
 * Definition for a point.
 * struct Point {
 *     int x;
 *     int y;
 *     Point() : x(0), y(0) {}
 *     Point(int a, int b) : x(a), y(b) {}
 * };
 */
class Solution {
public:
    int maxPoints(vector<Point>& points) {
        int res = 0, same_cnt, ver_cnt, cnt;
        unordered_map<double, int> mp;
        double k;
        for (int i = 0; i < points.size(); ++i) {
            same_cnt = ver_cnt = cnt = 0;
            mp.clear();
            for (int j = 0; j < points.size(); ++j) {
                if (points[i].x == points[j].x) {
                    if (points[i].y == points[j].y) {
                        ++same_cnt; 
                        continue;
                    }else {
                        ++ver_cnt;
                        cnt = max(cnt, ver_cnt);
                    }
                } else {
                    k = (double) (points[i].y - points[j].y) / (points[i].x - points[j].x);
                    ++mp[k];
                    cnt = max(cnt, mp[k]);
                }
            }
            res = max(res, cnt + same_cnt);
        }
        return res;
    }
};