#Leetcode# 149. Max Points on a Line

https://leetcode.com/problems/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.

Example 1:

Input: [[1,1],[2,2],[3,3]]
Output: 3
Explanation:
^
|
|        o
|     o
|  o  
+------------->
0  1  2  3  4

Example 2:

Input: [[1,1],[3,2],[5,3],[4,1],[2,3],[1,4]]
Output: 4
Explanation:
^
|
|  o
|     o        o
|        o
|  o        o
+------------------->
0  1  2  3  4  5  6

用判断三点共线的办法 时间复杂度为 $O(n^3)$

代码：

/**
 * 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 n = points.size();
        int res = 0;
        for(int i = 0; i < n; i ++) {
            int d = 1;
            for(int j = i + 1; j < n; j ++) {
                int cnt = 0;
                long long x1 = points[i].x, y1 = points[i].y;
                long long x2 = points[j].x, y2 = points[j].y;
                if(x1 == x2 && y1 == y2) {d ++; continue;}
                for(int k = 0; k < n; k ++) {
                    int x3 = points[k].x, y3 = points[k].y;
                    if(x1 * y2 + x2 * y3 + x3 * y1 - x3 * y2 - x2 * y1 - x1 * y3 == 0) 
                        cnt ++;
                }
                res = max(res, cnt);
            }
            res = max(res, d);
        }
        return res;
    }
};

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