<p>Given an array of <code>points</code> where <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> represents a point on the <strong>X-Y</strong> plane, return <em>the maximum number of points that lie on the same straight line</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/25/plane1.jpg" style="width: 300px; height: 294px;" />
<pre>
<strong>Input:</strong> points = [[1,1],[2,2],[3,3]]
<strong>Output:</strong> 3
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/25/plane2.jpg" style="width: 300px; height: 294px;" />
<pre>
<strong>Input:</strong> points = [[1,1],[3,2],[5,3],[4,1],[2,3],[1,4]]
<strong>Output:</strong> 4
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= points.length &lt;= 300</code></li>
	<li><code>points[i].length == 2</code></li>
	<li><code>-10<sup>4</sup> &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 10<sup>4</sup></code></li>
	<li>All the <code>points</code> are <strong>unique</strong>.</li>
</ul>

class Solution {
public:
    int maxPoints(vector<vector<int>>& points) {
        int i,j,k,max = 1,ct;
        vector<pair<double,double>> lines;
        for(i = 0; i < points.size(); i++){
            ct = 1;
            for(j = i + 1; j < points.size(); j++){
                if(points[j][0] == points[i][0]){
                    ct++;
                }
                else{
                    double m = (1.0*(points[i][1]-points[j][1]))/(1.0*(points[i][0] - points[j][0]));
                    double c = points[i][1] - m*points[i][0];
                    lines.push_back(make_pair(m,c));
                }
            }
            if(ct > max){
                max = ct;
            }
        }
        sort(lines.begin(),lines.end());
        for(i = 0; i < lines.size(); i++){
            ct = 1;
            while(i < lines.size() - 1 && (lines[i+1].first - lines[i].first) < 0.000001 && (lines[i+1].second - lines[i].second) < 0.000001){
                i++;
                ct++;
            }
            if(ct > max*(max-1)/2){
                for(j = max; j <= points.size(); j++){
                    if(ct == j*(j-1)/2){
                        max = j;
                        break;
                    }
                }
            }
        }
        return max;
    }
};
12998