<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 {
private:
    pair<double,double> getkn(vector<int> p1, vector<int> p2){
        double k = (double)(p2[1]-p1[1])/(p2[0]-p1[0]);
        double n = p1[1]-k*p1[0];
        return {k,n};
    }
public:
    int maxPoints(vector<vector<int>>& points) {
        if(points.size()==1) return 1;
        map<pair<double,double>,unordered_set<int>> m;
        int n = points.size();
        for(int i = 0; i<n; i++){
            for(int j = 0; j<n; j++){
                if(i!=j){
                    if(points[i][0]==points[j][0]){
                        m[{numeric_limits<double>::infinity(),points[i][0]}].insert(i);
                        m[{numeric_limits<double>::infinity(),points[i][0]}].insert(j);
                    }else{
                        auto [k,n] = getkn(points[i],points[j]);
                        m[{k,n}].insert(i);
                        m[{k,n}].insert(j);
                    }
                }
            }
        }
        int max_points = 0;
        for(auto it = m.begin(); it!=m.end(); it++){
            int len = it->second.size();
            max_points = max(max_points, len);
        }
        return max_points;
    }
};
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