<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) {

        vector<int > A={2,1}; 

        vector<int > B={2,2};

        cal_m_c(A,B);

        if(points.size()<2){

            return points.size();

        }

        map<pair<double,double>,set<vector<int>>> mp;

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

            for(int j=i+1;j<points.size();j++){

                vector<int> A=points[i];

                vector<int> B=points[j];

                if(mp.find(cal_m_c(A,B))!=mp.end()){

                    mp[cal_m_c(A,B)].insert(A);

                    mp[cal_m_c(A,B)].insert(B);

                }

                else{

                    set<vector<int>> s;

                    s.insert(A);

                    s.insert(B);

                    mp[cal_m_c(A,B)]=s;

                }

            }

            

        }

        int ans=0;

        for(auto i:mp){

            int b=(i.second).size();

            ans=max(ans,b);

        }

        return ans;

    }

    pair<double,double> cal_m_c(vector<int> A,vector<int> B){

        if(A[0]==B[0]){

            return {A[0],INT_MAX};

        }

        double m=(A[1]-B[1])/((A[0]-B[0])/1.0);

        double  c=A[1]-m*A[0];

        return {m,c};

    }

};


        
    

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