<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) {

        unordered_map<string, unordered_set<string>> kToPoints;
        int n=points.size();
        if(n<3){
            return n;
        }
        for(int i=0; i<n; i++){
            
            int x1 = points[i][0];
            int y1 = points[i][1];
            string p1 = to_string(x1)+","+to_string(y1);

            for(int j=0; j<n;j++){
                if(i==j){continue;}
                //calculate k 

                int x2 = points[j][0];
                int y2 = points[j][1];
                auto dx=x2-x1;
                auto dy=y2-y1;
                string k="";
                if(dx==0){
                    k="0,1";
                }else if(dy==0){
                    k="1,0";
                }else{
                    int flag=1;
                    if (dx<0){//overflow
                        flag*=-1;
                    }
                    if(dy<0){
                        flag*=-1;
                    }
                    dx=abs(dx);
                    dy=abs(dy);

                    int greatCommonDivisor = gcd(dx,dy);

                    dx /= greatCommonDivisor;
                    dy /= greatCommonDivisor;
                    //negtive be the first number,

                    k=to_string(flag*dx)+","+to_string(dy);
                }
                
                string p2 = to_string(x2)+","+to_string(y2);
                string key = p1+k;
                kToPoints[key].insert(p2);
                kToPoints[key].insert(p1);
            }
            
        }
        int maxPoint=0;
        for(auto& p:kToPoints){
            int size=p.second.size();
            maxPoint=max(maxPoint,size);
            // cout<<p.first<<": ";
            // for(auto point:p.second){
            //     cout<<point<<" ";
            // }
            // cout<<endl;

        }
        return maxPoint;

    }
};
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