<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 n = points.size(),res=0,max_p=0;
        for(int i=0;i<n;i++){
            unordered_map<string,unordered_map<string,int>> map;
            int d = 0;
            for(int j=i+1;j<n;j++){
                if(points[i][0]==points[j][0] && points[i][1]==points[j][1]){
                    d++;
                    continue;
                }
                int dx = points[i][0]-points[j][0];
                int dy = points[i][1]-points[j][1];

                if(dx==0){
                    map["Inf"][to_string(points[i][0])]++;
                    max_p=max(max_p,map["Inf"][to_string(points[i][0])]);
                    continue;
                }
                int gcd = __gcd(dx,dy);
                dx/=gcd;
                dy/=gcd;
                if(dx<0){
                    dx*=-1;
                     dy*=-1;
                } 
                 int intercept_numerator = dy * points[i][0] - dx * points[i][1];
                int intercept_denominator = dx;
                int gcd_intercept = __gcd(intercept_numerator, intercept_denominator);
                
                intercept_numerator /= gcd_intercept;
                intercept_denominator /= gcd_intercept;
                
                if(intercept_denominator < 0) {
                    intercept_numerator = -intercept_numerator;
                    intercept_denominator = -intercept_denominator;
                }
                string slope_key = to_string(dy) + "/" + to_string(dx);
                string intercept_key = to_string(intercept_numerator) + "/" + to_string(intercept_denominator);
                
                map[slope_key][intercept_key]++;
                max_p = max(max_p, map[slope_key][intercept_key]);
            }
            res = max(res,max_p+d+1);
        }
        return res;
    }
};
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