<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();

        if(n == 1){
            return 1;
        }
        
        //(m, c) -> {pair of xys}
        unordered_map<double, unordered_map<double, set<pair<double, double>>>> mcPoints;
        unordered_map<double, set<pair<int, int>>> alongYPoints;
        
        for(int idx = 0; idx < n; idx++){
            for(int idy = idx + 1; idy < n; idy++){

                double x1 = points[idx][0], y1 = points[idx][1];
                double x2 = points[idy][0], y2 = points[idy][1];

                if(x2 == x1){
                    alongYPoints[x1].insert({x1, y1});
                    alongYPoints[x1].insert({x2, y2});
                }else{
                    double m = (y2 - y1) / (x2 - x1);
                    double c = (y1 * x2 - x1 * y2) / (x2 - x1);

                    mcPoints[m][c].insert({x1, y1});
                    mcPoints[m][c].insert({x2, y2});
                }
            }
        }

        int maxPointsInLine = 0;

        for(auto el : alongYPoints){
            maxPointsInLine = max(maxPointsInLine, (int)el.second.size());
        }

        for(auto el : mcPoints){
            for(auto el2 : el.second){
                maxPointsInLine = max(maxPointsInLine, (int)el2.second.size());
            }
        }

        return maxPointsInLine;
    }
};
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