<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 < 2) return n;
        int max_points = 1;
        for(int i = 0; i < n-1; i++){
            unordered_map<double, int> slope_freq;
            int verticals = 0;
            int duplicates = 0;
            for(int j = i + 1; j < n; j++){
                auto p1 = points[i];
                auto p2 = points[j];

                if (p1 == p2) duplicates++;
                else if(p1[0] == p2[0]) verticals++;
                else{
                    double slope = double(p2[1] - p1[1])/double(p2[0] - p1[0]);
                    slope_freq[slope]++;
                }

            }
            int temp = verticals;
            for(auto [slope, freq] : slope_freq) temp = max(temp, freq);
            max_points = max(max_points, temp + duplicates + 1);
        }

        return max_points;
    }
};
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