<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();
        vector<double> v(n);
        vector<vector<double>> slopes(n, v);

        for(int i=0;i<n;i++) {
            for(int j=0;j<n;j++) {
                if(points[i][0]==points[j][0])
                slopes[i][j] = INT_MAX;
                else
                slopes[i][j] = double(points[j][1] - points[i][1])/(points[j][0] - points[i][0]);
            }
        }
        int ans = 1;
        for(int i=0;i<n;i++) {
            unordered_map<double, int> m;
            for(int j=0;j<n;j++) {
                
                if(i!=j){
                    m[slopes[i][j]]++;
                    ans = max(ans, m[slopes[i][j]]);
                }
                
            }

        }


        // for(int i=0;i<n;i++) {
        //     for(int j=0;j<n;j++) {
        //         cout<<slopes[i][j]<<" ";
        //     }
        //     cout<<"\n";
        // }
        if(ans==n)
            return n;

        
        return ans+1;
    }
};
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