<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) {
        //each pair of points forms a line
        //compute if an nth point is on that line by checking slope between points on that line
        //brute force is then checking the pairwise slopes for all pairs
        unordered_map<double, unordered_map<double, unordered_set<int>>> slopesToIntsToSets;    //ints represent indices

        //evaluate all pairs
        for(int i = 0; i < points.size(); i++){
            for(int j = i + 1; j < points.size(); j++){
                //compute slope a / b 
                double slope = ((points[i][0] - points[j][0]) != 0) ? ((double)(points[i][1] - points[j][1]) / (points[i][0] - points[j][0])) : 10001;

                //compute intercept y = mx - b --> b = mx - y --> b = m(points[i][0]) - points[i][1]
                double intercept = slope * (points[i][0]) - points[i][1];
                slopesToIntsToSets[slope][intercept].insert(i);
                slopesToIntsToSets[slope][intercept].insert(j);
            }
        }

        int out = 0;
        for(auto it = slopesToIntsToSets.begin(); it != slopesToIntsToSets.end(); it++){
            for(auto it2 = it->second.begin(); it2 != it->second.end(); it2++){
                out = max(out, (int)it2->second.size());
            }
        }
        return max(out, 1);
    }
};
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