<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(std::vector<std::vector<int>>& points) {
        // line equation y = mx + c
        // m - slope
        // c - intercept
        // c = mx + y
        std::map<std::pair<double, double>, std::set<std::vector<int>>> lines;
        for (int i = 0; i < points.size(); ++i) {
            for (int j = i + 1; j < points.size(); ++j) {
                const auto point1 = points[i];
                const auto point2 = points[j];
                double slope{0.0};
                double intercept{0.0};
                if ((point2.front() - point1.front()) == 0) {
                    slope = (double)point1.front();
                    intercept = std::numeric_limits<double>::max();
                } else {
                    slope = ((double)point2.back() - (double)point1.back()) /
                     (((double)point2.front() - (double)point1.front()) / 1.0);
                    intercept = (double)point1.back() - slope * (double)point1.front();
                }
                std::pair<double, double> curr_line{slope, intercept};
                if (lines.find(curr_line) == lines.end()) {
                    lines[curr_line] = {};
                }
                lines[curr_line].insert(point1);
                lines[curr_line].insert(point2);
            }
        }

        int res = points.size() <= 2 ? points.size() : 1;
        for (const auto& line: lines) {
            res = std::max(res, static_cast<int>(line.second.size()));
        }

        return res;
    }
};
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