<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>

struct Line {
    int slope_y;
    int slope_x;
    double y_intercept;
    bool operator==(const Line& other) const { return slope_y == other.slope_y && slope_x == other.slope_x && y_intercept == other.y_intercept; }
};

size_t hash(int a, int b) {
    return std::hash<uint64_t>()(((uint64_t)a << 32) + b);
}

namespace std {
    template <>
    struct hash<Line> {
        size_t operator()(const Line& line) const {
            return ::hash(line.slope_y, line.slope_x) ^ hash<double>()(line.y_intercept);
        }
    };

    template <>
    struct hash<vector<int>> {
        size_t operator()(const vector<int>& v) const {
            return ::hash(v[0], v[1]);
        }
    };
}


class Solution {

    int gdc(int a, int b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

public:

    int maxPoints(vector<vector<int>>& points) {
        if (points.size() == 1) return 1;

        unordered_map<Line, unordered_set<vector<int>>> lines;

        for (int i = 0; i < points.size(); i++) {
            for (int j = i + 1; j < points.size(); j++) {
                Line l;
                int y = (points[i][1] - points[j][1]);
                int x = (points[i][0] - points[j][0]);
                if (x == 0) {
                    l = { 0, 1, points[i][0] * 1.0 };
                } else if (y == 0) {
                    l = { 1, 0, points[i][1] * 1.0 };
                } else {
                    int g = gcd(x, y);
                    if (y < 0) g *= -1;
                    y /= g; x /= g;
                    double intercept = points[i][1] - (1.0 * y / x) * points[i][0];
                    l = { y, x, intercept };
                }
                lines[l].insert(points[i]);
                lines[l].insert(points[j]);
            }
        }

        int mx = 0;
        for (auto [_, s] : lines) mx = max(mx, (int)s.size());


        return mx;
    }
};
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