<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>

const double EPS = 1e-9;
class Solution {
public:
    struct pt {
        double x, y;

        pt(int x, int y) {
            this->x = x;
            this->y = y;
        }

        bool operator<(const pt& p) const {
            return x < p.x - EPS || (abs(x - p.x) < EPS && y < p.y - EPS);
        }
    };

    struct l {
        double a, b, c;

        l(pt p, pt q) {
            a = p.y - q.y;
            b = q.x - p.x;
            c = -a * p.x - b * p.y;
            norm();
        }

        void norm() {
            double z = sqrt(a * a + b * b);
            if (abs(z) > EPS)
                a /= z, b /= z, c /= z;
        }

        double dist(pt p) const { return a * p.x + b * p.y + c; }
    };

    int maxPoints(vector<vector<int>>& points) {

        if (points.size() == 1)
            return 1;

        vector<l> lines;

        for (int i = 0; i < points.size(); i++) {
            for (int j = i + 1; j < points.size(); j++) {
                l cur = l(pt(points[i][0], points[i][1]),
                          pt(points[j][0], points[j][1]));
                lines.push_back(cur);
            }
        }

        int ans = 0;

        for (auto i : lines) {
            int count = 0;
            for (int j = 0; j < points.size(); j++) {
                double cur = i.dist(pt(points[j][0], points[j][1]));
                cur = abs(cur - 0.0);
                if (cur < EPS)
                    count++;
            }

            ans = max(ans, count);
        }

        return ans;
    }
};
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