<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 gcd(int x, int y) {
        int upper_bound = min(abs(x), abs(y));
        for (int i = upper_bound; i >= 1; --i) {
            if (x % i == 0 && y % i == 0) {
                return i;
            }
        }
        return -1;
    }
    int maxPoints(vector<vector<int>>& points) {
        int result = 0;
        for (int i = 0; i < points.size(); ++i) {
            unordered_map<int, unordered_map<int, int>> cache;
            for (int j = 0; j < points.size(); ++j) {
                if (i == j) {
                    continue;
                }
                int dx = points[i][0] - points[j][0];
                int dy = points[i][1] - points[j][1];
                int common_divisor = gcd(dx, dy);
                dx /= common_divisor;
                dy /= common_divisor;
                // +dx +dy
                // -dx +dy
                if (dx == 0) {
                    dy = -100000;
                } else if (dy == 0) {
                    dx = -100000;
                } else if (dx < 0 && dy < 0) {
                    dx = -dx;
                    dy = -dy;
                } else if (dx > 0 && dy < 0) {
                    dx = -dx;
                    dy = -dy;
                }
                result = max(result, ++cache[dx][dy]);
            }
        }
        return result + 1;
    }
};
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