<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 {
private:
    int gcd(int a, int b) {
        return b? gcd(b, a%b) : a;
    }
    void fixSign(int &a, int &b) {
        int sa{a >= 0}, sb{b >= 0}, sign{sa^sb? -1 : 1};
        a = abs(a);
        b = sign * abs(b);
    }
public:
    int maxPoints(vector<vector<int>>& points) {
        unordered_map<string, unordered_set<string>> mp; // line -> points
        for (int i = 0; i < points.size()-1; i++) {
            int x1{points[i][0]}, y1{points[i][1]};
            for (int j = i+1; j < points.size(); j++) {
                int x2{points[j][0]}, y2{points[j][1]};
                int dx{x2-x1}, dy{y2-y1};
                int g{gcd(abs(dx), abs(dy))};
                dx /= g; dy /= g;
                fixSign(dx, dy);
                int dxb{dx*y1 - dy*x1};
                stringstream ss;
                ss << dy << "/" << dx << " " << dxb;
                string line(ss.str());
                ss.str("");
                ss << x1 << "," << y1;
                string p1(ss.str());
                mp[line].insert(p1);

                ss.str("");
                ss << x2 << "," << y2;
                string p2(ss.str());
                mp[line].insert(p2);
            }
        }
        size_t ans{1};
        for (auto it = mp.begin(); it != mp.end(); it++) {
            ans = max(ans, it->second.size());
        }
        return ans;
    }
};

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