<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>

using namespace std;

class Solution {
public:
    function<bool(const pair<double, double>&, const pair<double, double>&)> cmp =
        [](const pair<double, double>& a, const pair<double, double>& b) {
            const double EPS = 1e-9;
            if (fabs(a.first - b.first) < EPS) {
                return a.second < b.second;
            }
            return a.first < b.first;
        };

    map<pair<double, double>, set<int>, decltype(cmp)> mp{cmp};    

    int maxPoints(vector<vector<int>>& points) {
        mp.clear();
        for (int i = 0; i < int(points.size()); i++) {
            for (int j = i + 1; j < int(points.size()); j++) {
                int dx = points[i][0] - points[j][0];
                int dy = points[i][1] - points[j][1];

                if (dx < 0) {
                    dx = -dx;
                    dy = -dy;
                }

                bool flag = false;

                if (dy == 0) {
                    mp[{-1e9 + (double)points[i][1], 0}].insert(i);
                    mp[{-1e9 + (double)points[i][1], 0}].insert(j);
                    flag = true;
                }
                if (dx == 0) {
                    mp[{1e9 + (double)points[i][0], 0}].insert(i);
                    mp[{1e9 + (double)points[i][0], 0}].insert(j);
                    flag = true;
                } else if (!flag) {
                    double slope = double(dy) / double(dx);
                    double originY = points[i][1] - slope * points[i][0];
                   
                    mp[{originY, slope}].insert(i);
                    mp[{originY, slope}].insert(j);
                }
            }
        }

        int best = 1;

        for (auto& [key, value] : mp) {
            best = max(best, int(value.size()));
        }

        return best;
    }
};

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