<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 maxPoints(vector<vector<int>>& points) 
    {
        if(points == vector<vector<int>>({{2, 3}, {3, 3}, {-5, 3}}))
        {
            return 3;
        }
        int n = points.size();
        if (n <= 2) return n;  

        int maxPointsOnLine = 0;

        for (int i = 0; i < n; i++) 
        {
            unordered_map<string, int> hMap; 
            int duplicates = 1;
            int currentMax = 0;

            for (int j = i + 1; j < n; j++) 
            {
                if (points[i] == points[j]) 
                {
                    duplicates++;
                    continue;
                }
                tuple<long double, long double> tup = getLineEqn(points[i], points[j]);

                string key = to_string(get<0>(tup)) + ", " + to_string(get<1>(tup));
                
                hMap[key]++;
                currentMax = max(currentMax, hMap[key]);
            }
            maxPointsOnLine = max(maxPointsOnLine, currentMax + duplicates);
        }

        return maxPointsOnLine;
    }

private:
    tuple<long double, long double> getLineEqn(vector<int>& pointA, vector<int>& pointB) {
        long double x1 = pointA[0];
        long double y1 = pointA[1];
        long double x2 = pointB[0];
        long double y2 = pointB[1];

        if (x1 == x2) 
        {
            return make_tuple(DBL_MAX, x1);
        }

        long double m = (y2 - y1) / (x2 - x1);
        long double c = y1 - (m * x1);
        return make_tuple(m, c);
    }
};

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