<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 LinearFunction{
private:
    int b;
    int yConstant;
    int a;
    int xConstant;
    
public:
    LinearFunction(vector<int>& pointA, vector<int>& pointB){
        b = pointA[1];
        yConstant = pointA[0] -  pointB[0];
        a = pointA[0];
        xConstant = pointA[1] -  pointB[1];
    }

    bool isOnLine(vector<int>& point) {
        int value = (point[1] - b) * yConstant - (point[0] - a) * xConstant;
        return value == 0;
    }
};

int numPointsOnLine(LinearFunction& l, vector<vector<int>>& points) {
    int result = 0;
    for (auto& point: points) {
        if (l.isOnLine(point))
            result++;
    }
    return result;
}


class Solution {
public:
    int maxPoints(vector<vector<int>>& points) {
        if (points.size() <= 2)
            return points.size();

        int maxValue = 0;
        for (int i=0; i<int(points.size()); i++) {
            for (int j=i+1; j<int(points.size()); j++) {
                LinearFunction l(points[j], points[i]);
                maxValue = max(maxValue, numPointsOnLine(l, points));
            }            
        }

        return maxValue;
    }
};
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