<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:
    def maxPoints(self, points: List[List[int]]) -> int:

        if len(points) <= 2: 
            return len(points)
        
        dc_slopes = dict()

        for pointA in points: 
            for pointB in points: 
                if pointA == pointB: 
                    continue
                delta_x = pointA[0] - pointB[0]
                if delta_x == 0: 
                    if (tuple(pointA),pointA[0], 0, "X") not in dc_slopes:
                        dc_slopes[(tuple(pointA),pointA[0], 0, "X")] = 2
                    else:
                        dc_slopes[(tuple(pointA),pointA[0], 0, "X")] += 1
                    continue

                delta_y = pointA[1] - pointB[1]
                slope = delta_y / delta_x
                
                y_intersect = (pointA[0]*pointB[1] - pointB[0]*pointA[1]) / delta_x
                
                if (tuple(pointA),slope, y_intersect) in dc_slopes:
                    dc_slopes[(tuple(pointA),slope, y_intersect)] += 1
                else:
                    dc_slopes[(tuple(pointA),slope, y_intersect)] = 2

        return max(dc_slopes.values())

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