<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:
        res = 0

        def lies_on_line(x,y,a,b):
            return abs(a*x + b - y) < 10e-6
        
        def compute_line(x1, y1, x2, y2):
            #print(x1, y1, x2, y2)
            if x2 - x1 == 0:
                return None # TODO

            a = (y2-y1)/(x2-x1)
            b = y1 - a * x1
            return a, b
        
        # Edge cases: vertical lines 
        xs = [p[0] for p in points]
        x_counts = {}
        for x in xs:
            if x not in x_counts:
                x_counts[x] = 1
            else:
                x_counts[x] = x_counts[x] + 1
        for _, c in x_counts.items():
            if c>res:
                res = c
                

        lines = []
        for i, point_i in enumerate(points):
            for point_j in points[i+1:]:
                line = compute_line(*point_i, *point_j)
                if line is not None:
                    lines.append(line)
        print(lines)
        for line in lines:
            curr_res = 0
            for point in points:
                #print(point, line)
                if lies_on_line(*point, *line):
                    curr_res = curr_res + 1
            #print(line, curr_res)
            if curr_res>res:
                res = curr_res
        
        return res

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