<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:
        # find all pairwise lines
        # start with arbitrary unpaired point and another point
        # grow the line
        # remove need for pairwise compute for grown line

        if len(points) == 1:
            return 1

        for i in range(len(points)):
            points[i] = tuple(points[i])

        def get_line_params(p1, p2):
            if p1[0] == p2[0]:
                m = float('inf')
                yi = None
                xi = p1[0]
            elif p1[1] == p2[1]:
                m = 0
                yi = p1[1]
                xi = None
            else:
                m = (p1[1] - p2[1]) / (p1[0] - p2[0])  # slope
                yi = p1[1] - m * p1[0]                 # y-intercept
                xi = -yi / m                           # x-intercept
            return m, yi, xi

        lines = {}

        for i in range(len(points) - 1):
            for j in range(i + 1, len(points)):
                if i != j:
                    p1, p2 = points[i], points[j]
                    m, yi, xi = get_line_params(p1, p2)
                    if (m, yi, xi) in lines:
                        lines[(m, yi, xi)].add(p1)
                        lines[(m, yi, xi)].add(p2)
                    else:
                        lines[(m, yi, xi)] = {p1, p2}

        return max(len(v) for v in lines.values())
        
37040