<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>

from math import inf
import pprint

def slope_xint_yint(p1, p2):
    if p1[0] == p2[0]:
        return inf, p1[0], None
    res = (p2[1] - p1[1]) / (p2[0] - p1[0])
    y_int = p1[1] - res * p1[0]
    if p1[1] == p2[1]:
        x_int = None
    else:
        x_int = -y_int / res
    return res, x_int, y_int


class Solution:
    def maxPoints(self, points: List[List[int]]) -> int:
        if len(points) == 1:
            return 1
        if len(points) == 2:
            return 2

        max_points = 0

        slopes = dict()
        for i in range(len(points) - 1):
            p1 = points[i]

            for j in range(i + 1, len(points)):
                tup = slope_xint_yint(p1, points[j])

                if tup in slopes:
                    slopes[tup].add(i)
                    slopes[tup].add(j)
                    max_points = max(max_points, len(slopes[tup]))
                else:
                    slopes[tup] = set([i, j])
                    max_points = max(max_points, 2)

        return max_points

37040