<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 collections import defaultdict
import math

class Solution:
    def maxPoints(self, points: List[List[int]]) -> int:
        
        def find_slope(p1, p2):
            x1, y1 = p1
            x2, y2 = p2

            if x1 == x2: return (0, 1)
            if y1 == y2: return (1, 0)

            diff1 = x1 - x2
            diff2 = y1 - y2
            d = math.gcd(diff1, diff2)

            if diff1 < 0:
                diff1 = -diff1
                diff2 = -diff2

            return (diff1 // d, diff2 // d)
        
        
        # points -> slope counter

        count = {}
        for i in range(len(points)):
            count[i] = defaultdict(lambda : 1)

        for i in range(len(points)):
            for j in range(i+1, len(points)):
                slope = find_slope(points[i], points[j])

                count[i][slope] += 1
                count[j][slope] += 1
        
        max_freq = 1
        for key in count:
            for slope in count[key]:
                max_freq = max(max_freq, count[key][slope])

        return max_freq
22529