<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:
        """
        sort pints by x coordinate
        
        compare pairs of points
        
        """
        points.sort()
        n = len(points)
        
        
        def get_slope(i: int, j: int):
            numerator = points[j][1] - points[i][1]
            denominator = points[j][0] - points[i][0]
            if denominator == 0:
                return float("inf")
            else:
                return numerator / denominator
            
        slope = [[0] * n for i in range(n)]
        for i in range(n):
            for j in range(i + 1, n):
                slope[i][j] = get_slope(i, j)
        
        
        res = 0
        for i in range(n):
            freq = defaultdict(int)
            for j in range(i + 1, n):
                freq[slope[i][j]] += 1
                res = max(res, freq[slope[i][j]])
        
        return res + 1
18515