<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>

import numpy as np



class Solution:

    def num_on(self, p1: np.ndarray, p2: np.ndarray , points : np.ndarray):
        vec = (p2 -p1)
        if vec[0] == 0:
            #print((points[ :, 0] == p1[0]), points, p1)
            return int((points[:, 0] == p1[0]).sum())

        if vec[1] == 0:
            return int((points[:, 1] == p1[1]).sum())

        points_p1 = points - p1[None, :]
        alphas = points_p1 / vec[None, : ]
        mean_alpha = np.mean(alphas, axis=-1, keepdims=True)
        #print(alphas)
        linear = np.abs((mean_alpha - alphas)).max(axis=-1) == 0
        #print(linear)
        num = int((linear & (mean_alpha[:, 0] <= 1) & (mean_alpha[:, 0]>=0)).sum())
        return num


    def maxPoints(self, points: List[List[int]]) -> int:

        points = np.array(points)
        max_points = 1
        for idx , p1 in enumerate(points):
            for jdx, p2 in enumerate(points[idx+1:]):
                max_points = max(max_points, self.num_on(p1, p2, points))

        return max_points
                

        
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