<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:
        def param(p1,p2):
            try :
                a = (p1[1] - p2[1])/(p1[0] - p2[0])
                b = p1[1] - a*p1[0]
                return (a,b)
            except :
                return ( float("inf"), p1[0])
        def appartient(p3,para):
            return p3[1] == para[0] * p3[0] + para[1]


        d = {}
        if (len(points)<=2) : return  len(points)
        n =len(points)
        h = set()
        for i in range(n-1) :
            L = set()
            for j in range(i+1,n):
                coeff = param(points[i], points[j])
                if coeff in h : continue
                if (coeff in d.keys()):
                    d[coeff] += 1
                else : 
                    L.add(coeff)

                    d[coeff] = 2
            h.update(L)
            
        return max(d.values()) 
    
            
            
28086