<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:

        #Lines characterized by slope and intercept (unless vertical)

        ##For each line, compute the slope and intercept

        def findLine(point1,point2):

            ##vertical line; handle later
            if point1[0] == point2[0]:
                return (float('inf'),float('inf'))
            
            m = (point1[1] - point2[1])/(point1[0]-point2[0])
            b = point1[1] - m*point1[0]
            return (m,b)
        
        lines = {}
        seen_values = {}

        for i in range(len(points)):
            for j in range(i+1,len(points)):

                (m,b) = findLine(points[i],points[j])

                if (m,b) != (float('inf'),float('inf')):
                    if (m,b) not in lines:
                        lines[(m,b)] = 0
                    if (m,b,points[i][0],points[i][1]) not in seen_values:
                        seen_values[ (m,b,points[i][0],points[i][1]  )   ] = 0
                        lines[(m,b)] += 1
                    if (m,b,points[j][0],points[j][1]) not in seen_values:
                        seen_values[ (m,b,points[j][0],points[j][1]  )   ] = 0
                        lines[(m,b)] += 1
        
        ##vertical lines
        vertical_line = {}
        ans = 0

        for point in points:
            
            if point[0] not in vertical_line:
                vertical_line[point[0]] = 0
            
            vertical_line[point[0]] += 1
            ans = max(ans,vertical_line[point[0]])

        for key in lines:
            ans = max(ans,lines[key])
        
        return ans


            


        
        
38893