<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

class Solution:
    # map every pair of points by 'm,b' for y=mx+b
    # find the m,b key with the most segments in it, then return number of distinct points in it 
    # n^2 
    def maxPoints(self, points: List[List[int]]) -> int:
        pointToEq = defaultdict(lambda:set())
        maxNum = 1
        for i in range(len(points)):
            for j in range(i+1, len(points)):
                p1 = points[i]
                p2 = points[j]
                # y = mx + b
                # m = y/x
                yDiff = p1[1] - p2[1]
                xDiff = p1[0] - p2[0]
                if xDiff == 0:
                    m = "vertical"
                    b = p1[0]
                else:
                    mFloat = yDiff / xDiff
                    m = "{:.9f}".format(mFloat)
                    # y = mx + b
                    # b = y - mx
                    bFloat = p1[1] - mFloat * p1[0]
                    b = "{:.9f}".format(bFloat)
                key = f"{m},{b}"
                pointToEq[key].add(f"{p1[0]},{p1[1]}")
                pointToEq[key].add(f"{p2[0]},{p2[1]}")
                maxNum = max(maxNum, len(pointToEq[key]))
        return maxNum
37658