<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:
        if len(points) < 3:
            return len(points)
        keep_dict = {}
        for i in range(len(points) - 1):
            for j in range(i+1, len(points)):
                x1, y1 = points[i]
                x2, y2 = points[j]
                if x2 - x1 == 0:
                    if ("inf", x1) in keep_dict:
                        keep_dict[("inf", x1)] += 1
                    else:
                        keep_dict[("inf", x1)] = 1
                    continue
                m = (y2 - y1) / (x2 - x1)

                b = round(10**8 * (y2 - m * x2))
                m = round(10**8 * m)

                if (m, b) in keep_dict:
                    keep_dict[(m, b)] += 1
                else:
                    keep_dict[(m, b)] = 1
        x = 2 * max(keep_dict.values())
        print(keep_dict)
        return int((1 + (4 * x + 1)**(0.5)) / 2)
27469